SCIENCE
PART I:
1. All ecosystems taken together make up a
A. niche.
B. biosphere.
C. community.
D. population.
E. habitat.
2. Which of the following sequences of organization is likely to be
seen in a multicellular organism, going from smallest to largest?
A.
B.
C.
D.
E.
cell, organ, tissue, organism
cell, organ, system, tissue
cell, tissue, system, organism
organism, system, organ, tissue
tissue, system, cell, organ
3. All individuals of a given species living in a defined area at a
defined time are a(n)
A. population
B. community
C. ecosystem
D. biosphere
4. All members of one species form a:
A. biosphere
B. ecosystem
C. population
D. community
E. country
5. Which of the following does not comprise a logical hierarchy of
organization?
A.
B.
C.
D.
E.
molecules, atoms, organelles, tissues, systems
atoms, molecules, cells, tissues, organ systems
cells, tissues, organs, organ systems, organisms
organisms, populations, communities, biomes, biosphere
family, order, class, phylum, kingdom
6. All populations in one natural setting plus their physical
environment constitutes a(n):
A. biosphere
B. ecosystem
C. population
D. community
E. country
7. Which of the following represents the lowest level of organization
in the group?
A. Biosphere
B. Community
C. Population
D. Species
E. Ecosystem
8. Which correctly indicates the sequence of increasing organization?
A.
B.
C.
D.
E.
molecule, cell, organelle, organ
organelle, tissue, cell, organ
atom, molecule, organelle, cell
organ, tissue, cell, molecule
cell, organ, tissue, organ system
9. Which of the following levels in the hierarchy of biological
organization include all of the other levels in the list?
A. organ system
B. organism
C. population
D. ecosystem
E. community
10.
Which of the following levels in the hierarchy of biological
organization includes all of the other levels in the list?
A. organelles
B. macro molecules
C. cells
D. atoms
E. tissues
11.
With each step upward in the hierarchy of biological order,
novel properties emerge that were not present at the simpler levels
of organization. These emergent properties result from
A. vital forces that arise at each level.
B. the physical and chemical phenomena that operate only in
living things.
C. the arrangement and interactions between components.
D. simple summation of the individual behavior of the
component parts.
E. the emergence of supernatural forces.
12.
Organs are composed of tissues, which are composed of
cells. This is an example of which characteristic of life?
A.
B.
C.
D.
E.
13.
Living
Living
Living
Living
Living
things
things
things
things
things
grow and develop
respond to stimuli
maintain themselves by homeostasis
have levels of organization
are adapted to their environment
The study of tissues is called:
A. cytology
B. molecular biology
C. histology
14.
types
A.
B.
C.
D. parasitology
E. pathology
Which of the following is composed of two or more tissue
that come together to perform a function?
organs
D. cells
organ systems
E. macromolecules
organisms
15.
A physician specializes on surgery involving the esophagus,
stomach, and intestines. This physician is specialized at which
level of organization.
A. cell
D. organ system
B. tissue
E. organism
C. organ
16.
Which sequence correctly lists the different levels of
biological organization?
A.
B.
C.
D.
E.
cells - organs - tissues - organ systems - organism
cells - tissues - organ systems - organs - organism
tissues - cells - organs - organ systems - organism
tissues - organs - organ systems - organism - cells
cells - tissues - organs - organ systems – organism
17.
Which of the following is the correct order of levels of
organization from small to large?
A. cell - organ - tissue - organ system - population community - ecosystem
B. cell - tissue - organ system - organ - population community - ecosystem
C. cell - tissue - organ - organ system - community population - ecosystem
D. cell - tissue - organ - organ system - population community - ecosystem
E. cell - tissue - organ system - organ - community population – ecosystem
18.
An organism that uses carbon dioxide for its source of
carbon is referred to as a(n):
A. heterotroph
B. phototroph
C. organotroph
D. autotroph
E. chemotroph
19.
An organism that uses organic materials for its source of
carbon is referred to as a(n):
A. heterotroph
B. phototroph
C. organotroph
D. autotroph
E. chemotroph
20.
An organism that uses light is referred to as a(n):
A. heterotroph
B. phototroph
C. organotroph
21.
D. autotroph
E. chemotroph
An organism that uses chemical is referred to as a(n):
A. heterotroph
B. phototroph
C. organotroph
D. autotroph
E. chemotroph
22.
What is the process by which the sun's energy is trapped as
the source of energy used by virtually all living organisms?
A. evolution
B. metabolism
C. adaptation
D. homeostasis
E. photosynthesis
23.
What is the name of all the chemical energy transformations
that occur within a cell?
A. evolution
B. metabolism
C. adaptation
24.
D. homeostasis
E. photosynthesis
What is metabolism?
A. The consumption of energy.
B. The release of energy.
C. The sum of all chemical reactions taking place in an
organism.
D. The production of heat by chemical reactions.
E. The exchange of nutrients and waste products with the
environment.
25.
The sum total of the chemical activity at the cellular level
which enables an organism to meet its nutrient and energy
demands is termed:
A. Evolution
D. Growth
B. Responsiveness
E. Energy
C. Metabolism
26.
Why do animals require "food" for survival?
A.
B.
C.
D.
E.
Food is a source of energy.
Necessary chemicals are provided by food.
Food is a primary source of water for all animals.
a and b.
a, b, and c.
27.
Humans sweat when the temperature gets hot so that they
can cool themselves. This is an example of which characteristic of
life?
A. Growth
B. Reproduction
C. Homeostasis
D. Evolve
E. Response to stimuli
28.
Homeostatic control in living things is exerted over all of the
following EXCEPT
A. temperature
B. moisture level
C. response to stimuli
D. acidity level
29.
What do we call the maintenance of internal conditions of an
organism within a certain boundary range?
A. evolution
B. metabolism
C. adaptation
D. homeostasis
E. photosynthesis
30.
About twelve to twenty four hours after the lost meal, a
person’s blood sugar level normally varies from about 60 to 90
milligrams per 100 milliliters of blood, though it may attain 130
mg / 100 ml after meals high in carbohydrates. That the blood
sugar level is maintained within a fairly narrow range in spite of
uneven intake of sugar is due to the body’s ability to carry out
A. adaptation
B. inheritance
C. metabolism
D. homeostasis
E. all of the above
31.
Which of the following terms is based on the Greek root
words for "holding still" or "to be standing"?
A. evolution
B. metabolism
C. adaptation
32.
D. homeostasis
E. photosynthesis
Which of the following does NOT represent homeostasis?
A. Sensors detect CO2 levels in the blood and trigger an
increase or decrease in the rate of breathing.
B. When body temperature drops, you shiver to generate heat;
when your body heats up, you sweat and the evaporation
cools you.
C. Feelings of hunger and then fullness affect the length of time
and quantity of food you eat, keeping your weight near a "set
point."
D. Energy is captured by plants, then transferred to consumers
and decomposers, and eventually lost as heat.
E. Cells adjusting the openings on the bottom of leaves respond
to differences in water stress in order to maintain moisture
inside the leaf.
33.
The ability to maintain a constant internal environment is
A. metabolism
D. physiology
B. homeostasis
E. thermoregulation
C. development
34.
Homeostasis
A. prevents drastic changes in internal environmental
conditions.
B. duplicates the external environment inside the living
organism.
C. requires only the replacement for materials that are used up
by cells.
D. is controlled solely by positive feedback reactions
E. none of the above
35.
You drink a glass of lemonade, but your body's pH does not
change. This is an example of how organisms:
A.
B.
C.
D.
E.
maintain homeostasis.
maintain organization.
adapt to their environment.
are immune to acid.
are what they eat.
36.
Humans born without sweat glands usually do not survive.
Why not?
A. Sweating is an important mechanism for maintaining
temperature homeostasis.
B. Sweat glands create openings in the skin where gas
exchange occurs.
C. Sweating is an important way of ridding the body of excess
water.
D. Sweating is important for purging impurities from the body.
E. Sweat builds up in the body which causes swelling and
tissue damage.
37.
A sunflower follows the sun as it move across the sky during
the day. This is an example of which characteristic of life?
A. Growth
D. Evolve
B. Reproduction
E. Response to stimuli
C. Homeostasis
38.
A bacterium divides into two bacteria which are identical to,
but smaller than, the original bacterium. This is an example of
which characteristic of life?
A. Growth
B. Reproduction
C. Homeostasis
D. Evolve
E. Response to stimuli
39.
Which type of reproduction generates exact clones of each
other?
A. Sexual
B. Meiosis
C. Asexual
D. all of these
E. none of these
40.
At the beginning of the week a plant is 3 inches tall, and at
the end of the week it is 4 inches. This is an example of which
characteristic of life?
A. Growth
B. Reproduction
C. Homeostasis
D. Evolve
E. Response to stimuli
41.
Which of the following is/are important to the theory of
evolution?
A. environmental
change
B. variation in traits
within a population
42.
C. mutation
D. inheritance of traits
E. all of these
Which is NOT an example of evolution?
A.
B.
C.
D.
E.
Development of antibiotic-resistant bacteria.
Flightless birds on islands without predators.
This year's flu is different from last year's flu.
A dog learns how to open the cabinet where its food is kept.
Most commercial pesticides are effective for 2-3 years.
43.
Some members of a species have a genetic change that
causes them to be better suited to their environment. These
members survive to reproduce and pass these genetic changes to
their offspring. This is
A.
B.
C.
D.
E.
adaptation
natural selection
the driving force for evolution
All of the choices are correct.
None of the choices are correct.
44.
Which of these is the process by which changes occur in the
characteristics of species of organisms over time?
A. evolution
B. metabolism
C. adaptation
D. homeostasis
E. photosynthesis
45.
The changes in the human race since the time of the first
humans is an example of:
A. homeostasis
B. hydrolysis
C. evolution
D. metabolism
E. responsiveness
46.
Evolution is "the biological theme that ties together all the
others." This is because the process of evolution
A. explains how organisms become adapted to their
environment.
B. explains the diversity of organisms.
C. explains why all organisms have characteristics in common.
D. explains why distantly-related organisms sometimes
resemble one another.
E. All of these are appropriate answers.
47.
The bones in a bird are hollow so as to reduce its weight for
flight. This is an example of which characteristic of life?
A. Living things
B. Living things
environment
C. Living things
D. Living things
E. Living things
48.
grow and develop
utilize materials and energy from the
reproduce
are adapted
are homeostatic
All of the following are examples of adaptations, except
A.
B.
C.
D.
E.
49.
mice learning a maze to get food.
larger teeth in beavers for gnawing wood.
different beak shape for birds that eat seeds vs. insects.
insects that resemble twigs.
flower coloration that attracts pollinators.
A mutation is
A.
B.
C.
D.
E.
a physical deformity
a change in DNA sequence
a dose of radiation
a defective egg or sperm cell
the inability to speak
50.
Which of these is a peculiarity of form, function, or behavior
that promotes the likelihood of a species' continued existence?
A. evolution
D. homeostasis
B. metabolism
E. photosynthesis
C. adaptation
51.
Which of the following is/are characteristic of living
organisms?
A. Organized structure
B. Responsiveness to stimuli
C. Maintenance of homeostasis
D. b and c are correct
E. a, b, and c are correct
52.
Which of these is an organism?
A. oak tree
B. beetle
C. dog
D. bacterium
E. all of these
53.
The following statements are true about all living things
EXCEPT
A. They are made of cells or cell products.
B. They are the products of evolution.
C. They are composed of carbon, hydrogen, oxygen, and
nitrogen.
D. They undergo growth and development.
E. They have a cell wall as an outer boundary.
54.
Which of the following are properties of ALL life forms?
i. heritable programs in the form of DNA
ii. photosynthesis
iii. growth and development
A.
B.
C.
D.
55.
i
ii
iii
Only i and iii are
correct.
E. i, ii, and iii are
correct.
The reason plastics are not living is that:
A.
B.
C.
D.
they do not contain carbon
they are not responsive
they cannot diffuse
no one loves them
A.
B.
C.
D.
Living organisms are characterized by:
adapting to the environment.
evolving over time.
displaying homeostatic mechanisms.
all of the choices pertain to living organisms.
56.
57.
Organisms belonging to the same _____ would be the most
closely related.
A. kingdom
B. phylum
C. family
D. class
E. order
58.
Which of the following is NOT one of the characteristics of
living organisms?
A.
B.
C.
D.
to
to
to
to
be organized
respond
grow
metabolize
E. All of the choices are
characteristics of
living organisms.
59.
Which of the following characteristics is NOT required for
the life of an individual organism to continue?
A. to be organized
B. to respond
C. to metabolize
D. to reproduce
60.
A little boy is color-blind just as his grandfather was, even
though his mother had normal vision. This situation is the result
of
A. adaptation
D. homeostasis
B. inheritance
E. none of the above
C. metabolism
61.
Mitosis is a cellular division taking place in a __________.
A. organ cells
B. body cells
C. sex cells
62.
D. tissues
E. bones
Meiosis is a cellular division taking place in a _____________.
A. organ cells
D. tissues
B. body cells
E. bones
C. sex cells
63.
Mitosis is a cellular division taking place in a _____________.
A. organ cells
B. somatic cells
C. sex cells
64.
D. tissues
E. bones
Meiosis is a cellular division taking place in a ___________.
A. organ cells
B. body cells
C. gamete cells
D. tissues
E. bones
65.
How many chromosomes does each meiosis daughter cells
have?
A. 23 pairs of chromosomes
B. 23 chromosomes
C. 46 chromosomes
D. 24 chromosomes
E. 23 chromosomes plus the XY-chromosome
66.
How many chromosomes does each mitosis daughter cells
have?
A. 23 pairs of chromosomes plus the XY-chromosome
B. 23 chromosomes
C. 46 chromosomes
D. 24 chromosomes
E. 23 chromosomes plus the XY-chromosome
67.
How many stage/s of cellular division does mitosis undergo?
A. 1
B. 2
C. 3
68.
D. 4
E. 5
What is the language being used in binomial nomenclature?
A. Spanish
D. Italian
B. French
E. Latin
C. Portuguese
69.
It is a symbiotic relation where in the two organisms benefit
from each other?
A. Commensalism
B. Mutualism
C. Parasitism
D. Competition
E. predation
70.
Which of the following symbiotic relationships is considered
parasitic?
A.
B.
C.
D.
ticks feeding on a dog
bees transporting pollen from flowers
pilotfish swimming under sharks
birds eating the insects from the back of a hippopotamus
71.
Ants and acacia trees have a mutualistic relationship
because
A.
B.
C.
D.
72.
What type of relationship is mutualism?
A.
B.
C.
D.
73.
they benefit each other.
they are part of the same ecosystem.
they are both adapted to a humid climate.
the ants eat part of the acacia tree.
One species benefits and the other is not affected at all.
Both species involved benefit from the relationship.
One Species benefits and the other is harmed.
Both species harm each other
A bird living a tree is an example of
A. predator/prey
C. parasitism
B. mutualism
D. Commensalism
74.
Which of the following is a symbiotic relationship where one
partner benefits and the other does not benefit or lose from the
relationship?
A. commensalism
C. parasitism
B. mutualism
D. decomposition
75.
Which of the following is a symbiotic relationship where
both partners benefit?
A. commensalism
C. parasitism
B. mutualism
D. decomposition
76.
Which of the following is a symbiotic relationship where one
partner benefits and the other is harmed?
A. commensalism
C. symbolism
B. mutualism
D. parasitism
77.
Grass is eaten by a prairie dog. The prairie dog is eaten by a
coyote. This is an example of
A. an abiotic element.
C. a herbivore.
B. an omnivore.
D. a food chain.
78.
A bird eats a worm. Which is the predator?
A. the worm
B. the bird
C. both the bird and
the worm
79.
D. neither the bird nor
the worm
What do several different populations living together make?
A. a biosphere
B. an organism
C. a community
D. an ecosystem
80.
Which is an example of an abiotic element changing an
area?
A. introducing a new
C. two species of birds
type of grass
competing
B. water flooding the
D. algae growing on
area
crabgrass
81.
Grass that gains energy from the sun is an example of a
A. consumer
B. parasite
C. decomposer
D. producer
82.
In a food web arrows point in just one direction because
they show
A.
B.
C.
D.
which animal is bigger.
which animals are related.
how energy goes to the animal that is eating.
how energy goes to the animal that is eaten.
83.
Two members of the same species fight over who gets a
certain food. Members of different species try to take over a certain
nesting area. These are both examples of
A. community.
B. competition.
C. mutualism.
D. commensalism.
84.
If scientists are studying the egrets, herons, marsh crabs,
and cordgrass, but not the water or rocks in a salt marsh, what
level of organization would they be studying?
A. individual organism
B. population
C. community
D. ecosystem
85.
Coyotes prey on prairie dogs. In order for the prairie dog
population to survive, how many prairie dogs are needed
compared to coyotes?
A.
B.
C.
D.
fewer prairie dogs than coyotes
many more prairie dogs than coyotes
about the same number of prairie dogs as coyotes
there is no relationship between the number of prairie dogs
and coyotes
86.
When there is a lot of pollution, rain can be acidic, harming
plants and animals. What is this an example of?
A.
B.
C.
D.
competition between a population and a community
a mutualistic type of symbiosis
an abiotic factor affecting an ecosystem
an individual affecting a community
87.
What effect does biodiversity have on a community?
A.
B.
C.
D.
It
It
It
It
makes destruction by insects impossible.
makes primary succession more likely.
enables species to survive in a desert.
enables the community to withstand changes.
88.
The speed of water is an important abiotic factor in a
freshwater ecosystem because
A.
B.
C.
D.
a tributary has different plants than a river.
faster water has a higher salt content.
animals must adapt so they are not washed away.
animals cannot live in fast-moving water.
89.
What word describes the mammals, fish, birds, and plants
that live in an environment?
A. abiotic
C. the biosphere
B. the population
D. biotic
90.
A community is several species of animals interacting, while
a population is
A. members of one species in an area.
B. the biotic and abiotic elements of an area.
C. the nonliving elements of a habitat.
D. a single organism.
91.
The five levels of organization in the environment, from first
to fifth level are
A. organism, population, biosphere, ecosystem, community.
B. organism, population, biotic elements, abiotic elements,
community.
C. organism, population, community, ecosystem, biosphere.
D. organism, population, biosphere, abiotic elements, ecology.
92.
Which of the following is abiotic?
A. a gar
C. grass
B. an alligator
D. water
93.
Organisms that can make their own food from sunlight are
called
A. decomposers
C. producers
B. consumers
D. carnivores
94.
Grass is eaten by a prairie dog. The prairie dog is eaten by a
coyote. This is an example of
A. an abiotic element
C. a herbivore
B. an omnivore
D. a food chain
95.
One food web arrow goes from a prairie dog to a coyote,
showing that
A. the coyote is bigger.
B. the coyote eats the
prairie dog.
96.
97.
C. the prairie dog eats
the coyote.
D. the prairie dog is a
producer.
Without wolves, Yellowstone Park had
A. too many elk
C. too many rabbits
B. too much grass
D. too many cows
The largest population an environment can support is its
A. carrying capacity
C. population
B. Limiting factor
D. symbiosis
98.
One type of competition involves individuals competing for
resources. The other involves competition between different
A. Organisms
C. Environments
B. Populations
D. relationships
99.
Young wasps are eating the tomato hornworm that is their
host. What is this an example of?
100.
A. commensalism
C. parasitism
B. mutualism
D. competition
A bird eats a worm. Who is the predator?
A. the worm
B. the bird
C. both the bird and the worm
D. neither the bird nor the worm
101.
Rocks, temperature, and water are what part of the
environment?
102.
A. biotic
C. population
B. abiotic
D. living
What do several different populations living together make?
A. a biosphere
C. a community
B. an organism
D. an ecosystem
103.
Which is an example of an abiotic element changing an
area?
A. introducing a new
C. two species of birds
type of grass
competing
B. water flooding the
D. algae growing on
area
crabgrass
104.
Grass that gains energy from the sun is an example of a
A. consumer
C. decomposer
B. parasite
D. producer
105.
A diagram with arrows showing energy flow from grass, to a
rabbit, to a fox is
A. an energy pyramid
C. a food chain
B. a food web
D. a population chart
106.
In a food web, arrows point in just one direction because
they show
A. which animal is bigger.
B. which animals are related.
C. how energy goes to the animal that is eating.
D. how energy goes to the animal that is eaten.
107.
After one species disappears, the other species in the
ecosystem
A. benefit
C. die
B. are thrown out of
balance
D. are unaffected.
108.
Limiting factors determine an area’s carrying capacity
because
A. the number of animals is limited
B. ecosystems are small
C. animals need resources to survive
D. the number of animals is unlimited
109.
Two members of the same species fight over who gets a
certain food. Members of different species try to take over a certain
nesting area. These are both examples of
A. community
C. Mutualism
B. Competition
D. commensalism.
110.
An environmental study reporting on the way temperature,
water quality, and minerals affect the animals in a salt marsh
would be considering which level of organization?
A. individual organism
C. community
B. population
D. ecosystem
111.
The plants a ladybug lives on, the aphids the ladybug eats,
and the birds that would eat the ladybug are all
A. biotic elements of an ecosystem.
B. predators.
C. producers.
D. abiotic elements of an ecosystem
112.
Herbivores, carnivores, and omnivores are all
A. Decomposers
C. Predators
B. Producers
D. consumers.
113.
are
Animals that eat a variety of meats, fruits, and vegetables
A. Producers
C. Omnivores
B. Carnivores
D. herbivores
114.
A scientist studying the way egrets, herons, and crabs
interact, who is not interested in abiotic factors such as the rocks,
water, and temperature, is studying what level of environmental
organization?
115.
116.
A. population
C. community
B. ecosystem
D. biosphere
Rocks, temperature, and water are what kind of things?
A. biotic
C. population
B. abiotic
D. living
What level of organization comes after population?
A. biosphere
C. community
B. organism
D. ecosystem
117.
What word describes a community of organisms and their
environment?
A. individuals
C. population
B. ecosystem
D. community
118.
119.
What living things make food from sunlight?
A. consumers
C. decomposers
B. parasites
D. producers
What happened to other living things when the wolves no
longer lived in Yellowstone?
120.
A. They were better off.
C. They died.
B. They were out of
balance.
D. They were not
changed.
When is food a limiting factor?
A. when a population is
large
C. when a population is
small
B. when there’s too
much food
D. when there’s too
much water
121.
What is an animal that catches and eats another animal
called?
122.
123.
A. prey
C. producer
B. predator
D. herbivore
In which relationship do living things help each other?
A. parasitism
C. organism
B. mutualism
D. predator
Coyotes prey on prairie dogs. In order for the prairie dog
population to survive, how many prairie dogs are needed
compared to coyotes?
A. fewer prairie dogs than coyotes
B. many more prairie dogs than coyotes
C. about the same number of prairie dogs as coyotes
D. There is no relationship between the number of prairie dogs
and coyotes.
124.
What kind of elk do wolves kill?
A. the strong and healthy
B. the smart and quick
C. the old, injured, and diseased
D. the energetic and fast
125.
When there is a lot of pollution, rain can be acidic, harming
plants and animals. What is this an example of?
A. competition between a population and a community
B. a mutualistic type of symbiosis
C. an abiotic factor affecting an ecosystem
D. an individual affecting a community
126.
It has been a very harsh winter. The ground is covered in
snow, and the trees are covered in ice. Many deer die because they
cannot find food. This is an example of
A. producers providing food.
B. a limiting factor controlling a population.
C. a biosphere in trouble.
D. predators harvesting the weak and the sick.
127.
Bears eat fruits such as berries and animals such as fish.
They hibernate in the winter. They give birth to live young. Which
of these terms applies to bears?
A. They are decomposers.
B. They are at the bottom of the energy pyramid.
C. They have a mutualistic relationship with berries.
D. They are consumers.
128.
Suppose there were a bird that always sat on a horse's back
and ate the insects that would bite the horse. What would this be
an example of?
A. mutualism
B. parasitism
C. competition
D. commensalism
129.
When a parasitic worm invades an animal, who is
the host?
A. the producer
B. the animal
C. the decomposer
D. the worm
130.
As loggers take more trees out of a forest, there are
fewer places for a certain type of bird to build a nest.
What is this an example of?
A. a predator attacking prey
B. abiotic factor affecting orest's carrying capacity
becoming smaller
C. a food web becoming smaller
D. a symbiotic relationship
Part II
1. Which of the following is not a major part of a plant?
A. Roots
B. Stems
C. Bud
D. Leaves
2. Which of the following is not needed by the plants in order
to survive?
A. Air
B. Water
C. Minerals or nutrients from the soil
D. oxygen
3. Which of the following component of the air is needed by
the plants to carry out photosynthesis?
A. Carbon dioxide
B. Oxygen
C. Nitrogen
D. Phosphorous
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4. Which of the following parts of the plants holds the plant
in the soil and takes in water and nutrients from it?
A.
B.
Roots
Leaves
C. Stem
D. Flowers
5. Which of the following parts of the plants holds up the
plant and moves water and nutrients through it?
A. Roots
B. Leaves
C. Stem
D. Flowers
6. Which of the following parts of the plants make fruits
which hold the seeds?
A. Roots
B. Leaves
C. Stem
D. Flowers
7. What is the food production process is taking place in the
plant leaves and other green parts of it?
A. Respiration
B. Photosynthesis
C. Plasmolysis
D. Hydrolysis
8. Which of the following is the reproductive part of the
plant?
A. Roots
B. Leaves
C. Stem
D. Flowers
9. What is the source of the energy of all living things?
A. Star
B. Moon
C. Sun
D. grass
For question #10, use the following food chain
Grass
zebra
Lion
10. Where does a zebra get energy?
A.
B.
Grass
Lion
C. Both grass and lion
D. None of the above
26 | L E T - R e v i e w e r – G e n e r a l E d u c a t i o n
11. What is needed in the photosynthesis to convert carbon
dioxide and water into sugar and oxygen?
A. Sunlight
B. Air
C. Chlorophyll
D. Chloroplasts
12. If a plant produces more sugar that it can use, the sugar is
stored as _____________.
A.
B.
Fats
Glycerol
C. Glucose
D. Starch
13. Starch may be stored in the following
EXCEPT ___________.
A.
B.
stems
leaves
C. flowers
D. Roots
14. Which of the following is a biotic factor?
A.
B.
Temperature
Soil
C. Air
D. apple
15. Which of the following is abiotic factor?
A.
B.
grass
Temperature
C. Mango
D. man
16. ________________ are organisms that make its own food
from the primary energy source.
A.
C.
Primary consumers
Herbivores
B. Producers
D. carnivores
17. Which of the following is an example of a primary
consumer?
A.
B.
Rabbit
Snake
C. Grass
D. eagle
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18. Primary consumers are also called __________________.
A.
B.
Carnivores
Omnivores
C. Herbivores
D. scavengers
19. Carnivores are also called ______________________.
A. Primary consumers
B. Secondary producers
C. Herbivores
D. Secondary consumers
20. __________________ are animals that eat herbivores.
A.
B.
Primary consumers
C. Primary producers
Secondary producers D. Secondary consumers
21. Which of the following is a carnivore?
A.
B.
Snake
Cow
C. Rabbit
D. Grasshopper
22. Which of the following is a secondary consumer?
A.
B.
rat
Cow
C. lion
D. Grasshopper
23. ________________________ are animals that eat both animals
and plants.
A.
B.
Omnivores
Carnivores
C. Herbivores
D. decomposers
24. Which of the following is not an omnivore?
A.
B.
Human
Bear
C. Raccoons
D. elephant
25. ____________________ are organisms that breakdown dead
plants and animals.
A.
B.
Omnivores
Carnivores
C. Herbivores
D. decomposers
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26. __________________________ is needed for photosynthesis.
Without it organisms and plants that depend on plant will die.
A.
B.
Temperature
Light
C. Air
D. soil
27. It is important for plant growth. Plants take in water and
mineral salts from it.
A.
B.
Temperature
Light
C. Air
D. soil
28. It is essential for life processes such as digestion and
photosynthesis.
A.
B.
Temperature
Light
C. water
D. soil
29. Who is the “Father of Genetics”?
A.
B.
Gregor Mendel
Gregory Mendel
C. Carolous Linnaeus
D. Robert Hooke
30. _______________ is the principle that states “Inheritance of
one trait has no effect on the inheritance of another trait”.
A.
B.
Natural Selection
Co-dominance
C. Independent Assortment
D. Inheritance
31. _______________ is the passing of traits to offspring from its
parents or ancestor.
A.
B.
Natural Selection
Co-dominance
C. Heredity
D. Pedigree
32. This dominant trait is also called the photo sneeze reflex.
A.
B.
Achoo Syndrome
Chin Cleft
C. Early Onset Myopia
D. Bent Little Finger
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33. A dominant allele causes the last joint of the little finger to
dramatically bend inward toward the 4th finger is called
__________________
A.
B.
Achoo Syndrome
Chin Cleft
C. Early Onset Myopia
D. Bent Little Finger
34. _____________________ is a complex trait with at least 4
gene loci involved, however the heritability of myopia is very
high and shows a dominant pattern.
A.
B.
Achoo Syndrome
Chin Cleft
C. Early Onset Myopia
D. Bent Little Finger
35. ______________ is due to the bond structure which
underlies the Y-shaped fissure of the chin.
A.
B.
Achoo Syndrome
Chin Cleft
C. Early Onset Myopia
D. Bent Little Finger
36. _________________ is the study of how traits are passed
from parent to offspring.
A.
B.
Gene
Genetics
C. DNA
D. Chromosomes
37. _________________ is a segment of DNA that determines a
trait.
A.
B.
Gene
Genetics
C. DNA
D. Chromosomes
38. What determines the genes on the chromosomes?
A.
B.
Gene
Genetics
C. DNA
D. Chromosomes
39. How many pairs of chromosomes do humans have?
A.
B.
46 pairs
23 pairs
C. 20 pairs
D. 23 chromosomes
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40. How many Chromosomes do humans have?
A. 46 Chromosomes
C. 20 pairs of chromosomes
B. 24 pairs of chromosomes
D. 23 chromosomes
41. How many chromosomes does a sperm have?
A.
B.
46 Chromosomes C. 20 pairs of chromosomes
24 pairs of chromosomes D. 23 chromosomes
42. How many chromosomes does an egg have?
A.
B.
46 Chromosomes C. 20 pairs of chromosomes
24 pairs of chromosomes D. 23 chromosomes
PART III
1. A screw is a(n) _____________wrapped around a central
cylinder.
a. lever
b. wedge
c. inclined plane
d. wheel and axle
2. Which simple machine would stairs be an example?
a. a wedge
b. an inclined plane
c. a pulley
d. a lever
3. Which is an example of a wedge?
a. a doorknob
b. a clock
c. a zipper
d. a light bulb
4. Which is an example of a wheel and axle?
a. Hammer
b. Screwdriver
e. Flag Pole
c. Wagon
d. Ramp
5. An elevator is a pulley.
a. True
b. False
c. can’t be determined
d. none of the above
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6. A pulley is:
a.
b.
c.
d.
a bar used to lift heavy objects
a wheel with a groove for a rope
made of two inclined planes
has a lever arm and a fulcrum
7. A wedge is actually a kind of inclined plane.
a. True
b. False
c. can’t be determined
d. none of the above
8. An inclined plane:
a.
b.
c.
d.
uses a bar used to lift heavy objects
is a ramp
is made up of two inclined planes
has a lever arm and a fulcrum
9. How can you create a compound machine?
a.
b.
c.
d.
By adding more wheels to a pulley system
By combining two or more simple machines
By exerting more force to an object
None of the above
10. What is the best tool to pry a nail from a piece of wood?
a.
b.
c.
d.
e.
A lever such a claw ended hammer
A pulley system
A wheel and axle such as a wagon
An inclined plane such as ramp
None of the above
11. A _______________ is a machine used to hold two objects
together.
a. pulley
b. lever
c. inclined plane
d. screw
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12. What tool would be best to use to lift a heavy load, like a
washing machine?
a. Wedge
b. Lever
c. Wheel and axle
d. Screw
13. An object being lifted or moved by a machine is a:
a. fulcrum
b. load
c. work
d. force
e. friction
14. A screw is a(n) _________ wrapped around a central
cylinder.
a. lever
b. wedge
c. inclined plane
d. wheel and axle
15. Which simple machine turns a Ferris wheel?
a. pulley
b. wedge
c. inclined plane
d. wheel and axle
16. Which is an example of an inclined plane?
a. Ferris wheel
b. ramp
c. elevator
d. none of the above
17. Machine with a bar that pivots on a fixed point
a. watt
b. pulley
c. wheel and axle
d. lever
18. What is a machine with a grooved wheel that holds a
cable?
a. pulley
b. lever
c. wheel and axle
d. wedge
19. A flag pole is a wheel and axle.
a. True
b. False
c. can’t be determined
d. none of the above
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20. A car is a wheel and axle.
a. True
b. False
c. can’t be determined
d. none of the above
21. A wedge:
a.
b.
c.
d.
uses a wheel and axel to help move objects
is an inclined plane wrapped around an axel
is made up of two inclined planes
has a lever arm and a fulcrum
22. A water bottle lid is a screw.
a. True
b. False
c. can’t be determined
d. none of the above
23. A stiff bar that moves about a fixed point is a....
a. fulcrum
b. wedge
c. wheel and axle
d. inclined plane
24. A seesaw is a lever.
a. True
b. False
c. can’t be determined
d. none of the above
25. An axe is an inclined plane.
a. True
b. False
c. can’t be determined
d. none of the above
Part IV
1. A complete electric circuit is called______________ electric
circuit.
a. Open
c. Complete
b. Closed
d. None of these
2.
----------- is an insulator.
a. Metal
b. acid
c. Rubber
d. Salt solution
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3.
__________is a conductor.
a. Wood
b. Metal
c. Paper
d. Petrol
4. The electric current in a closed circuit always flows from
the ___________terminal of the electric battery to the
______terminal.
a.
b.
c.
d.
5.
Negative to positive
Positive to negative
Positive to positive
None of these
The base of an electric battery is its ___________terminal.
a.
b.
c.
d.
Positive terminal
Negative terminal
Negative and positive
None of these
6. The path along which electric current flows is_____________.
a. Switch
b. Electric current
7.
In _____________ electrical energy is transformed in to
mechanical energy.
a. Transistor
b. Mixer grinder
8.
c. Electric circuit
d. Electric battery
c. Electromagnet
d. Electric bell
------------- is an energy which flows in an electric circuit.
a.
b.
Electric circuit
Electromagnet
c.
d.
Electric current
None of these
9. The central _____________of an electric battery is always
positive.
a. Circuit
b. Chemical
c. Terminal
d. None of these
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10. Kerosene oil is an example of_______________.
a. Conductors
b. Insulators
c. Electrolyte
d. None of these
11. The cylindrical container of electric battery is made of
___________ _and acts as negative terminal.
a. Copper
b. Iron
c. Zinc
d. Silver
12. The wire which carries away the current to the power
house is called____________.
a. Earth wire
b. Neutral wire
c. Live wire
d. None of these
13. _____________ is a safety wire which protect us from
electric shocks and electric fire.
a. Earth wire
b. Neutral wire
c. Live wire
d. None of these
14. ____________ is a device which converts chemical energy in
to electrical energy.
a. Electrical bell
b. Electric lift
c. Electric batteries
d. Electric bulb
15. An electric batteries has ____________terminals.
a. 3
b. 4
c. 1
d. 2
Part V
1. The kinetic energy of the particles of solid is ____________.
a. low
b. high
c. constant
d. very low
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2. The kinetic energy of the particles of liquid is ____________.
a. low
b. high
c. constant
d. very low
3. The kinetic energy of the particles of gas is ____________.
a. low
b. high
c. constant
d. very low
4. The attractive force between particles of solid is _________.
a. weak
b. Very strong
c. normal
d. constant
5. The attractive force between particles of liquid is ________.
a. constant
b. weak
c. normal
d. strong
6. The attractive force between particles of gas is __________.
a. Very weak
b. constant
c. constant
d. strong
7. Which of the following substances has the lowest melting
point?
a. Oxygen
b. Ethanol
c. Ice
d. iron
8. Which of the following substances has the highest melting
point?
a. Oxygen
b. Ethanol
c. Ice
d. iron
9. Which of the following substances has the lowest boiling
point?
a. Oxygen
b. Ethanol
c. Water
d. iron
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10.Which of the following substances has the highest boiling
point?
a. Oxygen
b. Ethanol
c. Water
d. iron
11. What type of liquid that evaporates quickly at room
temperature?
a. Volatile liquid
b. immiscible liquid
c. miscible liquid
d. normal liquid
12. Which of the following is not an example of volatile liquid?
a. Petrol
b. Perfume
c. Water
d. None of the above
13. Which of the following is not a characteristic of
evaporation?
a.
b.
c.
d.
Occurs at temperature below boiling point
Occurs only at the surface of the liquid
Occurs slowly
Occurs rapidly
14. Which of the following is not a characteristic of boiling?
a.
b.
c.
d.
Occurs only at boiling point
Occurs throughout the liquid
Occurs rapidly
Occurs slowly
15. Which of the following is not a characteristic of
condensation?
a. Heat energy is given out
b. The gas particles lose energy and move slowly
c. Particles become slow enough for the gas to change
into liquid
d. None of the above
38 | L E T - R e v i e w e r – G e n e r a l E d u c a t i o n
PART VI
1. What is the energy of an object at rest?
a. Kinetic energy
c. Rest energy
b. Mechanical energy d. Potential energy
2. If a boy carried a 2kg box and move it in 10m distance.
How much is the work done?
a 19.6N
b. 20N
c. 196N
d. 0
3. If a man pushed a 50N crate but he wasn’t able to move it.
How much is done?
a. 50N
b. 25N
c. 10N
d. 0
4. What is the net force if a 15N object pushed a 7N box?
a. 22N
b. 8N
c. 20N
d. 105N
5. The potential energy of an object at the peak of a mountain
is 12,000J. What is the kinetic energy of the object at ¼ the
height of the mountain?
a. 6,000J
b. 4,000J
c. 9,000J
d. 3,000J
6. How much force is exerted by a 10kg object resting on the
ground?
a. 9.8N
b. 98N
c. 980N
d. 9,800N
7. What is true about friction?
a. It is described as mass times acceleration.
b. It acts in the same direction with an object.
c. It acts in opposite direction with an object.
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d.It acts effectively in smooth surfaces.
8. What is the energy conversion during photosynthesis?
a. light -> mechanical
b. solar -> mechanical
c. light -> chemical
d.thermal -> chemical
9. What is the energy conversion when an electric fan is in
use?
a. mechanical -> electrical
b. mechanical -> electrical -> wind
c. electrical -> wind -> mechanical
d. electrical -> mechanical -> wind
10. What is the name referring to the height of the wave?
a.
b.
crest
trough
c. wavelength
d. amplitude
11. In an ocean biome, which of the following is the primary
producer?
a. Algae
d. Small fish
b. Phytoplankton
e. None of the above
c. Grass
12. A food chain is characterized by the following except
___________.
a.
b.
How each living thing gets food.
How nutrients and energy are passed from
creature to creature.
c. It begins with plant life.
d. It ends with animal life.
e. How each living thing helps each other.
13. How much energy is taken by a consumer?
a. 10% of the energy
b. 20% of the energy
c. 5% of the energy
40 | L E T - R e v i e w e r – G e n e r a l E d u c a t i o n
d. 1% of the energy
e. None of the above
14. In an ocean biome, which of the following is the primary
consumer?
a.
b.
c.
Phytoplankton
Zooplankton
Herring
d. Mackerel
e. tuna
15. Which of the following is an autotroph?
a.
b.
c.
Grass
Grasshopper
Bird
d. Snake
e. Earthworm
16. Which of the following is not a heterotroph?
a.
b.
c.
d.
e.
First order consumer
Second order consumer
Third order consumer
Fungi
None of the above
17. Which of the following is a saprotroph?
a.
b.
c.
Grass
Chicken
Algae
d. Phytoplankton
e. Fungi
18. Which of the following relationships demonstrates
commensalism?
a.
b.
An orchid in a tree.
A rose and a chrysanthemum growing in the same
pot.
c. A tapeworm in a 5-year old boy.
d. Tuna and Sardines
e. None of the above
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19. How much energy does the third order consumer get from
eating the second order consumer with 5000 units of energy?
a. 50000 units
b. 500 units
c. 50 units
d. 5 units
e. 1000 units
20. Light energy is converted into what kind of energy during
the process of photosynthesis?
a. Food energy
b. Chemical energy
c. Physical energy
d. Mechanical energy
e. Potential energy
PART VII
1) To enter
a)
b)
c)
d)
e)
2)
or leave a cell, substances must pass through
a microtubule.
the Golgi apparatus.
a ribosome.
the nucleus.
the plasma membrane.
You would expect a cell with an extensive mitochondria to
a) make a lot of ATP.
b) secrete a lot of material.
c) move actively.
d) perform photosynthesis.
e) store large quantities of food
3) Which of the following correctly matches an organelle with
its function?
a) mitochondrion . . . photosynthesis
b) nucleus . . . cellular respiration
c) ribosome . . . manufacture of lipids
d) lysosome . . . movement
e) central vacuole . . . storage
42 | L E T - R e v i e w e r – G e n e r a l E d u c a t i o n
4) Of the following organelles, which group is involved in
manufacturing substances needed by the cell?
a)
b)
c)
d)
e)
lysosome, vacuole, ribosome
ribosome, rough ER, smooth ER
vacuole, rough ER, smooth ER
smooth ER, ribosome, vacuole
rough ER, lysosome, vacuole
5) A cell has mitochondria, ribosomes, smooth and rough ER.
Based on this information, it could not be
a)
b)
c)
d)
e)
a cell from a pine tree.
a grasshopper cell.
a yeast (fungus) cell.
a bacterium.
Actually, it could be any of the above.
6) A researcher made an interesting observation about a
protein made by the rough ER and eventually used to build
a cell's plasma membrane. The protein in the membrane
was actually slightly different from the protein made in the
ER. The protein was probably changed in the
a)
b)
c)
d)
e)
Golgi apparatus.
smooth ER.
mitochondrion.
nucleus.
chloroplast.
7) The structure in the nucleus which manufactures
ribosomes for protein synthesis.
a)
b)
c)
d)
e)
Nuclear envelope
Nuclear cytoplasm
Nucleolus
Nucleus
None of the above
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8)
Cellular structure that regulates what enters and leaves
the cell.
a)
b)
c)
d)
e)
Cell wall
Cell membrane
Cytoplasm
Phospholipids
ribosomes
9) Organelles that store materials such as water, salts, and
carbohydrates. They may occupy a large space within plant
cells.
a) Cytoplasm
b) Ribosomes
c) Vacuole
d) Mitochondria
e) Nucleus
10) Helps to support, strengthen and protect the cell. Not
found in animal cells.
a)
b)
c)
d)
e)
Cell membrane
Cell wall
Cytoplasm
Rough ER
Smooth ER
11) Photosynthetic organelles found in many plant cells only.
a)
b)
c)
d)
e)
Mitochondrion
Chlorophyll
Chloroplast
Chromatin
Lysosome
12) A system of channels that transport proteins through the
cell.
a) Mitochondrion
b) Chlorophyll
c) Endoplasmic reticulum
d) Chromatin
e) Lysosome
44 | L E T - R e v i e w e r – G e n e r a l E d u c a t i o n
13) The liquid inside the cell that all the organelles are
suspended in.
a)
b)
c)
d)
e)
Nucleus
Protoplasm
Cytoplasm
Golgi apparatus
Cell membrane
14) Organelles which provide cells with energy by using sugar
as a fuel source.
a)
b)
c)
d)
e)
Mitochondria
Nucleus
Chloroplast
Golgi apparatus
Lysosomes
15) Contain chemicals and enzymes necessary for digesting
certain materials in the cell.
a)
b)
c)
d)
e)
Ribosomes
Lysosomes
Chromosomes
Endoplasmic reticulum
Mitochondria
16) Organelle that collects, modifies and packages chemicals
made at one location in a cell and secretes finished products to
be used at another cellular local.
a)
b)
c)
d)
e)
Mitochondria
Nucleus
Chloroplast
Golgi apparatus
Lysosomes
17) The organelle responsible for manufacturing proteins.
a) Mitochondria
b) Ribosomes
c) Chloroplast
d) Golgi apparatus
e) Lysosomes
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18) The information and control center of the cell. It contains
genetic information.
a)
b)
c)
d)
e)
Mitochondria
Nucleus
Chloroplast
Golgi apparatus
Lysosomes
19) The chromosomes in your body
a)
b)
c)
d)
e)
Exist in 23 pairs
Each contain thousands of genes
Are about 40% DNA and 60% protein
Exist is 46 pairs
All of the above
20) A diploid cell is one that
a)
b)
c)
d)
e)
Has two homologues off each other
Is design by the symbol 2n
Has chromosomes found in pairs
Has 46 chromosomes
All of the above
21) The diploid number of chromosomes in a human skin cell
is 46. The number of chromosomes found in a human ovum is
a)
b)
c)
d)
e)
46
92
22
23
24
22) How many chromosomes are in the body cells of an
organism that has a haploid number of 8?
a) 4
b) 8
c) 12
d) 16
e) 20
46 | L E T - R e v i e w e r – G e n e r a l E d u c a t i o n
23) Binary
a)
b)
c)
d)
e)
fission
Occurs when two cells collide with each other
Produces excess energy
Creates new species
Occurs when two cells split with each other
Is the process by which bacteria reproduce
24) The phase of mitosis that is characterized by the
arrangement of all chromosomes along the equator of the cell
is called
a) Telophase
b) Anaphase
c) Metaphase
d) Prophase
e) G-phase
25) A typical human cell contains 46 chromosomes. After
mitosis and cell division, each of the two new cells formed
from the original cell
a) Gets 23 chromosomes
b) Grows new chromosomes from existing DNA
c) Get a complete set of 46 chromosomes
d) Gets 23 pairs of chromosomes
e) Both c and d
26) As a result of mitosis, each of the two new cells produced
from the original cell during division
a) Receives a few chromosomes from the original cell
b) Receives an exact copy of all the chromosomes
present in the original cell
c) Donates a chromosome to the original cell
d) Receives exactly half the chromosomes from the
original cell
e) None of the above
27) In plant cells, cell division is complete when
a) the chromosomes make exact copies of
themselves.
b) spindle fibers are formed.
c) A new cell wall forms
d) Osmotic pressure is too low
e) None of the above
|LET-Reviewer – General Education
47
28) Amino acids are the building blocks of which
macromolecule?
a)
b)
c)
d)
e)
Carbohydrates
DNA
Lipids
Proteins
None of the above
29) An organism’s genetic information is stored in which type
of macromolecule?
a)
b)
c)
d)
e)
Nucleic Acid
Carbohydrates
Lipids
Proteins
None of the above
30) Which of the following is NOT a function of proteins?
a)
b)
c)
d)
e)
Build tissues such as bone and muscle
Transport molecules such as oxygen
Control the rate of reactions and regulate cell
processes
Store and transmit genetic information
Both B and C
31) Identify the reactants (s) in the chemical reaction
𝐶𝑂2 + 𝐻2 𝑂
𝐻2 C𝑂3.
a)
b)
c)
d)
e)
𝐶𝑂2 , 𝐻2 𝑂 , 𝐻2 C𝑂3.
𝐶𝑂2 , 𝐻2 𝑂
𝐻2 C𝑂3
𝐶𝑂2 only
None of the above
32) In humans, and other multicellular organisms, which
substance is the main energy source?
a) Carbohydrates
b) Fats
c) Nucleic acid
d) Water
e) None of the above
48 | L E T - R e v i e w e r – G e n e r a l E d u c a t i o n
33) How does an enzyme influence a biological reaction?
a) It reduces the speed or rate of the reaction
b) It speeds up the rate of the reaction
c) It does not affect the reaction
d) It changes the products into reactants
e) None of the above
34) A substance that accelerates the rate of a chemical
reaction is called a (an)
a) catalyst
b) lipid
c) molecule
d) element
e) None of the above
35) Enzymes affect reactions in living cells by increasing the
a) products of the reaction
b) rate of product formation
c) pH of the reaction
d) temperature of the reaction
e) None of the above
36) Which
a)
b)
c)
d)
e)
of the following is NOT a carbohydrate?
Chitin
Cellulose
Lactase
Starch
None of the above
37) What is the term used to describe the energy needed to get
a reaction started?
a) Adhesion energy
b) Cohesion energy
c) Activation energy
d) Chemical energy
e) None of the above
38) Which of the following is NOT an example of a protein?
a) Enzyme
b) Haemoglobin
c) Glucose
d) Egg whites
e) None of the above
|LET-Reviewer – General Education
49
39) Which of following statements is true about catalysts
a) Catalysts slow down the rate of chemical reaction
b) All enzymes are catalysts
c) All catalysts are enzymes
d) All catalysts lower the activation energy of a
chemical reaction
e) None of the above
40) Which of following statements is true about catalysts
a) It becomes sugar
b) It is denatured
c) It becomes stronger
d) It speeds up the rate of the reaction
e) None of the above
41) Which term is the monomer for carbohydrates ?
a) monosaccharide
b) disaccharide
c) starch
d) lipids
e) fats
42) Hydrolysis could be correctly described as the
a) heating of a compound to drive off its excess water
and concentrate its volume
b) breaking of a long-chain compound into its
subunits by adding water molecules to its structure
between the subunits
c) linking of two or more molecules by the removal of
one or more water molecule
d) constant removal of hydrogen atoms from the
surface of a carbohydrate
e) none of the above
43.) The formation of large molecules from small repeating
units is accomplished by a(n) ______ reaction.
a)
b)
c)
d)
e)
oxidation
reduction
dehydration
hydrolysis
decarboxylation
50 | L E T - R e v i e w e r – G e n e r a l E d u c a t i o n
44.) A macromolecule is composed of smaller units called:
a)
b)
c)
d)
e)
45.)
polymers
cells
isomers
monomers
isotopes
Which of the following is not a macromolecule?
a)
b)
c)
d)
e)
protein
starch
nucleotide
lipid
DNA
46.) A(n) ____________ is a basic unit of a carbohydrate.
a)
b)
c)
d)
e)
monosaccharide
starch
nucleotide
glycerol
amino acids
47.) Which of the following includes all the others?
a)
b)
c)
d)
e)
48.)
sucrose
glucose
cellulose
glycogen
carbohydrate
Which of the following is not a monosaccharide?
a)
b)
c)
d)
e)
glucose
fructose
deoxyribose
starch
ribose
|LET-Reviewer – General Education
51
49.)ORGANIC COMPOUNDS that are composed of carbon,
hydrogen, and oxygen in a 1:2:1 ratio are called:
a) proteins
b) nucleotides
c) sugars
d) fatty acids
e) nucleic acids
50.) STARCH and CELLULOSE are ALIKE in that both are:
a) composed of covalently bonded glucose molecules
b) found only in animal cells
c) contain sugars bonded together in identical ways
d) contain non-polar, fatty acid side chains
e) made up of sugars that contain carbon, hydrogen,
oxygen, and nitrogen
51.) A CARBOHYDRATE (polysaccharide) that makes PLANT
CELLS and tissues STRUCTURALLY RIGID is:
a)
b)
c)
d)
e)
sucrose
glycogen
starch
cellulose
nucleotides
52.) A carbohydrate (polysaccharide) that is formed by plants
and used later by the plant as a reserve food supply and
made up of only glucose molecules covalently bonded
together is:
a)
b)
c)
d)
e)
cellulose
starch
glycogen
triglycerides
sucrose
53.) In a lipid bilayer ___________ tails point inward and form a
region that excludes water.
a) acidic
b) basic
c) hydrophilic
d) hydrophobic
e) none of these
52 | L E T - R e v i e w e r – G e n e r a l E d u c a t i o n
54.) Lipids
a) serve as food reserves in many organisms
b) include cartilage and chitin
c) include fats that are broken down into three fatty
acid molecules and one glycerol molecule
d) are composed of monosaccharides
e) none of the above
55.) What type of LIPIDS are found in ALL biological
MEMBRANES?
a)
b)
c)
d)
e)
triglycerides
waxes
phospholipids
diglycerides
cholesterol
56.) Amino acids are the building blocks for
a)
b)
c)
d)
e)
proteins
steroids
lipids
nucleic acids
carbohydrates
57.) Of the following functional groups, which one is known as
the AMINO GROUP?
a)
b)
c)
d)
e)
-SH
-COOH
-NH2
-OH
-CHO
58. Nucleotides are the building blocks for
a)
b)
c)
d)
e)
proteins
steroids
lipids
RNA
carbohydrates
|LET-Reviewer – General Education
53
PART VIII
1. The following are features of mitosis EXCEPT ________.
a. Two daughter cells are produced from one parent
cell.
b. It involves only one nuclear division.
c. It has crossing over.
d. Daughter cells contain the same number of
chromosomes as the parent cell.
2. How many chromosomes do daughter cells of mitosis have?
a. 23
b. 36
c. 46
d. 24 pairs
3. The following are members of fibrous root system EXCEPT
__________.
a. Carrot
b. Rice
c. Corn
d. onion
4. Which of the following is not true about meiosis?
a. Daughter cells contain half the number of
chromosomes as the parent cell.
b. Variations do not occur in the daughter cells.
c. Involves two nuclear divisions.
d. Occurs in gamete cells.
5. The exchange of gases in plants is made possible by what
cells?
a. Mesophyll
b. Cuticle
c. Midrib
d. Stomata
6. ___________ covers the blade of a leaf to prevent water loss.
a. Mesophyll
b. Cuticle
c. Midrib
d. Stomata
54 | L E T - R e v i e w e r – G e n e r a l E d u c a t i o n
7. Which of the following protects the plant cells from
damage?
a. Cell membrane
b. Cell wall
c. Cytoplasm
d. protoplasm
8. Which of the following belong to the taproot system?
a. garlic
b. raddish
c. grass
d. sweet potato
9. When two gamete cells meet and form into zygote, how
many pairs of chromosomes does the zygote have?
a. 24
b. 23
c. 22
d. 25
10. How many chromosomes do daughter cells of meiosis
have?
a. 23
b. 24
c. 25
d. 46
|LET-Reviewer – General Education
55
ENGLISH
PART I
1. I saw Lisa at the station when I was going to work this
morning but she ________ me.
a. didn’t see
b. don’t see
c. hasn’t seen
d. didn’t saw
2. My friend __________ for me when I arrived.
a. was waiting
b. has been waiting
c. has waited
d. waited
3. Where’s Jandy? _________ a shower at the moment.
a. He is taking
b. He have
c. He has
d. He has had
4. Linda is from Davao. She ______ there all her life.
a. is living
b. has lived
c. lives
d. lived
5. Martin is English but he lives in France ______ three years.
a. for
b. at
c. during
d. on
6. What _______ next weekend?
a. do you do
b. are you doing
c. will you do
d. will you be doing
7. Henry is studying law _______ the university.
a. at
b. in
c. on
d. of
8. What is the largest river ______ the Philippines?
a. on
b. for
c. in
d. at
56 | L E T - R e v i e w e r – G e n e r a l E d u c a t i o n
9. Is there anything _____ television this evening?
a. in
b. on
c. at
d. of
10. We arrived _____ the hotel after midnight.
a. at
b. in
c. on
d. to
11. ‘Where’s Mike? ‘He’s ______holiday!
a. in
b. on
c. for
d. of
12. Tom hasn’t got up yet. He’s still _____ bed.
a. in
b. on
c. by
d. for
13. Linda is away. She’s been away _____ Monday.
a. since
b. for
c. on
d. In
14. The next meeting is _____ 15 April.
a. of
b. on
c. by
d. with
15. I usually go to work _____ car.
a. by
b. with
c. in
d. on
16. There’s too much sugar ____ my coffee.
a. with
b. in
c. at
d. on
17. Kevin has lived in Baguio ______ six months.
a. by
c. at
b. since
d. for
|LET-Reviewer – General Education
57
18. Were there a lot of people _____ the party?
a. in
b. on
c. at
d. with
19. What are you doing ___ the moment? Are you writing?
a. in
b. at
c. since
d. on
20. I don’t know any of the people ____this photograph.
a. for
b. by
c. in
d. at
21. The train was very slow. It stopped ____ every station.
a. with
b. at
c. in
d. by
22. I like this room. I like the pictures ____the walls.
a. by
b. of
c. in
d. on
23. Did you buy that picture? ‘No, it was given to me ___ a
friend of mine.
a. for
b. by
c. with
d. of
24. I’m going away ____ a few days.
a. since
b. at
c. for
d. on
25. I’ll be back ____ Thursday.
a. by
b. for
c. in
d. on
58 | L E T - R e v i e w e r – G e n e r a l E d u c a t i o n
26. Silvia has gone ____ Italy.
a. for
b. to
c. in
d. by
27. She is ____ Manila at the moment.
a. in
b. to
c. at
d, for
28. Ann left school _____ fifteen.
a. with
b. at
c. in
d. on
29. She got a job ____ a shop.
a. by
b. in
c. with
d. by
30. Who is ___ best player in your team?
a. the
b. an
c. a
d. none of the above
31. Is there ____ bank near here?
a. the
b. an
c. a
d. none of the above
32. I can’t ride ____ horse.
a. the
b. an
c. a
d. none of the above
33. Are you ____ tourist?
a. the
b. an
c. a
d. none of the above
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59
34. Who was ____ first President of ___ United States?
a. the – a
b. a – the
c. the – the
d. a – a
35. I haven’t got ____ watch.
a. the
b. an
c. a
d. none of the above
36. Last year we had ____ wonderful holiday in ____ south.
a. a – the
b. the – a
c. the – the
d. a – a
37. After ___ dinner, we watched ___ television.
a. the – the
b. a – a
c. the – a
d. none of the above
38. My apartment is on ____ second floor.
a. a
b. an
c. the
d. none of the above
39. Turn left at ____ top of ___ stairs, and it’s on __ right.
a. the – the – a
b. the – a – a
c. the – the – the
d. none of the above
40. Julia is ___ doctor. Her husband is ___ art teacher.
a. a –an
b. an – the
c. the – the
d. none of the above
41. I like ___ sports. My favorite sport is ____ soccer.
a. a – a
b. an – the
c. the – the
d. none of the above
60 | L E T - R e v i e w e r – G e n e r a l E d u c a t i o n
42. I usually listen to _____ radio while I’m having breakfast.
a. the
b. a
c. an
d. none of the above
43. Everest is ____ highest mountain in _____ world.
a. the –the
b. a – the
c. the – a
d. none of the above
44. Gary was ill ____ last week, so he didn’t go to ____ work.
a. a –a
b. an – the
c. the – the
d. none of the above
45. Kate never writes ____ letters.
a. a
b. an
c. the
d. none of the above
46. I can’t remember ___ names.
a. an
b. all
c. a
d. none of the above
47. Shall I phone the restaurant ___ a table?
a. in reserving
b. for reserve
c. to reserve
d. none of the above
48. I wasn’t feeling very well but the medicine made me ___
better.
a. feel
b. feeling
b. to feel
d. none of the above
49. Would you like ___ for dinner on Saturday?
a. come
b. to come
c. coming
d. to coming
|LET-Reviewer – General Education
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50. Did you use a dictionary ___ the letter?
a. translate
b. for translating
c. to translate
d. for translate
51. I _____ because my shoes were too big for me.
a. fell over
b. fell down
c. fall over
d. hold on
52. The plane ____ late but landed on time
a. took off
b. take off
c. take on
d. take up
53. Sandara was very late because her car _______.
a. break down
b. break up
c. broke down
d. none of the above
54. A man was ___ by a car in the accident.
a. knock down
b. knock over
c. knocked over
d. none of the above
55. Tom ____ smoking five years ago.
a. give up
b. gave up
c. rip up
d. put away
56. If you make mistakes, _______.
a. cross them up
b. cross them down
c. cross them out
d. none of the above
57. Jancee ____ the picture in the trash box last night.
a. throw away
b. threw away
c. thrown away
d. none of the above
62 | L E T - R e v i e w e r – G e n e r a l E d u c a t i o n
58. The water wasn’t clean ___ we didn’t go swimming.
a. so
b. but
c. and
d. Because
59. It’s a nice house ____ it hasn’t got a garden.
a. so
b. because
c. but
d. and
60. My brother is married ____ lives in London.
a. so
b. and
c. or
d. because
61. Jamalul is _____ writing letters.
a. bad in
b. bad at
c. bad on
d. none of the above
62. I’m not _____ sports.
a. interested in
b. interested on
c. interested at
d. none of the above
63. She always goes to work _____ foot.
a. in
b. at
c. by
d. on
64. The car was travelling ___ 50 kilometers an hour when
accident happened.
a. in
b. on
c. at
d. by
65. He is reading a book ____ grammar ___ Vera P Bull.
a. on – by
c. of – by
c. about – by
d. none of the above
|LET-Reviewer – General Education
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66. Trains can travel _____ very high speeds.
a. at
c. in
b. on
d. none of the above
67. Do you know how to put a film ____ this camera?
a. on
b. in
c. at
d. none of the above
68. I was walking _____ the road with my dog.
a. on
b. in
c. at
d. none of the above
69. I’m going to meet Fahad Jandy ____ the station.
a. on
b. in
c. at
d. none of the above
70. What does she usually ____ at the weekend?
a. do
b. does
c. did
d. none of these
71. I don’t understand what do you _______.
a. means
b. mean
c. ment
d. meant
72. Julia wants to go to the concert but she _____ a ticket.
a. haven’t got
b. hasn’t got
c. haven’t get
d. didn’t have
73. It’s a nice house but it _____ a garden.
a. doesn’t has
b. doesn’t had
c. doesn’t have
d. didn’t have
74. Was the weather good when you _____ on holiday?
a. was
b. are
c. were
d. weren’t
64 | L E T - R e v i e w e r – G e n e r a l E d u c a t i o n
75. Andrea came into the room, took off her coat and ______.
a. sit down
c. sat down
b. seat down
d. sats down
76. Nathaniel Adrian has been studying medicine at the
University ____three years now.
a. since
b. within
c. in
d. for
77. In what way ____ the heroes of Philippine Epics similar to
the oldest epic, Beowulf?
a. is
b. was
c. were
d. are
78. The school’s auditorium can ____ seven hundred heads.
a. held
b. hold
c. holded
d. none of these
79. The Germans practice truth, frankness and straight
dealing but loyalty ___ their greatest virtue.
a. was
b. is
c. were
d. are
80. The business solution company of the Ayalas ___ the
leading company in the industry.
a. is
b. was
c. are
d. were
81. The landlord of these apartments ____ my best friend.
a. were
b. has
c. are
d. is
82. The guy carrying the goods ____ tired.
a. look
b. looks
c. looking
d. is looking
|LET-Reviewer – General Education
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83. One of those methods ____ the best to answer the problem
that we have.
a. were
b. was
c. is
d. are
84. The second batch of applicants ___ now on their way to the
manager’s office.
a. are
b. is
c. was
d. has
85. The University of the Philippines, as well as the UST and
ADMU_____ to top 100 Universities in Asia.
a. is
b. belong
c. belongs
d. Belonged
86. The mountaineering group, together with the medical
group, ____ on top of the mountain now.
a. are
b. was
c. is
d. were
87. The President, together with his secretaries`, ___ on
holiday.
a. are
b. were
c. is
d. was
88. The Chairman if the committee, as well as the members,
______ on his way to Hong Kong.
a. is
b. have been
c. were
d. are
89. Some of the residents in the village ____ not in favor of the
law.
a. was
b. is
c. am
d. are
66 | L E T - R e v i e w e r – G e n e r a l E d u c a t i o n
90. Somebody in one of the rooms ___ screaming.
a. is
b. are
c. am
d. were
91. The main store, as well as the branches, ______ at 9:30 am.
a. opened
b. open
c. opens
d. opening
92. Nobody ____ interested in my proposal.
a. seems
b. seem
c. seemed
d. seeming
93. The jeepney, as well as the tricycles, ___ a genuine Filipino
invention.
a. is
b. are
c. were
d. was
94. The producer and director ____ an alumnus of the
University of Southeastern Philippines.
a. are
b. is
c. was
d. were
95. The producer and the director ____ alumni of the
University of Southern Mindanao.
a. has
b. is
c. are
d. was
96. Either Peter or his children ____ going on holiday.
a. is
b. has
c. have
d. are
97. Either the cabinet secretaries or the Head of State ____
going to attend the meeting.
a. are
b. have
c. has
d. is
|LET-Reviewer – General Education
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98. The theory of equation professor and academic contest
coach ______Engr. Charito Labao.
a. is
b. are
c. has
d. have
99. Either the wife or the husband ____ managing the family
business.
a. is
b. have
c. were
d. are
100. Neither the President nor the Senators ____ having a
meeting right now.
a. has
b. is
c. are
d. do
101. Either the members or the manager of the El Nido group
___ a problem.
a. has
b. are
c. have
d. were
102. Mathematics ___ been the most hated subject by most
students.
a. have
b. are
c. is
d. has
103. Three hundred thousand pesos ____ enough to open a
grocery store.
a. has
b. is
c. have
d. are
104. The five hundred peso bills ____ being faked by big-time
syndicates.
a. was
b. have
c. are
d. seen
68 | L E T - R e v i e w e r – G e n e r a l E d u c a t i o n
105. Many of the young boys ____ older than me.
a. looking
b. look
c. see
d. seen
106. A number of survivors ____ been brought to hospital.
a. has
b. have
c. will
d. have been
107. Ten years ___ a very long time to wait.
a. is
b. are
c. has
d. have been
108. Seventy kilometers ____ a very long distance to travel.
a. have
b. has
c. are
d. is
109. The number of retirees ____ claiming their benefits at the
GSIS.
a. are
b. is
c. has
d. have been
110. Two hundred miles ___ the distance between the two
cities.
a. is
b. are
c. has
d. were
111. One-half of the cake ___ been eaten by Janise.
a. has
b. have
c. are
d. is
112. Two-thirds of the men ___ being affected by the pandemic
a. has
b. have
c. is
d. are
|LET-Reviewer – General Education
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113. Seventy percent of the cooking oil ___ placed in the
warehouse.
a. are
b. is
c. has
d. have
114. Eighty nine percent of the students ___ Catholics.
a. is
b. was
c. are
d. have been
115. ______ the end of the course all the students have to take
a test.
a. in
b. at
c. on
d. after
116. ______ a photograph of your brother in the newspaper.
a. there is
b. there are
c. there has been
d. none of these
117. ____ a party at the club last Friday but I didn’t go.
a. there was
b. there are
c. there has been
d. none of these
118. When we arrived at the cinema, ____ a long queue to see
the film.
a. there is
b. there were
c. there was
d. none of these
119. I’ll do my packing today because_____ time tomorrow.
a. there will be
b. there will be no
c. there is a
d. there is no
120. ______ ten kilometers from the airport to the city center.
a. It is
b. Its
c. Is it
d. there are
70 | L E T - R e v i e w e r – G e n e r a l E d u c a t i o n
121. Anna Marie isn’t ____ this week.
a. work
b. working
c. to work
d. none of these
122. It ______ rain, so take an umbrella with you.
a. might
b. can
c. could
d. will
PART II
1. Please be quiet. ___________________.
a. I work
b. I working
c. I’m working
d. I’m at work
2. The water looks nice. I’m going _______________.
a. on a swim
b. to swim
c. To swimming
d. swimming
3. I will visit you ___________ summer.
a. At
b. On
c. In
d. with
4. Ceppee _______________ a shower every day.
a. Takes
b. Taking
c. Take
d. Is taking
5. I’m going ______________.
a. To shop
b. Shopping
c. At shopping
d. In shopping
6. Our Christmas vacation starts ________ December 13.
a. Of
b. On
c. In
d. at
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7. Maria isn’t feeling well. She __________ a headache.
a. Have got
b. Had
c. Have
d. has got
8. Gregorio is studying math _____ college.
a. On
b. At
c. In
d. for
9. My brother _____________ traveled by plane.
a. Has never
b. Have never
c. Has never been
d. Have never been
10. I bought _______ jacket and ______ shirt. I like _____ jacket
so much!
a. The, the, a
b. A, the. The
c. A, a, the
d. The, the, the
11. James has gone _____ Italy. She’s __________ Milan right
now.
a. In , at
b. On, at
c. To, at
d. To, in
12. “Is there _____ bank near here?” “Yes, at _____ end of this
block.”
a. The, an
b. A, an
c. The, the
d. A, the
13. His birthday is ___________ January.
a. In
b. On
c. At
d. until
14. she has been waiting __________ ten minutes.
a. For
b. since
c. by
d. of
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15. They traveled across the Philippines _________ bus.
a. Through
b. By
c. On
d. with
16. ____________________ late tonight, don’t wait for me.
a. If I’ll be
b. If I am going
c. When I’m
d. When I’ll be
17. She has been there _______ 1999.
a. Since
b. In
c. For
d. at
18. She is interested in the news. She _______________________.
a.
b.
c.
d.
Reads every day a newspaper
Reads a newspaper every day
Every day reads a newspaper
Is reading every day
19. Earl Christian quit school __________ sixteen and got a job
_________ a bookstore.
a. In, at
b. By, at
c. At, in
d. For, on
20. The next conference is ________ January 10.
a. At
b. On
c. In
d. For
PART III
1. My best friend lives _________ Boretz Road.
a. on
c. at
b. in
d. by
2. Both drill captains ________ with the band.
a. practices
c. is practiced
b. practice
d. are practiced
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3. One-fourth of the cake ______ not enough for him.
a. is
c. has
b. are
d. have
4. One-fourth of the cakes ______ not enough for him.
a. is
c. has
b. are
d. have
5. Two-thirds of the chicken _______ eaten.
a. is
c. were
b. are
d. have
6. Two-thirds of the chickens _______ eaten.
a. is
c. was
b. are
d. has
7. Seventy years ________ a very long time to wait.
a. is
c. were
b. are
d. have
8. Sixty Kilometers ________ a long ride.
a. is
c. were
b. are
d. have
9. Ten thousand pesos _______ not enough to pay the bills.
a. is
c. were
b. are
d. have
10. Twenty 500-peso bills ___________ gone.
a. is
c. has
b. are
d. was
11. Since he met his new girlfriend, Juan never seems to be
_____ home.
a. on
c. at
b. in
d. inside
12. The child responded to his mother's demands _______
throwing a tantrum.
a. with
c. at
b. for
d. by
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13. I think she spent the entire afternoon ______ the phone.
a. at
c. in
b. on
d. with
14. My fingers were injured so my sister had to write the note
______ me.
a. for
c. with
b. to
d. of
15. The police caught the thief _______ the corner of Cascade
and Plum Streets.
a. on
c. in
b. at
d. from
16. It's been snowing _______ Christmas morning.
a. for
c. for
b. since
d. until
17. What are the main ingredients _______ this casserole?
a. about
c. of
b. to
d. with
18. My best friend, John, is named _______ his greatgrandfather.
a. about
c. after
b. for
d. to
19. Grandpa stayed up ______ two in the morning.
a. in
c. For
b. of
d. Until
20. Most of the work _______ to be completed this month.
a. need
c. needs
b. needing
d. is needed
21. Neither Ben nor his sisters _______ at school yesterday.
a. was
c. am
b. were
d. be
22. The director and producer ______ the best.
a. is
c. were
b. are
d. has
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23. The director and the producer ______ the best.
a. is
c. was
b. are
d. has
24. Gold, as well as platinum, ____________ recently risen in
price.
a. is
c. have
b. has
d. are
25. The boss, as well as his colleagues, ____________ been
robbed by the robber.
a. have
c. has or have
b. has
d. none of the above
26. One of the most intelligent students who ____________ full
marks ________ (be) John.
a. score – is
c. score – are
b. scores – is
d. scores - are
27. The Internationl Club, as well as the Choral Society and
the Rowing Club, ________ to submit a new constitution.
a. need
c. has needing
b. needs
d. has need
28. The milk ________ gone bad. Six gallons of milk ______ still
in the refrigerator
a. has – is
c. has – are
b. have – was
d. have - was
29. The large number of votes still _________ straight-party
lines.
a. vote
c. has votes
b. votes
d. had votes
30. To an outsider, the economics of the country _________ to
be in disarray.
a. seem
c. has seems
b. seems
d. have seems
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PART IV
1. My brother and I _______ good swimmers.
a. am
b. are
c. is
d. was
2. The weather is nice today. __________ warm and sunny.
a. Its
b. It’s
c. They’re
d. They are
3. Dante ____________ a book when the phone rang.
a. am reading
b. was reading
c. were reading
d. have read
4. I am tired. I ____________ to go home.
a. am wanting
b. had wanted
c. want
d. has wanted
5. It _____________ when we went out.
a. is raining
b. was raining
c. has rained
d. rained
6. James ________ asleep while he __________ .
a. fall – was reading c. fell – was reading
b. fell – is reading
d. is falling – was reading
7. I _____________ a lot of books, but I don’t read much these
days.
a. use to read
b. had used to read
c. have used to read
d. used to read
8. Jane and Mike _________ married for ten years.
a. are
b. has been
c. have been
d. were
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9. I know Mary. I _________ her for a long time.
a. knew
c. has known
b. know
d. have known
10. Reynaldo has been in Canada ______ six months.
a. by
b. since
c. for
d. at
11. I’ve lived in North Cotabato _______ I was 10.
a. since
b. for
c. at
d. on
12. I don’t think it _________ this afternoon.
a. rains
b. will rain
c. will be raining
d. is going to rain
13. I think Paul __________ the LET exam.
a. passes
b. will be passing
c. will pass
d. is passing
14. When I was young, I ________ very fast.
a. can run
b. could run
c. can ran
d. could ran
15. “I’m happy.” “I’m happy _________.”
a. either
b. also
c. too
d. more
16. “I can’t cook.” “I can’t cook ________.”
a. either
b. also
c. too
d. more
17. _________ kind of music do you like?
a. Which
b. What
c. Which or What
d. None of the above
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18. _________ is the capital of the Philippines?
a. Which
b. What
c. Which or What
d. None of the above
19. Sonia suggested _________ to the movies.
a. to go
b. going
c. to be going to
d. to have gone to
20. I prefer ________ by car.
a. going
b. go
c. to be gone
d. to have gone
21. Are you going ______________ this afternoon?
a. to shop
b. on shopping
c. shopping
d. for shopping
22. They went _________________.
a. fishing
b. to fish
c. on fishing
d. for fishing
23. Tanya ___________ coffee for us.
a. is doing
b. is making
c. have made
d. does
24. Somebody asked “________ book is this?”
a. who’s
b. whom
c. whos’
d. whose
25. I would like to get ____________ about hotels in Cebu?
a. some informations c. any information
b. any informations d. some information
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PART V
1. Our human resources department will help you acclimate to
the San Francisco area __________ your arrival there.
(A) when
(B) while
(C) upon
(D) if
2. For being the top ________ real estate saleswoman of the
quarter, Susan Miller received the accolades of her manager
(A) produce
(B) production
(C) produced
(D) producing
3. Your accommodations at the Pan-Pacific Hotel in Vancouver
__________ been confirmed for two nights.
(A) having
(B) has
(C) have
(D) have to
4. President Smith's ________ assistant will accompany her on
her trip to New York this week.
(A) executing
(B) executive
(C) execution
(D) executable
5. ________ John accomplished little as production
supervisor,he was fired.
(A) Even though
(B) In spite of
(C) While
(D) Because
6. It was quite an accomplishment to turn the company
around in such ________.
(A) time a short
(B) short, a time
(C) time a short
(D) a short time
7. Talks have broken off because the two companies have been
unable ________ an accord.
(A) to reach
(B) reaching
(C) reach
(D) they reached
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8. According to our records, your checking account is $123.00
________ as of this morning.
(A) overdrawn
(B) overdrawing
(C) was overdrawn
(D) to overdraw
9. You ________ an accountant calculate your taxes and
complete your return.
(A) should let
(B) can
(C) could have been
(D) might need
10. Should you decide to take our money market ________
account, interest will accrue at a rate of 4.5% per year.
(A) to check
(B) check
(C) checking
(D) checked
11. She has yet to achieve her goal ________ the company on
sound financial footing.
(A) by putting
(B) with putting
(C) of putting
(D) on putting
12. William's ________ of accomplishment within the company
is only exceeded by his record of service to the community.
(A) record
(B) recorded
(C) recording
(D) records
13. Pacific Gas and Electric refused to acknowledge receiving
our letter ________ complaint.
(A) by
(B) of
(C) in
(D) to
14. Mr. Young is a business acquaintance whom I met at our
annual convention ________ year.
(A) past
(B) passed
(C) prior
(D) last
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15. Dutch Telecom is reportedly seeking to acquire
VoiceStream Technologies for ________ fifty billion dollars.
(A) some
(B) any
(C) much
(D) many
16. AOL's acquisition of Time Warner was accomplished
mainly as a result of selling shares in ________ company.
(A) their
(B) it's
(C) its
(D) they're a
17. As of Mr. Jones' ________ from the company, Janet Jackson
has been appointed acting head of the Trust Division.
(A) dismissive
(B) dismiss
(C) dismissal
(D) dismissed
18. You may activate your credit card by calling 1-800-8880002 at any ________ 24 hours a day.
(A) timing
(B) times
(C) time
(D) timer
19. According to actuarial calculations, the average male born
in the United States has a life ________ of 74 years.
(A) expectation
(B) expectancy
(C) expecting
(D) expect
20. To become the CEO of a corporation, one must ________
extraordinary business acumen and aggressive leadership
skills.
(A) possess
(B) possessed
(C) have possessing
(D) have been possessed
21. We cannot count on ________ changing their negotiating
position because their response to our latest offer was
adamant.
(A) they are
(B) them
(C) their
(D) that they
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22. The addendum to the agreement has yet to be formulated
but ________ crucial points which must be worded carefully.
(A) include
(B) includes
(C) including
(D) its including
23. Please note that the address which is listed on our
business card has been changed ________ 512 Valencia
Avenue.
(A) in
(B) on
(C) by
(D) to
24. I would like to send this letter by ________ return receipt so
that the addressee will have to sign for it.
(A) certify
(B) certification
(C) certifiable
(D) certified
25. ________ our program this afternoon, the meeting will be
adjourned promptly at 5:00 p.m.
(A) In accordance by
(B) To accord with
(C) According to
(D) Accord in
26. The adjuster will be out to review your insurance claim and
inspect the damage to your car at 10 a.m. ________ Monday.
(A) at
(B) on
(C) in
(D) by
27. If there is any problem with the administration of these
tests, it should be reported immediately to the ________
authority.
(A) supervising
(B) supervise
(C) to supervise
(D) supervision
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28. We need to find a new administrator for the Human
Resources Department ________ has experience in all sectors of
our corporation.
(A) who
(B) whom
(C) which
(D) in whom
29. With this credit card, you may ________ an advance of up
to $5000 at any of our branch locations.
(A) obtain
(B) to obtain
(C) obtaining
(D) be obtained
30. ________ adverse business conditions, the corporation has
decided to postpone its hiring of new employees.
(A) Because
(B) Even though
(C) Nonetheless
(D) Due to
31. The advertisement is for a ________ writer who is fluent in
both English and Chinese.
(A) technique
(B) technical
(C) technician
(D) technological
32. Because the advertising budget is so small this year,
breakthroughs ________ new international markets will be
minimal.
(A) on
(B) into
(C) at
(D) during
33. Following the advice of her broker, Mrs. Tang ________ to
diversify her investments into stocks and bonds.
(A) deciding
(B) decides
(C) has decided
(D) has been decided
34. As an Amazon business affiliate, ________ company
receives the benefit of the Amazon logo on its homepage.
(A) a
(B) these
(C) which
(D) that the
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35. We are able to state categorically that our ________ to your
proposal is affirmative.
(A) respond
(B) responsive
(C) responsively
(D) response
36. Please affix your signature on the line above the ________
"President of the Company."
(A) describe
(B) description
(C) descriptive
(D) descriptively
37. The company cannot afford to ignore the volatility of
________ Nasdaq stock market.
(A) a
(B) an
(C) the
(D) these
38. The marketing agency has proposed a three year campaign
________ focuses on television, radio, and internet advertising.
(A) it
(B) what
(C) in which
(D) that
39. For her role in ________ the property, the real estate agent
received a ten percent commission.
(A) sell
(C) selling
(B) sales
(D) sold
40. It is only through an aggressive ________ strategy that the
new company can hope to make a dent in the market.
(A) marketers
(B) to market
(C) marketing
(D) marketed
41. The final agreement is set ________ signed on Friday at the
law offices of Ernst, Rabin and Stravinsky.
(A) to be
(B) being
(C) have been
(D) been
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42. ________ continued allegations of money laundering, the
banks of the Grand Cayman Islands have opened their books
to auditors.
(A) Even though
(C) However
(B) Despite of
(D) Because of
43. R.J. Reynolds, formerly a tobacco company, has formed
alliances with ________ food producing companies in an effort
to diversify.
(A) vary
(B) various
(C) variety
(D) variant
44. Allies in the fight ________ AT & T, Sprint and Vonage have
attempted to broaden their market share.
(A) to
(B) on
(C) during
(D) against
45. Cutbacks in funding mean ________ allocation for the
development end of our organization will fall short of
expectations.
(A) what
(B) which
(C) that
(D) while
46. The allotment for personnel clothing is not limited to
clothes ________ on site.
(A) worn
(B) wearing
(C) are worn
(D) which worn
47. The university travel allowance covers all lodging, food, and
transportation expenses incurred by the university ________.
(A) represent
(B) to represent
(C) representation
(D) representative
48. Once the contract has been signed, it cannot be altered
________ by mutual agreement of the signing parties.
(A) except
(B) however
(C) without
(D) nonetheless
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49. Minister Smith's inability ________ the economic summit
means that an alternate representative must be selected.
(A) attend
(B) attending
(C) and attending
(D) to attend
50. In case our primary plan fails to succeed, we need to have
an alternative plan ________.
(A) at place
(B) in place
(C) on place
(D) by place
51. Last year's ________ alumni fundraising drive raised over
100 million dollars for university research projects.
(A) annual
(B) annually
(C) annum
(D) annuity
52. As we look to put together this new company, we are
seeking an amalgamation of ideas ________ incorporates
different approaches.
(A) in which
(B) by which
(C) through which
(D) which
53. Because of the firm's amateurish approach to the project,
the corporation decided to terminate its ________.
(A) relation
(B) relative
(C) relatively
(D) relationship
54. Maintaining a ________ economic ambassador to handle
crises is an important element of any government.
(A) rove
(B) rover
(C) roved
(D) roving
55. We regret ________ we are unable to sign the contract
because of critical ambiguities in the fifth and sixth clauses.
(A) that
(B) what
(C) which
(D) who
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56. Creating desalinization projects to water the entire north
African region is an ambitious project _____ millions of dollars.
(A) involve
(B) involved
(C) involving
(D) involvement
57. Because Mr. Yang remains ambivalent about the position
he has been offered, we are recommending ________ the offer.
(A) withdraw
(B) withdrawal
(C) withdrawn
(D) withdrawing
58. We went to the meeting anticipating the usual agenda,
_____ expecting to be ambushed on our activities of last week.
(A) no
(B) none
(C) not
(D) nothing
59. President Al-Khabar has expressed that he is ________ to
the merger of the two companies.
(A) amenity
(B) amenable
(C) amenably
(D) amenability
60. One of the amendments to the contract calls for the two
companies to exchange progress reports on a biannual
________.
(A) base
(B) basic
(C) based
(D) basis
61. _________ the amiable relationship between the two
companies, the management teams decided the time is not yet
ripe for merger.
(A) Despite
(B) Even though
(C) However
(D) Although
62. By amortizing our purchase of computers over the
________, we can write off most of our tax liability.
(A) next years five
(B) five years next
(C) years, next five
(D) next five years
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63. Due to the ________ demand for our new Palm computers,
we will need to have an ample supply on hand.
(A) expectant
(B) expected
(C) expecting
(D) expectorant
64. At the ________ meeting, you will be called on to amplify
your statements concerning the future of the company.
(A) bored
(B) board
(C) boarded
(D) boarding
65. In today's environment of e-commerce, companies ________
anachronistic policies will be left behind.
(A) that pursue
(B) that pursue its
(C) they that pursue
(D) they pursue
66. Because of the similarities between the Coca-Cola and
Pepsi-Cola companies, certain analogies about their
management structure ________.
(A) drawn
(B) drawing
(C) can be drawing
(D) can be drawn
67. Analyzing sales data is an important prerequisite to
ordering ________ goods.
(A) manufacture
(B) manufacturer
(C) manufactured
(D) manufacturing
68. The supervisor's analysis of the problem in interdepartmental communication was ________.
(A) highly accurate
(B) high accuracy
(C) accurate of highness
(D) an accurate height
69. The duty of a financial analyst is to scrutinize money
income and outflow ________ a company more efficient.
(A) orders making
(B) in order to make
(C) ordered making
(D) on order made
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70. Ancillary responsibilities of your new job are listed in the
employee handbook ________ been given.
(A) what you have
(B) why you have
(C) when you have
(D) you have
71. During the vice-chairwoman's ________, she gave many
anecdotes about her years in the business.
(A) speak
(B) speech
(C) speaking
(D) spoken
72. Corporations can not merely rely ________ anecdotal
information but must also pursue meticulous research.
(A) in
(B) about
(C) on
(D) among
73. We should look at the problem from all possible angles
________of environmental impact.
(A) despite that
(B) that
(C) in that
(D) including that
74. It is fair to say ________ such an increase in sales has never
occurred in the annals of our company.
(A) when
(B) that
(C) which
(D) although
75. Thus far, all attempts by the city to annex the land
adjacent to ours have ________ futile.
(A) proof
(B) proving
(C) proved
(D) been proved
76. On the fifth anniversary of your ________, your vacation
time will be doubled from five to ten days a year.
(A) employ
(B) employable
(C) employee
(D) employment
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77. We are happy to announce the ________ of this month's
Employee of the Month Awards.
(A) champions
(B) winners
(C) victors
(D) receptors
78. IBM's announcement of impending layoffs _________ with
surprise and dismay.
(A) was met
(B) was meeting
(C) meet
(D) has being met
79. The annual report clearly shows the areas of difficulty
________ we have experienced this year.
(A) in spite of
(B) in that
(C) where
(D) which
80. ________ being able to buy stock, employees receive an
annual annuity based on yearly sales.
(A) Coupled
(B) As well
(C) Alike
(D) In addition to
81. ________ a shift in market prices, both sides decided to
annul the agreement before it went into effect.
(A) Whereas
(B) Because of
(C) Because
(D) Even though
82. We appreciate your ________ of our offer and eagerly await
your answer.
(A) consider
(B) considerable
(C) consideration
(D) considerability
83. There is no antecedent which _________ predict yesterday's
stock market crash.
(A) could have helped (C) could helped
(B) could be helped
(D) helped
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84. I have been asked to request that you wait in the anteroom
________ the president can see you.
(A) without
(B) until
(C) nevertheless
(D) however
85. Anticipating the creation of a new IPO, the Nasdaq traders
raced ________ around the floor of the stock exchange.
(A) exciting
(B) was excited
(C) excitement
(D) excitedly
86. Given the hype for Donna Faran's new line of summer
wear, the actual _________ was an anticlimax.
(A) present
(B) presenting
(C) presentment
(D) presentation
87. The fall in interest rates is a much ________ antidote to the
rapid decrease in stock prices.
(A) need
(B) needy
(C) needing
(D) needed
88. Suffering from an antiquated investment strategy which
failed to take technological stocks into ________, the Berkshire
group made only modest gains in its portfolio.
(A) accountant
(C) account
(B) accountable
(D) accounting
89. In bringing antitrust action against Microsoft, the
U.S.government sought ________ the company up into two
separate companies.
(A) break
(C) to break
(B) broke
(D) breakage
90. Because the season is scheduled to start in two days, the
umpires are extremely anxious about the outcome ________ the
talks with management.
(A) in
(B) on
(C) of
(D) about
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91. Despite the increasing number of bank failures and
personal bankruptcies during the 1920s, the vast majority of
the public remained apathetic to signs of ________ difficulties.
(A) economy
(B) economical
(C) economic
(D) economics
92. ________ her new assignments with aplomb, Evelyn rapidly
advanced through the company hierarchy.
(A) Handle
(B) Handled
(C) Handles
(D) Handling
93. The Board feels that due to the food poisoning incident, an
apology ________ for and will be made.
(A) calls
(B) is calling
(C) called
(D) is called
94. The caterer's ________ of religiously forbidden food at the
OPEC buffet displayed an appalling lack of cultural sensitivity.
(A) use
(B) useful
(C) usefulness
(D) uselessness
95. ________ customers continually trip over the first step of
the escalator, the apparatus that warns them of this danger
needs to be redesigned.
(A) Because
(B) Because of
(C) Even though
(D) Although
96. Her casual apparel at the business meeting was so
inappropriate that she ________ to leave the room to change.
(A) forces
(B) forcing
(C) is forcing
(D) was forced
97. We apologize ________ the apparent misunderstanding
concerning your room reservation.
(A) to
(B) for
(C) in
(D) from
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98. ________ as no surprise when Microsoft decided to appeal
the decision of the federal judge.
(A) There came
(B) It came
(C) While it came
(D) During it came
99. His appearance ________ the board of directors meeting
was dramatic and insightful.
(A) into
(B) through
(C) at
(D) for
100. The chairwoman has requested that the following items
________ appended to the tentative agreement.
(A) be
(B) being
(C) been
(D) have been
101. You may find the appendix ________ the report on page
234, just after the conclusion.
(A) at
(B) on
(C) during
(D) to
102. Because of the ________ value of the company, the recent
actions of the board were applauded at the annual
stockholders' meeting.
(A) increase
(B) increased
(C) it increased the
(D) increasing by the
103. No electrical appliances ________ in the lavatories at any
time during the flight.
(A) used
(B) may use
(C) may be using
(D) may be used
104. Mr. Sung does not believe that the solution ________
proposed is applicable to our current dilemma.
(A) that has
(B) that have
(C) that
(D) that you have
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105. All applicants __________ the job must have a graduate
degree, three years of professional work experience, and five
recommendations.
(A) for
(B) in
(C) on
(D) at
106. We thank you for your application, but feel that your
talents may best lie ________.
(A) somewhere
(B) elsewhere
(C) anywhere
(D) everywhere
107. Teletext Corporation is an equal opportunity employer
and all interested people are _________ to apply.
(A) encouraging
(B) encouraged
(C) being encouraging
(D) having been encouraged
108. Ms. Sanders' appointment to the position was widely
expected based on her ________ qualifications.
(A) imminent
(B) eminent
(C) preimminent
(D) imitative
109. In spite of the fact that the project _________ millions of
dollars with no visible result, the foundation has agreed to
apportion additional funds for the project.
(A) has already consuming
(B) has already been consumed
(C) has already being consumed
(D) was already consumed
110. Before the house can be sold, it must be appraised to
determine its market _________.
(A) value
(B) valuable
(C) valuability
(D) invaluable
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111. We appreciate the response of our readers to this survey
and will try to implement as many suggestions _________.
(A) if possible
(B) if possibility
(C) as possible as
(D) as possible
112. Jack ________ an apprenticeship as an automobile
mechanic at the Folsom Toyota dealership.
(A) is served
(B) is serving
(C) serving
(D) serve
113. President Jackson has asked ________ immediately
apprised of any changes in the current situation.
(A) be
(B) to have been
(C) to be
(D) to being
114. The company's marketing approach needs to be revamped
in order to keep in touch with today's buying ________.
(A) public
(B) publican
(C) publicity
(D) publisher
115. The Office of Research and Development has received a
budget appropriation of 50 million dollars for ________.
(A) the fiscal current year
(B) fiscal, the current year
(C) fiscal current, the year
(D) the current fiscal year
116. Final approval may not _________ in the foreseeable future
due to the unsettled economic situation.
(A) forthcome
(C) be forthcoming
(B) being forthcoming (D) have been forthcoming
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117. Approximately ten percent of the ________ is unemployed
at any given time.
(A) force work French
(B) work French force
(C) French force work
(D) French work force
118. The banker's _________ were not very apropos in light of
recent developments in the banking system.
(A) commendable
(B) commentary
(C) comments
(D) commensurate
119. Ms. Gonsalves' aptitude for the job is obvious ________ of
her coworkers and supervisors.
(A) for all
(B) in all
(C) to all
(D) at all
120. The union ________ an independent arbiter be chosen to
settle the strike against management.
(A) that has asked
(B) has what asked
(C) has asked that
(D) which has asked that
121. ________ in arbitrage, Jackson Lyman is widely sought
after by most Wall Street firms.
(A) Specializing
(B) To specialize
(C) His specialty
(D) Special
122. Both management and labor ________ to submit to
binding arbitration to bring their problems to an end.
(A) agrees
(B) have agreed
(C) have been agreed
(D) is agreed
123. Taking over a company ________ lost over a million dollars
in each of the last five years is an arduous task.
(A) who have
(B) that it has
(C) which has
(D) it has
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124. In the arena of internet bookstores, ________ has achieved
the success of Amazon.
(A) none is the entity
(B) there is no entity
(C) no entity that
(D) no entity
125. With no _________ in her personal job security, Melissa
dramatically criticized her supervisor in the company meeting.
(A) interest
(B) interested
(C) interesting
(D) interestingly
126. Mrs. Jones’ argument _________ of the proposal was welltaken and changed many minds.
(A) in favor for
(B) in favor of
(C) at favor for
(D) by favor in
127. If any problems _________, please do not hesitate to
contact me at 530-753-0557.
(A) arising
(C) should arise
(B) should have arisen (D) arose
128. This is _________ of one arm of the company having no
idea what the other arm is doing.
(A) a case classic
(B) classic a case
(C) a classic case
(D) case, a classic
129. My secretary has arranged a meeting _______ the situation
this afternoon at 4:00.
(A) discussion
(B) discussing
(C) to discuss
(D) will be discussed
130. We believe ________ our new office arrangement better
facilitates communication between management and workers.
(A) what
(B) that
(C) that when
(D) in that
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131. Intel's vast array of computer chips ________ its way into
the majority of the world's computers.
(A) has found
(B) have found
(C) have been finding
(D) having been found
132. Because your account is more than six months ________,
it has been referred to collection.
(A) on arrears
(B) in the rear
(C) in arrears
(D) in a rear
133. Because of weather conditions over Europe, there will be
a two hour delay in the _________ arrival time of Swiss Air
Flight 1590.
(A) schedule
(B) schedules
(C) scheduling
(D) scheduled
134. With so many weapons in our arsenal, we can drag this
case though the courts for ________.
(A) years
(B) yearly
(C) the years
(D) the year
135. The article in the newspaper indicated that the cruise
________ in Seattle during the first week of April.
(A) will begin
(B) will have been begun
(C) beginning
(D) begun
136. Unable to articulate its position clearly, ________ saw
public opinion swing against it.
(A) a company which
(B) the company that
(C) it was the company that
(D) the company
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137. Free market economists deplore the ________ of artificial
trade barriers between nations.
(A) exist
(B) existing
(C) existence
(D) existential
138. By paying his dues, Mr. Washington _________ the
business ladder slowly but surely.
(A) is ascended
(B) was ascended
(C) will have ascended
(D) ascended
139. I am calling on behalf of our Purchasing Department
_________ the status of our order of July 15th.
(A) ascertained
(B) who can ascertain
(C) to ascertain
(D) ascertaining
140. What the final cost will be cannot be known yet, but the
________ price is $225,000.
(A) asked
(B) ask
(C) asks
(D) asking
141. His favorite aspect of the business is forging the
interpersonal connections _________ to increase business
exposure.
(A) necessitate
(B) necessitating
(C) necessary
(D) necessarily
142. Before you begin to assemble this ________, carefully read
the directions given in the owner's manual.
(A) productive
(B) production
(C) product
(D) produces
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143. The assembly decided to recommend an increase in
import duties by ________.
(A) percent of twelve
(B) twelve of a percent
(C) twelth percentage
(D) twelve percent
144. ________ the assent of the Board, we are obliged to
postpone our plans to implement the
strategy.
(A) Without
(B) However
(C) Unless
(D) Nevertheless
145. In her _________ conference, the Chairwoman asserted
her belief that the economy was beginning to expand.
(A) press
(B) pressing
(C) pressure
(D) impression
146. In the wake of the Concorde crash, Air France was forced
to assess ________ requirements for the supersonic aircraft.
(A) to maintain (C) maintained
(B) maintain
(D) maintainance
147. The manager’s assessment of the economic downturn
was disheartening to all _________ present.
(A) who
(B) whose
(C) that
(D) those
148. The county tax assessor has reappraised our parcel, and
_________ our property taxes for the year.
(A) therefore increasing
(B) thereby increased
(C) there he increased
(D) is increased that
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149. Her assets include ________, life insurance policies, and a
large number of municipal bonds.
(A) property estate real
(B) estate real property
(C) estate property real
(D) real estate property
150. Jennifer Wong _________ the responsibility of
reorganizing the files of every corporate client.
(A) assigning
(C) has been assigned
(B) has being assigned (D) who assigned
151. In advance of the impending visit by our _________, your
assignment is to rent a large meeting hall in which we can hold
meetings and buffets.
(A) distribution
(B) distribute
(C) that distribute
(D) distributors
152. With the merger, Oracle will assimilate three computer
start-ups into its ________ structure.
(A) corporate
(B) incorporate
(C) corporation
(D) incorporation
153. In order to assist us in our ongoing efforts to improve
service, this call may be _________ or tape-recorded for future
use.
(A) a monitor
(B) monitoring
(C) monitored
(D) being monitored
154. If you need ________ assistance, a Delta representative
will be waiting in the entry hall as you deplane.
(A) those
(B) each
(C) any
(D) every
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155. The job announcement ________ an assistant curator for
the University of California-Davis Art Museum.
(A) that is for
(B) it is for
(C) who is for
(D) is for
156. Mr. Assaf, a close business associate of mine, will be
________ during the week of
August 10th.
(A) into town
(B) in town
(C) on town
(D) onto town
157. This original play has been brought to you by our
__________.
(A) student graduate association
(B) association student graduate
(C) graduate association student
(D) graduate student association
158. From these x-rays of your lungs, I assume ________ are a
heavy smoker.
(A) that you
(B) whom you
(C) why you
(D) in that you
159. My assumption is _______ transportation will be provided
from the JFK airport to the downtown Hyatt Regency.
(A) when
(B) why
(C) whose
(D) that
160. You have my personal assurance ________ be cancelled,
you will receive an immediate and full refund.
(A) when this cruise should
(B) that should this cruise
(C) since this cruise should
(D) while this cruise should
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161. This traveler's health insurance policy assures you of
treatment at ________.
(A) any emergency room hospital
(B) any hospital emergency room
(C) any room emergency hospital
(D) any hospital room emergency
162. _________ the booming economy, astronomical stock
market gains have been registered in every sector.
(A) When
(B) While
(C) Although
(D) As a result of
163. The Monsanto company attaches ________ significance to
its customer-client relationships.
(A) hard
(B) hardly
(C) great
(D) greatly
164. As an attachment to this email _________ the technical
specifications for the hydraulic pumps under consideration.
(A) please find
(B) please to find
(C) please finding
(D) please found
165. Because of the constantly shrinking job market, college
graduates are finding it ________ difficult to attain a job.
(A) increased and
(B) increase that
(C) increasingly
(D) to increase so
166. All attempts ________ a reservation on any flight to
Hawaii for the Christmas vacation have proved futile.
(A) it obtained
(B) which it obtained
(C) who obtained
(D) to obtain
167. As a stockholder of the Coca-Cola Company, you are
invited to attend the annual stockholder's meeting to be held
________ April 15th.
(A) in Atlanta on
(B) at Atlanta in
(C) at Atlanta during
(D) by Atlanta at
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168. Because of the great importance ________ the President
places on this project, attendance at the meeting is mandatory.
(A) who is
(B) which
(C) that he is
(D) whose
169. You ________ your car with the attendant in the parking
garage who will return it to you upon your return.
(A) may have left
(B) may be leave
(C) may leaving
(D) may leave
170. In today's ________, each company must be attentive to
even the slightest changes.
(A) environment changing quickly business
(B) quickly changing business environment
(C) changing quickly business environment
(D) business environment changing quickly
171. Finally, in this letter of recommendation, I ________ to
attest to the great work ethic which Ms. Abrahamson has
brought to the company.
(A) had better
(B) would rather
(C) would like
(D) had rather
172. Formal attire will be required for all company events
_______ during the conference.
(A) attended
(B) that attend
(C) which are attending
(D) who are being attended
173. Here at Allied Van Lines, we believe ________ the attitude
you bring to your job helps determine whether we can receive
repeat orders from our customers.
(A) that
(B) in that
(C) in whose
(D) in which
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174. Without attorneys _________ possible legal situations,
corporations may find themselves mired in endless court
challenges.
(A) to handle
(B) who are handled
(C) whom they are handling
(D) handling to
175. The combination of wildly interesting graphics ________ of
navigation attracts over a million visitors a day to the site.
(A) but ease
(B) also ease
(C) and ease
(D) though ease
176. One attraction of this potential job is its offer of
unlimited _______ for all employees.
(A) children care
(B) cared for children
(C) caring for children
(D) childcare
177. I believe that business success is _________ to not only
what you do but also how you do it.
(A) an attribute
(B) that attribute
(C) what an attribute
(D) attributable
178. The newspaper article attributed K-Mart's _______ to the
changing demographics of the suburban shopper.
(A) decline
(B) declension
(C) declining
(D) declined
179. Rather than implement immediate layoffs, the company
has decided to reduce its _______ through attrition.
(A) working force
(B) force of work
(C) work force
(D) force work
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180. As usual, the audience was captivated by the speaker's
ideas for a _______ business organization.
(A) to revitalize
(B) revitalization
(C) revitalized
(D) revitalize
181. The annual audit of our financial records will be
conducted _______ accounting firm of
Ernst and Young.
(A) with an
(B) with the
(C) by an
(D) by the
182. In the coming months, Ford intends to augment its
Taurus division with over ________.
(A) lines new ten assembly
(B) assembly new lines ten
(C) ten new assembly lines
(D) new ten lines assembly
183. To reduce expenditures, ________ the department heads
to embark upon a series of austere budget cuts.
(A) the Dean who has asked
(B) the Dean that has been asked
(C) the Dean has asked
(D) has the Dean that asked
184. On this tour, we _______ to view authentic Native
American mounds and talk to the descendants of the people
who made them.
(A) are being able
(B) will be able
(C) being able
(D) be able
185. The author of the company's report on reorganization
recommends _______ least profitable divisions be divested.
(A) that its
(B) their
(C) whose those
(D) what they’re
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186. The Blue Book distributed to all banks and savings and
loan _______ the authoritative book on used car prices.
(A) associations is
(B) associations are
(C) associations that are
(D) association is
187. Lee Iacocca was one of the leading authorities _______ of a
particular business management style.
(A) in the implementation
(B) at the implementation
(C) on the implementation
(D) inside the implementation
188. Because the expenditures were not authorized, you will
be asked to reimburse the company from your ________ funds.
(A) person
(B) personal
(C) personality
(D) personalized
189. The new contract, which was recently signed by
management, calls for all workers to receive an automatic 5%
_______ increase each year.
(A) living costs
(B) living and cost
(C) cost of living
(D) costs for living
190. Not autonomous, _______ of the Disney company's
amusement parks is operated according to the direction of
Walt Disney Corporation headquarters.
(A) All
(B) Every
(C) Some
(D) Each
191. _______ an unforeseen electrical event, the plane has an
auxiliary system that can provide the necessary power.
(A) With the case with
(B) At the case in
(C) On the case of
(D) In case of
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192. The results of your blood test should be available within
________ 48 hours.
(A) approximate
(B) approximation
(C) approximately
(D) approximater
193. The Dow Jones average advanced over 150 points today
on news of increased profits and low ________.
(A) inflationary
(B) inflation
(C) inflated
(D) inflate
194. _______ the pitfalls of other franchise companies, the
Merry Maids cleaning service requires a large franchise fee.
(A) To seek avoiding
(C) Seeking avoidance
(B) To seek avoidance (D) Seeking to avoid
195. The impact of the merger of Daimler Benz and Chrysler
was so awesome that the automobile industry was changed
_______.
(A) as ever
(C) ever
(B) and ever
(D) forever
196. Perhaps the most common axiom in business _______
the customer is always right.
(A) is that
(B) that is
(C) what is
(D) is what
197. Jack Roberts _______ as the company's new CEO because
the former CEO lacked the backbone to make important
decisions.
(A) bring in
(B) is bringing in
(C) brought in
(D) was brought in
198. The decision to replace the original formula of Coca-Cola
backfired causing the company to create _______ of Classic
Coke.
(A) a brand new
(B) a new brand
(C) the brand new
(D) the new brand
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199. With an MBA from Harvard and ________ at Proctor and
Gamble, Sarah McLendon brings the necessary background to
fill the needs of her new job admirably.
(A) experience previous work
(B) previous experience work
(C) experience work previous
(D) previous work experience
200. The supervisor's comment that Jack was performing his
work well _______ his obvious deficiencies was a backhanded
compliment at best.
(A) despite the fact that
(B) even though
(C) in spite of
(D) because
201. With heavy backing _______ governmental subsidies, the
European aircraft company has begun to achieve parity with
Boeing.
(A) in a form with
(C) in the form of
(B) on the form in
(D) on a form that of
202. We regret that due to a large backlog of orders, we will be
unable to process your shipment _______.
(A) without next month
(B) unless next month
(C) regardless of next month
(D) until next month
203. No company that willingly takes a back seat to other
companies in _______ can succeed.
(A) their fields
(B) their field
(C) its fields
(D) its field
204. The results of your medical exams are so baffling that I
have decided to call for _______.
(A) an opinion that is second
(B) a second opinion
(C) of which opinion twice
(D) the opinion twice
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205. Please make sure that you keep your baggage with you at
all times while in the airport as ________.
(A) a secure consideration
(B) a securely considerate
(C) a security consideration
(D) a securable consideration
206. The _______ sheet reveals that our company had an
overall profit of some 24 million dollars last year.
(A) balance
(B) balanced
(C) balancing
(D) imbalanced
207. We have done all _______ to resolve the situation; now the
ball is in their court.
(A) that can do
(B) that we can be done
(C) we can do
(D) we can be done
214. Would you care to have your bank account connected to
your credit card for _______?
(A) overprotecting the draft
(B) protecting over the draft
(C) overprotect the draft
(D) overdraft protection
215. I would like to order a bank draft of $5000 _______ by our
representative this afternoon.
(A) to be picked up
(B) to pick up
(C) pick up
(D) picking up
216. The bank note ________ is due to be paid in 36 months.
(A) in the building
(B) at the building
(C) on the building
(D) around the building
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217. After using up all of their investor's venture capital,
many high-tech startups _______ bankrupt.
(A) have found
(B) have seen
(C) have gone
(D) have recorded
218. We offer 60 x 24 banner _______ on our website at a rate
of $100 per month per character.
(A) advertise
(B) advertisement
(C) advertising
(D) to advertise
219. I am happy to announce that the company awards
banquet will again be held _______ the Sullivan building.
(A) at December 10th at
(B) on December 10th in
(C) in December 10th at
(D) in December 10th inside
220. It is illegal for any restaurant to bar entrance _______
because of the race or gender of its potential customer.
(A) to those premises
(B) to their premises
(C) to its premises
(D) to that premises
221. The company barbecue _______ during the first week in
July and will feature country music, a no-host bar, and plenty
of ribs.
(A) that will take place (C) took place
(B) it will take place
(D) will take place
222. Though it ________ like it at first, the purchase of Daimler
Chrysler for 10 billion dollars was a bargain.
(A) may not seem
(B) may not be seeming
(C) may not have been seen
(D) may not have seen
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223. Penny stocks are ________ they are sold at bargain
basement prices and yield negligible returns.
(A) so named that
(B) named so which
(C) because named so
(D) so named because
224. ________ to continue marketing its tobacco products to
minors exposed it to a barrage of criticism.
(A) The company’s cigarette decision
(B) The decisive company cigarette
(C) The cigarette company’s decision
(D) The decision of the company’s cigarette
225. The price of a barrel of oil depends on such factors as
________ and seasonal vagaries.
(A) demand that is industrial
(B) demands which are industry’s
(C) industry’s demanding
(D) industrial demand
226. Whether to erect protectionist trade barriers is a decision
________ every government seeking to protect native
manufacturers.
(A) that faces
(B) that it faces
(C) it faces
(D) faces
227. While some activities such as knitting clothes and making
cheese lend themselves to a barter system, _______ such as
purchasing airplane ticket do not.
(A) the others are activities
(B) another activities
(C) the other activities
(D) other activities
228. ________ to have been a boon to domestic industries, free
trade agreements have wreaked havoc in developed and
developing countries.
(A) One time thinking (C) Thought at once
(B) It was at one time (D) Once thought
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229. In the United States, most high tech companies have
located their _______ of operations in Silicon Valley, California.
(A) base
(B) basis
(C) basic
(D) baseness
230. In the world of stock rumors, even a baseless allegation
can have a _________ impact on stock prices.
(A) drama
(B) dramatic
(C) dramatize
(D) dramatized
231. According to ________, prices in a free market system
depend on supply and demand.
(A) basic economic theory
(B) economic basic theory
(C) theoretical basic economy
(D) theoretically economy basic
232. The federal judge indicated that the _______ of her
decision was her belief that Microsoft had deliberately tried to
monopolize the market.
(A) base
(B) basic
(C) basis
(D) basically
233. Pegging the value of a currency against a basket of
currencies _______ the deuschmark, yen, and dollar is one way
of establishing its value.
(A) includes
(B) include
(C) including
(D) include those
234. One quality of a business leader is the ability to step up
to bat and make the hard decisions _______ to ensure business
viability.
(A) necessary
(B) necessarily
(C) necessitate
(D) necessitating
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235. The battle lines have long been drawn in the
transatlantic air market as European carriers vie with
American carriers _______.
(A) for market share
(B) in shared market
(C) to share market
(D) on shared markets
236. The Wall Street Journal is often the bearer of significant
business news which affects individuals _______.
(A) alike corporations
(B) and too corporations
(C) and corporations alike
(D) also corporations
237. Because of the bearish economy, _______ brokerage jobs
have been lost on Wall Street.
(A) a hundred of
(B) hundred of
(C) hundreds of
(D) the hundred
238. _______ communistic economic theory can be found in
Karl Marx's Das Kapital.
(A) A bedrock in
(B) The bedrock of
(C) The bedrock on
(D) A bedrock at
239. _______ wildly fluctuates whenever the Federal Reserve
Bank makes pronouncements.
(A) Market behavior that
(C) Market behavior
(B) Marketing behavior
(D) Marketable behavior
240. In the world of cruise lines, Carnival is an economic
behemoth ________ existing passenger liners.
(A) by over a half in all
(B) with over half of all
(C) at over the half of all
(D) in over a half to all
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241. It is believed that Bank of America is behind Nestle's
________ over General Foods.
(A) attempted taking over
(B) to attempt to take over
(C) attempting take over
(D) attempt to take over
242. _______ the world's population will eventually outstrip the
world's supply of food is a central tenet of Malthusian
economics.
(A) The belief is that
(B) Believing when
(C) It is to believe why
(D) The belief that
243. The price of General Electric stock dropped four dollars a
share _______ that quarterly earnings were below expectations.
(A) in reports
(B) at reports
(C) on reports
(D) through reports
244. To start his ________, the President called for various belt
tightening measures.
(A) economic austerity program
(B) austerity economic program
(C) program economic austerity
(D) program austerity economic
245. In an attempt to bend the rules, many passengers try
_______ more than one carry-on onto their airplane.
(A) and take
(B) and took
(C) to take
(D) taking them
246. On Wednesday morning, OPEC set ________ of oil at $27
per barrel.
(A) the benchmark new price
(B) the new benchmark price
(C) the price, new benchmark
(D) the benchmark price, new
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247. One beneficiary of the NAFTA trade agreement was the
Mexican shoe industry _______ has doubled its exports to the
United States.
(A) that it
(B) it
(C) which
(D) whose
248. When looking for a job, the prospective employee must
look at the package of benefits offered by the ________.
(A) employing
(B) employed
(C) employment
(D) employer
249. _______, John Smith bequeathed $50 million dollars to
the Harvard Medical School.
(A) After his dead
(B) On his dying
(C) Upon his death
(D) In his demise
250. Mrs. Ann Richard's generous bequest of 10 acres of
prime real estate land will enable the university to build a new
complex of _______.
(A) housing students
(B) students housing
(C) student housing
(D) housing student
Vocabulary
1. Our human resources department will help you __________
to the San Francisco area upon your arrival there.
(A) acclimate
(B) accommodate
(C) accentuate
(D) accelerate
2. For being the top producing real estate saleswoman of the
quarter, Susan Miller received the ________ of her manager.
(A) anxieties
(B) wishes
(C) dreams
(D) accolades
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3. Your __________ at the Pan-Pacific Hotel in Vancouver have
been confirmed for two nights.
(A) acceptances
(B) actualities
(C) accordance
(D) accommodations
4. President Smith's executive assistant will ________ her on
her trip to New York this week.
(A) acquire
(B) accede
(C) acknowledge
(D) accompany
5. Because John ________ little as production supervisor, he
was fired.
(A) refused
(B) witnessed
(C) accomplished
(D) retaliated
6. It was quite an ________ to turn the company around in
such a short time.
(A) agglomeration
(B) accent
(C) aptitude
(D) accomplishment
7. Talks have broken off because the two companies have been
unable to reach an ________.
(A) acceptance
(B) acquisition
(C) accord
(D) actuality
8. According to our records, your checking ________ is $123.00
overdrawn as of this morning.
(A) accumulation
(B) account
(C) accommodation
(D) acclaim
9. You should let an __________ calculate your taxes and
complete your return.
(A) actor
(B) accountant
(C) adjuster
(D) adjutant
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10. Should you decide to take our money market checking
account, interest will ________ at a rate of 4.5% per year.
(A) accept
(B) account
(C) accord
(D) accrue
11. She has yet to _______ her goal of putting the company on
sound financial footing.
(A) arrange
(B) achieve
(C) acquire
(D) aspire
12. William's record of ________ within the company is only
exceeded by his record of service to the community.
(A) achievement
(B) distress
(C) proportion
(D) repugnance
13. Pacific Gas and Electric refused to ________ receiving our
letter of complaint.
(A) accede
(B) accentuate
(C) acknowledge
(D) accredit
14. Mr. Young is a business ________ whom I met at our
annual convention last year.
(A) acumen
(B) accelerator
(C) acquaintance
(D) acquisition
15. Dutch Telecom is reportedly seeking to ________
VoiceStream Technologies for some fifty billion dollars.
(A) acclaim
(B) acquit
(C) accord
(D) acquire
16. AOL's ________ of Time Warner was accomplished mainly
as a result of selling shares in its company.
(A) accumulation
(B) acquisition
(C) acknowledgement
(D) accrual
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17. As of Mr. Jones' dismissal from the company, Janet
Jackson has been appointed ________ head of the Trust
Division.
(A) acceding
(B) acting
(C) accostive
(D) accomplishing
18. You may ________ your credit card by calling 1-800-8880002 at any time 24 hours a day.
(A) activate
(B) actualize
(C) accompany
(D) acclimate
19. According to ________ calculations, the average male born
in the United States has a life expectancy of 74 years.
(A) acceptance
(B) actuarial
(C) acquisitive
(D) accountable
20. To become the CEO of a corporation, one must possess
extraordinary business ________ and aggressive leadership
skills.
(A) acknowledgement (C) acceleration
(B) acumen
(D) activation
21. We cannot count on their changing their negotiating
position because their response to our latest offer was
________.
(A) tentative
(B) adamant
(C) preliminary
(D) provisional
22. The ________ to the agreement has yet to be formulated but
includes crucial points which must be worded carefully.
(A) adherent
(C) acquaintance
(B) acknowledgement (D) addendum
23. Please note that the ________ which is listed on our
business card has been changed to 512 Valencia Avenue.
(A) accord
(B) advancement
(C) advantage
(D) address
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24. I would like to send this letter by certified return receipt so
that the ________ will have to sign for it.
(A) addressee
(B) addendum
(C) accommodation
(D) accomplishment
25. According to our program this afternoon, the meeting will
be ________ promptly at 5:00 p.m.
(A) accomplished
(B) adjourned
(C) acquired
(D) accrued
26. The ________ will be out to review your insurance claim and
inspect the damage to your car at 10 a.m. on Monday.
(A) accrue
(B) acknowledger
(C) adjuster
(D) adjourner
27. If there is any problem with the ________ of these tests, it
should be reported immediately to the supervising authority.
(A) administration
(B) adhesion
(C) advocacy
(D) addressee
28. We need to find a new ________ for the Human Resources
Department who has experience in all sectors of our
corporation.
(A) accompaniment
(C) adjuster
(B) acknowledgement (D) administrator
29. With this credit card, you may obtain an ________ of up to
$5000 at any of our branch locations.
(A) accumulation
(B) advance
(C) advice
(D) accomplishment
30. Due to ________ business conditions, the corporation has
decided to postpone its hiring of new employees.
(A) admonished
(B) accomplished
(C) adverse
(D) actuarial
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31. The ________ is for a technical writer who is fluent in both
English and Chinese.
(A) acceleration
(B) advertisement
(C) acceptance
(D) accumulation
32. Because the _________ budget is so small this year,
breakthroughs into new international markets will be minimal.
(A) advertising
(B) adjusting
(C) adamant
(D) administration
33. Following the ________ of her broker, Mrs. Tang has
decided to diversify her investments into stocks and bonds.
(A) adjournment
(B) addendum
(C) advice
(D) activation
34. As an Amazon business _________, a company receives the
benefit of the Amazon logo on its homepage.
(A) acknowledgement (C) affiliate
(B) actuary
(D) addressee
35. We are able to state categorically that our response to your
proposal is ________.
(A) actuarial
(B) absolute
(C) affirmative
(D) acting
36. Please ________ your signature on the line above the
description "President of the Company."
(A) affix
(B) afford
(C) affect
(D) accept
37. Generous packages of stock options have created a class of
________ executives.
(A) affected
(B) affluent
(C) accruable
(D) accumulative
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38. The company cannot ________ to ignore the volatility of the
Nasdaq stock market.
(A) afflict
(B) accommodate
(C) acquire
(D) afford
39. The marketing ________ has proposed a three year
campaign that focuses on television, radio, and internet
advertising.
(A) advertisement
(C) agency
(B) acknowledgement (D) aggression
40. For her role in selling the property, the real estate
_________ received a ten percent commission.
(A) assistant
(B) affect
(C) acquisition
(D) agent
41. It is only through an ________ marketing strategy that the
new company can hope to make a dent in the market.
(A) affirmed
(B) administrative
(C) activated
(D) aggressive
42. The final ________ is set to be signed on Friday at the law
offices of Ernst, Rabin and Stravinsky.
(A) actuary
(B) acumen
(C) acquisition
(D) agreement
43. Because of continued ________ of money laundering, the
banks of the Grand Cayman Islands have opened their books
to auditors.
(A) allowances
(B) alliances
(C) alloys
(D) allegations
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44. R.J. Reynolds, formerly a tobacco company, has formed
________ with various food producing companies in an effort to
diversify.
(A) alternates
(B) alliances
(C) alterations
(D) alliterations
45. ________ in the fight against AT & T, Sprint and Vonage
have attempted to broaden their market share.
(A) Allegations
(B) Alternatives
(C) Allies
(D) Acknowledgers
46. Cutbacks in research mean that ________ for the
development end of our organization may exceed expectations.
(A) account
(B) allocation
(C) accord
(D) allowance
47. The ________ for personnel clothing is not limited to clothes
worn on site.
(A) amalgamation
(B) alloy
(C) addressee
(D) allotment
48. The university travel ________ covers all lodging, food, and
transportation expenses incurred by the university
representative.
(A) alleviation
(B) allergy
(C) allowance
(D) allegation
49. Once the contract has been signed, it cannot be ________
except by mutual agreement of the signing parties.
(A) adjourned
(B) altered
(C) aspired
(D) allotted
50. Minister Smith's inability to attend the economic summit
means that an ________ representative must be selected.
(A) alternate
(B) affluent
(C) actual
(D) accordant
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MATHEMATICS
PART I
1. If the first positive even integer is 2x + 6, then find the next
three positive even integers.
a.
b.
c.
d.
2x + 3, 2x + 4, 2x + 5
2x + 6, 2x + 7, 2x + 8
2x + 8, 2x + 10, 2x + 12
2x + 4, 2x + 2, 2x
2. If 4x – 7 is the first odd integer, then find the 7th even
integer after it.
a. 4x – 6
b. 4x – 5
c. 4x + 6
d. 4x + 5
3. If x + y = 17, then find (x + y)² = _________.
a. 289
b. 34
c. 49
d. 389
4. If 3x – 18y = - 21, then x – 6y = ________.
a. 7
b. -7
c. -63
d. 63
5. If (x – y)² = 49, then x² - 2xy + y² = __________.
a. 89
b. 49
c. 13
d. 7
6. If x – 2y = 14, then x² = ____________.
a.
b.
c.
d.
y² + 56y +196
y² + 6y +6
4y² + 6y +16
4y² + 56y +196
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7. If x² - y² = 264 and x - y = 6 then x + y = __________.
a. 32
b. 44
c. 9
d. 81
8. If the first integer is 2x + 1, then find the sum of the next
two.
a. x – 5
b. x + 5
c. 4x + 5
d. 4x - 5
9. The product of the first two of the seven consecutive
positive odd integers is 99. Find the sum of the fifth and the
seventh integers.
a. 76
b. 38
c. 93
d. 8
10. What is the slope of the line perpendicular to 3x + 2y = 6.
a. 2
b. 2/3
c. -3/2
d. -2
11. What is the slope of the line parallel to 2x – 3y = 8.
a. 2/3
b. 3/2
c. -3/2
d. -2
12. The inverse of the function f(x) = 7x + 4 is ___________.
a.
b.
c.
d.
f -1(x) = (y – 4)/7
f-1(x) = (x + 4)/7
f-1(x) = (y + 4)/7
f-1(x) = (x – 4)/7
13. If 3x + 2 is the 6th integer, then the sum of the 9th and the
11th integers is _______________.
a. 6x – 33
b. 6x + 33
c. 6x + 12
d. 6x -23
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14. Find the value of the expression 4a + 2x + d when a = 7,
x = -2 and d = 4.
a. 23
b. 28
c. 56
d. 78
15. If (a + b)² = 64, and ab = 3, then a² + b² = ________________.
a. 76
b. 58
c. 82
d. 13
16. Find the sum of the first 22 positive odd integers.
a. 564
b. 648
c. 253
d. 484
17. Find the sum of the first 100 positive even integers.
a. 10,100
b. 9,550
c. 9,505
d. 10,500
18. Find the sum of the first 50 positive even integers.
a. 3,500
b. 2,550
c. 3,550
d. 2,500
19. Find the sum of all positive even integers between 40 to 60
inclusive.
a. 750
b. 650
c. 450
d. 550
20. Let f(x) = 3x² - 2x + 5 and g(x) = 2x + 1, find (f + g)(-2).
a. 15
b. 16
c. 17
d. 18
21. Let f(x) = 3x² - 5 and g(x) = 2x + 1, find (f • g)(-1).
a. 2
b. 18
c. 11
d. 6`
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22. The sale price of a camera after a 20% discount is 7,200.
What was the price before the discount?
a. 5760
b. 1,440
c. 9,000
d. 8,640
23. Which of the following is a real number?
a. a + bi, b ≠ 0
b. 2 + 0i
c. 2 + 3i
d. 3 + 8i
24. Which of the following is equal to zero?
a. 4 – 4i
b. 0 + 0i
c. 0 – 3i
d. -3 + 3i
25. How many multiples of 20 are there in the first 100
positive even integers inclusive?
a. 10
b. 5
c. 7
d. 9
26. Which of the following is not a pure imaginary number?
a. 0 – 3i
b. 2 + 2i
c. 8 – 11i
d. 1 + 0i
27. Which of the following is not a complex number?
a. 0 – 3i
b. 2 + 2i
c. 8 – 0i
d. 0 + 4i
28. What is 104% of 740?
a. 790.66
b. 769.60
c. 967.90
d. 679.60
29. Express 2,600 in scientific notation.
a. 2.6 x 10²
b. 26 x 10²
c. 2.6 x 10³
d. 0.26 x 10³
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30. Express 0.00387 in standard form.
a. 3.87 x 10²
b. 3.87 x 10
c. 3.87 x 10³
d. 3.87 x 〖10〗^(-3)
31. Express 1.96 x 〖10〗^(-9) in expanded form.
a. 0.00000000196
b. 196,000,000
c. 19,600,000
d. 0.000000196
32. The population of Manila in 2005 was 5.68 million. The
population in 2006 was lower by 325,000. What was the
population in 2006?
a. 5.355 million
b. 5.553 million
c. 3.555 million
d. 5.535 million
33. How many grams are there in 2.03 kilograms?
a. 203 grams
b. 20,300 grams
c. 2,030 grams
d. 200,300 grams
34. Given that 32.6 x 145 = 4,727, find the exact value of
3.26 x 0.145.
a. 4.727
b. 47.27
c. 472.7
d. 0.4727
35. Express 7/20 as percentage.
a. 7%
b. 35%
c. 14%
d. 28%
36. A man earns 15,000 per month. If he receives his 13th
month pay and a bonus equivalent to 150% of his monthly
salary, calculate his total annual salary?
a. 218,000
b. 217,500
c. 217,000
d. 216,500
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37. Given that 22.5 x 225 = 5,062.5, find the exact value of
0.225 x 2.25.
a. 5.0625
b. 50.625
c. 0.50625
d. 0.050625
38. There are 6,000 people in a village. 30% of the people are
men, and 32% are women. What is the total number of
children in the village?
a. 2,280
b. 2,180
c. 2,380
d. 2,820
39. A bike was bought at 3,250 pesos and sold at 20% profit.
What was the cost price of the bike?
a. 3,700
b. 3,800
c. 3,900
d. 4,000
40. A jacket was sold at 550 pesos after a loss of 15%, what
was the cost price of the jacket?
a. 647.50
b. 647.60
c. 647.06
d. 647.40
41. If I paid 225 pesos for an article after a discount of 15%,
then what was the marked price?
a. 264.71
b. 274.73
c. 284.75
d. 294.77
42. A businessman bought a product for 1,600 and sold it at
6% profit. How much did he earn?
a. 94
b. 95
c. 96
d. 97
43. A 650-peso polo shirt was sold at 18% discount plus 5%
sales tax. How much did the customer pay for the product?
a. 559.85
b. 559.25
c. 559.90
d. 559.65
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44. A pair of shoes costs 1,250. How much will the customer
pay if there is a 10% discount to be deducted plus 12% VAT?
a. 1,230
b. 1,240
c. 1,250
d. 1,260
45. A finance company charges 5% annual simple interest on
a car loan of 750,000 pesos for five years. How much interest
is payable?
a. 185,500
b. 186,500
c. 187,500
d. 188,500
PART II
1. If the scores in mathematics test of 61 students are
arranged from the highest to the lowest, the 31st score is the
___________.
a. mode
b. median
c. mean
d. standard deviation
2. The vertex angle of an isosceles triangle is 45 degrees.
What is the measure of one of the base angles?
a. 64.5 degrees
b. 65.5 degrees
c. 66.5 degrees
d. 67.5 degrees
3. What number is next to the sequence 23450, 23850,
24250, 24650.
a. 24850
b. 24950
c. 25050
d. 25150
4. What value of x will make the proportion correct?
12:x = 2.4:5
a. 15
b. 20
c. 25
d.30
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5. There are 70 men in a committee consisting of 120
members. What is the ratio of women to the men?
a. 3:7
b. 4:5
c. 5:6
d. 5:7
6. A letter is picked at random from the English alphabet.
What is the probability that the letter is contained in the word
“great”?
a. 4/26
b. 5/26
c. 5/13
d. 4/13
7. A vehicle consumes 2.5 liters of gasoline to travel 30
kilometers. To the nearest tenth, how many liters of gasoline
will it take for the vehicle to travel 418 kilometers?
a. 31.83L
b. 32.83L
c. 33.83L
d. 34.83L
8. What is the equivalent fraction of the decimal 0.725?
a. 2/29
b 29/40
c 30/40
d. 29/30
9. 24% of 6400 = _____
a 1,236
b. 1,336
c 1,436
d. 1,536
10. What percent of 650 is 13?
a. 1%
b. 2%
c. 3%
d. 4%
11. What number is 70% of 3,400?
a. 2,180
b. 2,280
c. 2,380
d. 2,480
12. What is the equivalent decimal form of 650/900?
a. 11/18
c. 1/19
b. 17/18
d. 13/18
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13. What is the sum of the factors of 24?
a. 60
b. 61
c. 62
d. 63
14. The difference of two numbers is 40. Their sum is 80. Find
the two numbers.
a. 21 and 59
b. 20 and 60
c. 19 and 61
d. 18 and 62
15. What is ½ of the 50% of 250?
a. 62.5
b. 72.5
c. 52.5
d. 82.5
16. What is the product of a number and its reciprocal?
a. 0
b. 1
c. 2
d. 3
17. What number completes the sequence?
320,440,560,______,800
a. 580
b. 600
c. 640
d. 680
18. If a box contains 9 yellow, 5 black, and 14 green balls.
Find the probability of getting green.
a. 0.35
b. 0.14
c. 0.5
d. 0.55
19. Which of the following must be true about the sum of all
the prime numbers between 20 and 30?
a. It is a prime number.
b. It is an odd number.
c. It is a factor of 156
d. It is a multiple of 5
e. It is a factor of 10
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20. At a dinner party each table can seat eight people. If 100
people attend the party, what is the minimum number of
tables that are needed?
a. 12
b. 13
c. 14
d. 15
e. 16
21. What is the greatest integer that evenly divides both 48
and 64?
a. 12
b. 16
c. 24
d. 6
e. 8
22. When x is divided by 8, the remainder is 3. What is the
remainder when 4x is divided by 8?
a. 1
b. 2
c. 3
d. 4
e. 5
23. Let x, y, and z be positive integers such that y is a multiple
of x and z. All of the following statements are true except for:
a. y z is a multiple of x
b. x is a factor of y
c. x z is a factor of y
d. z divides evenly into y
e. x divides evenly into y z
24. When a two-digit number is divided by 5 the remainder is
2. Which of the following statements must be true about the
two-digit number?
a. The sum of all the digits is odd
b. The digit in the one’s place is odd
c. The number is prime
d. The number is odd
e. The digit in the one’s place is prime
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25. How many distinct composite numbers can be formed by
adding 2 of the first 5 prime numbers?
a. 3
b. 4
c. 5
d. 6
e. 7
26. Alice is three more than twice Tom’s age. If Tom is 15
years old, how old is Alice?
a. 30
b. 31
c. 32
d. 33
27. A store is having a sale on all items for 20% off the original
price. If x represents the original price of an item, what
expression represents the sale price of the item?
a. 0.20x
b. 0.08x
c. 0.8x
d. 0.02x
28. At the end of the school year, Anthony was 66 inches tall.
When he came back from summer break for school this year
he was 6 feet tall. What percentage has Anthony’s height
increased since the end of last school year?
a. 0.99%
b. 9.99%
c. 9.09%
d. 99.9%
29. On Tuesday Ray rode his bike 10 miles. On Wednesday he
increased Tuesday’s distance by 5 miles. On Thursday he
decreased Wednesday’s distance by 7 miles. On Friday he
increased Thursday’s distance by 12 miles. How many total
miles did Ray ride over the 4-day period?
a. 50
b. 51
c. 52
d. 53
e. 54
30. 4 times x is equal to x increased by 6. x =
a.1
b.2
c. 3
d. 4
e. 5
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31. 2 times x plus 6 is equal to 5 times x less 3. x =
a.1
b. 2
c. 3
d. 4
e. 5
32. 40% of the students in a class are female. If there are 10
females in the class, how many mal
es are there in the class?
a. 5
b. 10
c.15
d. 20
e. 25
33. Lindsey earns $15 hour for the first 40 hours she works in
a week and 50% more for every hour over 40. How many hours
did Lindsey work in a week, when she was paid $937.50 before
taxes?
a.15hours
b. 30hours
c. 40hours
d. 45hours
e. 55hours
34. Tim earns $2,000 more a year than Pete. If Pete gets a 5%
raise, their earnings would be equal. How much money does
Pete earn a year?
a. 35,000
b. 40,000
c. 45,000
d. 50,000
e. 55,000
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ANALOGY: SINGLE WORD APPROACH
1. Egypt : Pharaoh :: Khan :____________
a) Thailand
b) Cambodia
c) Mongolia
d) Khmer
2. Caesar : Roman Empire :: Czar : ___________
a) The Philippines
b) Bulgaria
c) Russia
d) Greece
3. Iraq : Mesopotamia :: Iran : _____________
a) Macedonia
b) Persia
c) Phoenicia
d) Babylon
4. Inca : America :: Mesopotamia : ___________
a) Asia
frica
b) Europe
c) A
d) Australia
5. Myanmar : Burma :: France : ___________
a) Lombard
b) Visigoth
c) Ostrogoth
d) Gaul
6. Taiwan : Formosa :: Thailand : _____________
a) Ceylon
b) Formosa
c) Gaul
d) Siam
7. Abandon : discard :: accord :
a) Peace
b) Agree
c. Disgrace
d. tyranny
8. Mammalogy : mammals :: morphology :
a) morphine
b) words
c) sentences
d) grammar
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9. Mycology : fungi :: numismatology :
a) Numbers
b) Letters
c) writing
d) coins
10. Oncology : tumors :: ophthalmology :
a) Ears
b) Throat
c) nose
d) eyes
11. Ornithology : birds :: paleontology :
a) Artifacts
b) Old tools
c) Fossils
d) Ancient
12. Parasitology : parasites :: pathology :
a) Ways
b) Cures
c) Medicines
d) diseases
13. Philology : language :: primatology :
a) Primes
b) Premiers
c) Primate
d) None of the above
14. Thanatology : death :: toxicology :
a) Potions
b) Fossils
c) artifcts
d) poisons
15. Urology : urine :: virology :
a) Parasites
b) Bacteria
c) Protists
d) viruses
16. Zoology : animals :: taxonomy :
a) Classification
organisms
b) Naming organisms
c) naming and classifying
organisms
d) studies evolution
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17. Animalia : platypus :: plantae :
a) Fern
b) Fluke
c) zooplankton
d) ascaris
18. Dicot : beans :: monocot :
a) Rose
b) Mango
c) beans
d) corn
19. Dicot : gumamela :: monocot :
a) Mahogany
b) Molave
c) chrysanthemum
d) rice
20. Whirl : coconut :: opposite :
a) Mongo
b) Rice
c) Corn
d) banana
21. Opposite : peanuts :: alternate :
a) Ginger
b) Beans
c) Mango
d) carrot
22. Rice : parallel :: mango :
a) Opposites
b) alternate
c) netted
d) whirl
23. Parallel : netted :: corn :
a) Bamboo
b) Raddish
c) onion
d) banana
24. Taproot : carrot :: fibrous :
a) Raddish
b) Mongo
c) shrub
d) grass
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25. Cell : tissue :: tissue :
a) Organ system
b) Organism
c) cell
d) organ
26. Ribosome : protein synthesis :: golgi apparatus :
a) Packaging
b) Transport
c) Synthesis
d) hydrolysis
27. Chloroplast : photosynthesis :: ribosome :
a) Cellular
respiration
b) Packaging
c) protein synthesis
d) glucose hydrolysis
28. Tapeworm : endoparasite :: lice :
a) Phagocyte
b) Endocyte
c) ectocyte
d) ectoparasite
29. Amphibian : frog :: aves :
a) Crocodile
b) Bacteria
c) fungi
d) chicken
30. Aves : mollusca :: parrot :
a) seahorse
b) sea shells
c) sponges
d) polyps
31. Monosaccharide : simple :: polysaccharide :
a) double
b) complex
c. cellulose
d. starch
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32. Monosaccharide : simple :: disaccharide :
a) Double
b) Simple
c) Complex
d) cellulose
33. Plants : producers :: animals :
a) Consumers
b) Decomposers
c) Scavengers
d) producers
34. Plants : autotrophs :: animals :
a) Saprotrophs
b) homotrophs
c) heterotrophs
d) scavengers
35. 100 : 10 :: 20 :
a) 2
b) 3
c) 4
d) 5
36. Chromosomes : 46 :: pairs of chromosomes :
a) 24
b) 23
c) 22
d) 21
37. Meiosis : gamete cells :: mitosis :
a) Sex cells
b) somatic cells
c) brain cells
d) red blood cells
38. Meiosis : sex cells :: mitosis :
a) Sex cells
b) somatic cells
39. Meiosis : 4 :: mitosis :
a) 2
b) 3
c) brain cells
d) red blood cells
c) 4
d) 5
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40. Meiosis : 2 phases :: mitosis :
a) 1 phase
b) 2 phases
c) 3 phases
d) 4 phases
41. Meiosis : Haploid :: mitosis :
a) Diploid
b) Multiploid
c) Haploid
d) None of the above
42. Haiku : 3 :: Sonnet :
a) 12
b) 13
c) 14
d) 15
43. Linnaeus : Swedish :: Hippocrates :
a) Roman
b) Greek
c) Macedonian
d) Persian
44. Mendel : Pasteur :: Austrian :
a) German
b) Albanian
c) French
d) Swiss
45. Mendel : Pasteur :: Genetics :
a) Geocentric Theory
c) Germ Theory
b) Heliocentric Theory d) Viral Theory
46. Cattle : Bull :: Chicken :
a) Hen
b) Cow
c) Rooster
d) Chick
47. September : 2 x 15 :: February :
a) 2 x 15
c) 2 x 16
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b) 2 x 13
d) 2 x 14
48. Comparative : worse :: superlative :
a) Bad
b) Baddest
c) Most worst
d) worst
49. Fruit : wine :: grain :
a) malt
b) beer
c) coffee
d) wine
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TECHNIQUES IN SOLVING
ALGEBRAIC WORD PROBLEMS
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TECHNIQUES IN SOLVING ALGEBRAIC WORD PROBLEMS
THE BASICS
Word problems are series of expressions that fits into an
equation.
A mathematical equation is a combination of mathematical expressions having an equal sign.
Examples:
x + y = 12
2y = 24
A mathematical expression is a combination of variables
and numbers.
Examples:
x+y
abc
2xy
2a2
25xy
SUGGESTIONS IN SOLVING WORD PROBLEMS:
• Read the problem entirely
Get a feel for the whole problem
• List information
identify.
and
the
variables
you
Attach units of measure to the variables (gallons,
miles, inches, etc.)
• Define
what answer you need, as well as its
units of measure
• Work in an organized manner
Working clearly will help you think clearly
 Draw and label all graphs and pictures clearly
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 Note or explain each step of your process; this
will help you track variables and remember their
meanings
• Look for the “key” words
Certain words
operations.
indicate
certain
mathematical
MORE VOCABULARY AND KEY WORDS:
• Per” means “divided by”
as “I drove 70 miles on two gallons of gas, so I got
35 miles per gallon” (Also 35 miles/gallon)
• “a” sometimes means “divided by”
as in “When I tanked up, I paid Php 150.00 for
three gallons, so the gas was Php 50 a gallon, or
Php 50/gallon
• “Less than”
If you need to translate “6 less than x”, the
temptation is to write “6 - x”. DON’T! Put a “real
world” situation in, and you’ll see how this is
wrong: “He makes Php 50.00 an hour less than
me.” You do NOT figure his wage by subtracting
your wage from Php 50.00. Instead, you subtract
Php 50.00 from your wage
• “quotient/ratio of” constructions
If a problems says “the ratio of x and y”, it
means “x divided by y” or x/y or x÷y
• “difference between/of” constructions
If the problem says “the difference of a and
b”, it means “a - b”
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MATHEMATICAL EXPRESSIONS (EXAMPLES):
Addition:
• 3+x
• y+6
• x + 25
Subtraction:
• 67 - x
• y – 76
• x – 50
Multiplication:
• (45)(x)
• 65x
• 7y
Division:
• 52 ÷ x
• 85/x
• x/15
KEY WORDS TO REMEMBER IN SOLVING WORD PROBLEMS
Key words for addition (+) :
• plus
• total of
• increased by
• sum
• more than
• added to
• combined together
• combined
Examples
Verbal statements
Mathematical
What is the sum of 45 and y?
statements
45 + y
Express the number (x) of apples
increased by twenty five
x + 25
Express the total weight of the dog (x)
and the cat (y)
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x+y
147
Key words for Subtraction (-):
• diminish by
• difference of
• less than
• subtracted from
• fewer than
• smaller than
• reduced by
• difference between
• decreased by
Examples
Verbal statements
Mathematical statements
What is forty -four less than y
y – 44
What is twenty-nine less than a
number (y)
y – 29
What if the number (x) of children
was reduced by 16?
x – 16
Key words for multiplication (x)
or integers next to each other (5y, xy)
• of
• Increased/decreased
• twice
• times
by a factor of (this
• thrice
• multiplied by
type can involve
• product of
both addition or
• as much as
subtraction and
multiplication!)
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Verbal statements
Mathematical statements
What is x multiplied
by 43
43x or (43)(x)
Three runners
averaged “x” minutes.
(Express their total
running time:)
3x
I drive my car at 85
miles per hour.
How far will I go in
“x” hours?
85x
Key words for division (÷,/)
• per
• ratio of
•a
• quotient of
• out of
• percent (divide by 100)
Verbal statements
Mathematical statements
What is the quotient
of y and 8
y/8 or y ÷ 8
Ten students rent an
apartment for
Php “x” /month.
What will each have to pay?
x/10 or x ÷ 10
“y” items cost a total
of Php 225.00.
Express their average cost.
225/y or 225 ÷ y
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Equals (=)
• is
• results to
• are
• gives
• was
• yields
• were
• sold for
• will be
Note that “per” means “divided by”, as in “I drove 90 miles on three
gallons of gas, so I got 30 miles per gallon”. Also, “a” sometimes
means “divided by”, as in “When I tanked up, I paid $3.90 for three
gallons, so the gas was $1.30 a gallon”.
IMPORTANT NOTE:
Let me emphasize that “less than” is backwards in the English
from what it is in the math. If you need to translate “1.5 less than x”,
the temptation is to write “1.5 – x”. Do not do this. If you put a “real
world” situation in, you’ll see how this is wrong: “He makes $1.50 an
hour less than me.” You do not figure his wage by subtracting your
wage from $1.50. Instead, you subtract $1.50 from your wage. Just
remember; the “less than” construction is backwards.
Also note that order is important in the “quotient/ratio of” and
“difference between/of” constructions. If a problems says “the ratio of
x and y”, it means “x divided by y”, not “y divided by x”. If the
problem says “the difference of x and y”, it means “x – y”, not “y – x”.
Now we need to learn to extract the keywords from the word
problems.
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TRANSLATING
EXPRESSIONS
ENGLISH
PHRASES
INTO
MATHE-MATICAL
Examples
•
Translate “the sum of 48 and 3y” into an algebraic
expression.
This translates to “48 + 3y”
•
Translate “thrice the product of x and y” into an algebraic
equation.
This translates to “3(x)(y) or 3xy”
•
Translate “twice the product of x and z diminished by 5”
into an algebraic equation.
This translates to “2xz – 5 or (2xz) - 5”
•
Translate “the difference of 3x and 6y” into an algebraic
equation.
This translates to “3x - 6y”
•
Translate “twice the sum of 6x and 6y subtracted from a
certain number” into an algebraic equation.
This translates to “c - 2(6x + 6y)”
•
Translate “the product of d and b divides the sum of 3x
and y” into an algebraic equation.
This translates to “(3x + y)/db”
•
Translate “The quotient of two numbers is 4” into an
algebraic equation.
This translates to “x/y = 4”
•
Translate “a number increased by 4 divided by their
product is 60” into an algebraic equation.
This translates to “(x + 4)/4x = 60”
•
Translate “the product of x and y gives 35” into an
algebraic equation.
This translates to “xy = 35”
•
Translate “46 less than x” into an algebraic expression.
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This translates to “x – 46”
•
Translate “x multiplied by 124” into an algebraic
expression.
This translates to “124x”
•
Translate “the quotient of 7x and 3” into an
algebraic expression.
This translates to “7x/3”
•
Translate “the difference of 50 and y” into an
algebraic expression.
This translates to “50 – y”
•
Translate “the ratio of 9 more than x to 9” into an
algebraic expression.
This translates to “(x + 9)/9”
•
Translate “nine less than the total of a number and
two” into an algebraic expression, and simplify.
This translates to “(n + 2) – 9”, which then simplifies to
“n – 7”
Here are some more wordy examples:
•
The length of a football field is 30 yards more than
its width. Express the length of the field in terms of
its width w.
Whatever the width w is, the length is 30 more than this.
Recall that “more than” means “plus that much”, so
you’ll be adding 30 to w.
The expression they’re looking for is “w + 30”.
GEOMETRIC PROBLEMS
In dealing with geometric word problems, you have to
take note of the formulas of the areas and perimeters of all
geometric figures. Most of the time, the problems only deal
with triangles, squares, rectangles and circles.
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Triangles
Square
Rectangle
Circle
Areas
Perimeters
(bh)/2 or
s2
lxw
πr 2
a+b+c
4s
2l + 2w
2ππ or πD
Examples:
1. If a rectangular garden has a perimeter of 360m, find
the dimensions if the length is three more than three
times the width?
Step 1: Read and understand the problem
We are asked to find the dimensions of the rectangle.
Step 2: Assign variables. Draw a diagram or table if
necessary
Let l be the length of the rectangular garden.
Let w be the width of the rectangular garden.
L
W
Step 3: Write the equations
The perimeter is 360m.
P = 360m
The length is three more than three times the width.
l = 3w + 3
Since P = 2l + 2w and P = 360, therefore:
360 = 2l + 2w
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Since l = 3w + 3, then
360 = 2 (3w + 3) + 2w
Step 4: Solve for w:
360 = 2 (3w + 3) + 2w
360 = 6w + 6 + 2w
360 = 8w + 6
360 - 6 = 8w
354 8w

8
8
44.25 m= w
To solve for l,
l = 3w + 3
= 3(44.25) +3
= 132.75+ 3
l = 135.75 m
Step 5: State the answer
The width of the rectangular garden is 44.25 m and
the length is 135.75 m.
Step 6: check your answer
360 = 2l + 2w
360 = 2(135.75) + 2(44.25)
360 = 271.5 + 88.5
360 = 360
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PRICES PROBLEMS
In this kind of world problem, you would be dealing with the
quantity and the cost of the items considered in the problem.
Examples
Quantity/Total number of items
1. The total number of softballs and baseballs is 25.
Let x be the number of softballs
Let y be the number of baseballs
Therefore, the total is
x +y = 25
2. The total number of tickets for adult and children is 1,500.
Let x be the number of tickets for adult
Let y be the number of tickets for children
Therefore, the total is
x + y = 1,500
Cost /Total amount of the items
1. If there are 15 softballs and 25 baseballs. The total cost of
both items is 500. How much is the price of each kind of
ball?
Let x be the cost of softballs
Let y be the cost of baseballs
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15x is the total cost for the softballs
25y is the total cost for the baseballs
Therefore, the total cost is
15x + 25y = 500
2. The are 250 and 200 tickets for adults and children,
respectively. The total cost of the tickets is 4,500. How
much does each ticket cost?
Let x be the cost of tickets for adults
Let y be the cost of tickets for children
250x is the total cost of the tickets for adults
200y is the total cost of tickets for children
Therefore, the total is
250x + 200y = 1,500
Sample problems
1.
Mike Andrew is working in a fast food restaurant.
Two days ago, he sold 20 burgers and 10 footlongs
and the total sale was 750 pesos. Yesterday he sold
35 hamburgers and 15 footlongs and the sales was
1,225 pesos. How much is the cost of each item?
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Step 1: Read and understand the problem
We are asked to find the cost of each item
being sold.
Step 2: Assign variables. Draw a diagram or
table if necessary
Let x be the cost of each burger
Let y be the cost of each footlong
Step 3: Write the equations
Two days ago,
20x is the total cost of burgers
10y is the total cost of footlongs
Yesterday,
35x is the total cost of burgers
15y is the total cost of footlongs
The total cost 2 days ago is,
20x + 10y = 750
The total cost yesterday is,
35x + 15y = 1,225
Step 4: Solve for x and y.
20x + 10y = 750
35x + 15y = 1,225
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Using the elimination method in solving systems of
linear equations,
(20x + 10y = 750) multiplied by 3
(35x + 15y =1,225) multiplied by -2
60x + 30y = 2,250
-70x + (-30)y = - 2,450
10x 200

 10
 10
x = 20
Solving for y, if x = 20
20x + 10y = 750
20 (20) + 10y = 750
400+ 10y = 750
10y = 750 – 400
10y = 350
y= 35
Step 5: State the answer
The cost of each burger is Php20 and the
cost of each footlong is Php35.
Step 6: check your answer
20x + 10y = 750
20 (20) + 10 (35) = 750
400+ 350 = 750
750 = 750
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MIXTURE PROBLEMS
In this type of problem, you need to draw a
diagram so that you would be able to picture out and
understand the problem. The approach in solving this
type of problem is almost the same with the approach
being used in solving the word problems involving prices.
Sample Problems
1. How many ounces of each 15% and 25%
hydrochloric (HCL) acid solutions must be
combined to produce a 20 oz of the solution
that is 20% hydrochloric acid?
Step 1: Read and understand the problem
We are asked to find the amount of each
solution to be combined to get that 20 oz at 20%
HCL acid solution.
Step 2: Assign variables. Draw a diagram or
table if necessary
Let x be the amount of 15% HCL acid.
Let y be the amount of 25% HCL acid.
X
y
+
15%
20
=
25%
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20%
159
Step 3: Write the equations
The total amount of the solution is,
x + y = 20
and
15% x + 25% y = 20% (20)
Or
0.15x + 0.25y = 0.2 (20)
Step 4: Solve the equations
x +y = 20
[ 0.15x + 0.25y = 0.2 (20) ] – multiplied by 100 to
eliminate the decimal point
[Multiplying by 100 to eliminate the decimal point would
still be the same as to deal the problem in decimal
notation.]
So,
x + y = 20
15x + 25y = 20 (20)
Solving for x in the first equation,
x + y = 20
x = 20- y
Substituting it in the 2nd equation,
15x + 25y = 400
15(20 – y) + 25y = 400
300 – 15y + 25y = 400
300 + 10y = 400
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10y = 400 - 300
10y = 100
10
10
y = 10
Solving for x, if y = 10
x + y = 20
x+ 10 = 20
x= 20 – 10
x= 10
Step 5: State the answer
The amount of each solution to be combined
to get 20 oz of 20% HCL acid is 10 oz each.
Step 6: check your answer
x + y = 20
10 + 10 = 20
20 = 20
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INVESTMENT PROBLEMS
The approach in solving this type of problem is the
same with the approach we used in prices and mixture
problems
Sample problems
1. An amount of money is invested at 5% annual
simple interest and Php9,000.00 more than that
amount is invested at 6%. The total annual
interest earned is Php2,300.00 . How much is
invested at each rate?
Step 1: Read and understand the problem
We are asked to find the amount of money
invested at each rate.
Step 2: Assign variables. Draw a diagram or
table if necessary
Let x be the amount invested at 5%
Let y be the amount invested at 6%
Amount
Invested:
x
y
+
Interest:
5%x
=
6%y
Step 3: Write the equations
y = x + 9,000
5%x + 6%y = 2,300
or
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2,300
[ 0.05x + 0.06y = 2,300] 100
or
5x + 6y = 230,000
Step 4: Solve for x,
5x + 6y = 230,000
5x + 6 (x + 9,000) = 230,000
5x + 6x + 54,000 = 230,000
11x = 230,000 – 54,000
11x 176,000

11
11
x = 16,000
Solving for y, if x = 16,000
y = x + 9,000
y = 16,000 + 9,000
y = 25,000
Step 5: State the answer
The amounts invested at 5% and 6% are
Php16,000.00 and Php25,000.00 respectively.
Step 6: check your answer
y = x + 9,000
25,000 = 16,000 + 9,000
25,000 = 25,000
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COIN PROBLEMS
The equation that describes the number of coins is
x +y = total
The equation the describes the amount of money is
(amount of each coin) (x) + (amount of each coin) (y) =
total amount
Sample problems
1. When Alma emptied her pocket one morning, she
had 29
5-centavo and 10-centavo coins with the total
value of Php2.45. How many coins of each denomination
does she have?
Step 1: Read and understand the problem
We are asked to find the number of coins in each
denomination.
Step 2: Assign variables. Draw a diagram or
table if necessary
Let x be the number of 5- centavo coins
Let y be the number of 10-centavo coins
Step 3: Write the equations
The total number of coins is,
x + y = 29
and
[0.05 x + 0.1 y = 2.45] 100
or
5x + 10y = 245
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Step 4: Solve for x,
x + y = 29
5x + 10y = 245
Solving for x in the first equation,
x + y = 29
x = 29 – y
substituting it in the 2nd equation,
5x + 10y = 245
5(29 – y) + 10y = 2245
145 – 5y + 10y = 245
145 + 5y = 245
5y = 245 – 145
5y
5

100
5
y = 20
solving for x,
x + y = 29
x + 20 = 29
x= 29 – 20
x= 9
Step 5: State the answer
The number of coins is 9 and 20 for 5centavo and 10-centavo coins respectively.
Step 6: check your answer
x + y = 29
9 + 20 = 29
29= 29
|LET-Reviewer – General Education
165
WORK PROBLEMS
A. Working together situation
The goal of a “working together” problem is
generally to figure how fast a job can be completed if
two or more workers do the job together.
1. It takes Ceppee 6 hours to build a fence. If he asks
Jandy to help him, together they can do the job in
just 4 hours. How long would it take Jandy to build
the same fence if he works alone?
Step 1: Read and understand the problem
We are asked to find how long would it take
Jandy to do the job if he works alone.
Step 2: Assign variables. Draw a diagram or
table if necessary
Let x be the amount of time it takes Jandy to
build the fence (in hours) if he works alone.
Step 3: Write the equations
Ceppee would need 6 hours if he did the
entire job by himself, so his working rate is onesixth (1/6)of the job per hour.
Likewise, Jandy’s rate is one over x (1/x) of the job
per hour. And the rate, if they worked together, is onefourth (1/4) of the job per hour.
Step 4: Solve the equations
166 | L E T - R e v i e w e r – G e n e r a l E d u c a t i o n
1 1 1
 
6 x 4
1 1 1
 
6 x 4
x6 1

6x
4
4 (x+6) = 6x (1)
4x + 24 = 6x
24 = 6x - 4x
24 = 2x
x = 12
Step 5: State the answer
Remember that x represents the amount of
time it takes Jandy to build the fence (in hours) if
he works alone. So, working alone, he can build
the fence in only 12 hours.
Step 6: check your answer
1 1 1
 
6 x 4
|LET-Reviewer – General Education
167
1 1
1


6 12 4
1(2) 1
1


6(2) 12 4
2 1 1

12
4
3
1

12 4
1 1

4 4
AGE PROBLEMS
1. Jandy is three times as old as Ceppee. Four
years ago, he was four times as old as Ceppee.
How old are they now?
Step 1: Read and understand the problem
We are asked to find the ages of the two
guys.
Step 2: Assign variables. Draw a diagram or
table if necessary
Let x be the age of Ceppee now
Age now
Jandy
3x
Ceppee
x
Age four years ago
3x - 4
168 | L E T - R e v i e w e r – G e n e r a l E d u c a t i o n
x-4
Step 3: Write the equations
We have to equate their ages four years ago.
3x – 4 = 4 (x - 4)
Step 4: Solve for x,
3x – 4 = 4 (x - 4)
3x – 4 = 4x – 16
– 4 + 16 = 4x – 3x
12 = x
Step 5: State the answer
Ceppee’s age now is 12. Since Jandy is 3
times as old as Ceppee, 3(12) or 36 years old.
Step 6: check your answer
3x – 4 = 4 (x - 4)
3(12) – 4 = 4 (12 - 4)
36 – 4 = 4(8)
32
= 32
|LET-Reviewer – General Education
169
NUMBER PROBLEMS
The common mistake in number problem is how to
represent or translate the phrase “consecutive
Integers, consecutive even Integers and consecutive
odd Integers”
1. consecutive Integers
Let x be the first integer, so
x + 1 would be the second
x + 2 would be the third
x + 3 would be the fourth, and so on
If x= 2, then
x+1=3
x+2=4
x+3=5
2, 3, 4 and 5 are consecutive integers.
2. consecutive even Integers ( all numbers that are
divisible by 2)
Let x be the first even integer, so
x + 2would be the second
x + 4 would be the third
x + 6 would be the fourth, and so on
if x= 2, then
x+2=4
x+4=6
2, 4, 6 and 8 are consecutive even integers.
3. consecutive odd Integers (numbers that are not
divisible by 2)
Let x be the first integer, so
x + 2 would be the second
x + 4 would be the third
170 | L E T - R e v i e w e r – G e n e r a l E d u c a t i o n
x + 6 would be the fourth, and so on
if x= 3, then
x+2=5
x+4=7
3, 5, 7 and 9 are consecutive odd integers.
As a conclusion, the representation of the
consecutive even and odd integers are just the same.
1. Find the three consecutive odd integers whose sum is
129.
Step 1: Read and understand the problem
We are asked to find the three consecutive
odd integers.
Step 2: Assign variables. Draw a diagram or
table if necessary
Let x be the first integer, so
x + 2 would be the second
x + 4 would be the third
Step 3: Write the equations
We have to equate the three consecutive odd
integers and their sum.
x + (x+2) + (x+4) = 129
Step 4: Solve for x,
x + (x + 2) + (x + 4) = 129
3x + 6 = 129
3x = 129 – 6
|LET-Reviewer – General Education
171
3x 123

3
3
x = 41
The second integer is:
x + 2 = 41 + 2
= 43
The third integer is:
x + 4= 41 + 4
= 45
Step 5: State the answer
The three consecutive odd integers are 41, 43 and
45.
Step 6: check your answer
x + (x + 2) + (x + 4) = 129
41 + (41 + 2) + (41 + 4) = 129
41 + 43 + 45 = 129
129 = 129
172 | L E T - R e v i e w e r – G e n e r a l E d u c a t i o n
MOTION PROBLEMS
In this type of problem, you have to draw a
diagram or a picture of the problem so that you would be
able to understand the word problem very well.
Here are some things to remember in this type of
problem:
•
distance = rate x time
d = rt, where: t = seconds (s)
r = meter/seconds (m/s)
d = meters (m)
•
Upstream – going against the current of the
water/wind. The speed in still water is always
deducted by the speed or rate of the current.
•
Downstream – going with the current of the
water/wind.The speed in still water is always
added to the speed or rate of the current.
There are also four most common situations in this type
of problem:
 Both moving objects are going on the same
direction.
 Both moving objects are going towards each
other.
|LET-Reviewer – General Education
173
 Both moving objects are going away from
each other.
 If a moving object is returning to its original
position or starting point.
Starting point
destination point
Sample problems:
1. A truck travels 400 km at the same time as a car
travels at 550 km from the same starting point
travelling on the same direction. If the speed of the car
is 9 km/hr more than the speed of the truck, find the
speed of both vehicles.
Step 1: Read and understand the problem
We are asked to find the speed of each
vehicle.
Step 2: Assign variables. Draw a diagram or
table if necessary
Let x be the speed of the truck
Let y be the speed of the car
174 | L E T - R e v i e w e r – G e n e r a l E d u c a t i o n
Truck
400 km
Car 550 km
Step 3: Write the equations
Since both vehicles travel at the same time,
therefore the time of travel of both vehicles are
equal.
From, d=rt
t = d/r
For the truck,
t = 400/x
For the car
t = 550/y
But the speed of the car which is the y is 9 km/hr
more than the speed of the truck,
y = x + 9, so, t = 550/(x + 9)
Since their time of travel are equal,
Time for the truck = time for the car
400/x = 550 /(x + 9)
Step 4: Solve for x,
400/x = 550 /(x + 9)
400(x + 9) = 550x – by cross multiplication
|LET-Reviewer – General Education
175
400x + 3600 = 550x
400x – 550x = -3600
150x 3600

 150
 150
x = 24
Solving for y,
y=x+9
y = 24 + 9
y = 33
Step 5: State the answer
The speed of the truck is 24 km/hr and the car
travels at 33km/hr.
Step 6: check your answer
y = x+ 9
33 = 24 + 9
33 = 33
176 | L E T - R e v i e w e r – G e n e r a l E d u c a t i o n
ANSWER KEYS
SCIENCE
PART I
Answer key
1. B
2. C
3. A
4. C
5. E
6. D
7. D
8. C
9. D
10.
11.
12.
13.
14.
15.
16.
17.
18.
19.
20.
21.
22.
23.
24.
25.
26.
27.
28.
29.
30.
31.
32.
33.
E
D
D
C
A
D
E
D
D
A
D
E
E
B
C
C
D
C
C
D
D
C
D
B
34.
35.
36.
37.
38.
39.
40.
41.
42.
43.
44.
45.
46.
47.
48.
49.
50.
51.
52.
53.
54.
55.
56.
57.
58.
59.
60.
61.
62.
63.
64.
65.
66.
A
A
A
E
B
A
A
E
D
A
A
C
E
D
A
B
C
D
E
E
D
B
D
C
E
A
B
B
C
B
C
B
C
67.
68.
69.
70.
71.
72.
73.
74.
75.
76.
77.
78.
79.
80.
81.
82.
83.
84.
85.
86.
87.
88.
89.
90.
91.
92.
93.
94.
95.
96.
97.
98.
99.
A
E
B
A
A
B
D
A
B
D
D
B
C
B
D
C
B
C
B
C
D
C
D
A
C
D
C
D
B
A
A
B
C
|LET-Reviewer – General Education
100.
101.
102.
103.
104.
105.
106.
107.
108.
109.
110.
111.
112.
113.
114.
115.
116.
117.
118.
119.
120.
121.
122.
123.
124.
125.
126.
127.
128.
129.
130.
177
C
B
C
B
D
C
C
B
C
B
D
A
D
C
C
B
C
B
D
B
A
B
B
B
C
C
B
D
A
A
B
PART II
1. C
2. D
3. A
4. A
5. C
6. D
7. B
8. D
9. C
10. A
11.
12.
13.
14.
15.
16.
17.
18.
19.
20.
A
D
C
D
B
B
A
C
D
D
21.
22.
23.
24.
25.
26.
27.
28.
29.
30.
A
C
A
D
D
B
D
C
A
C
31.
32.
33.
34.
35.
36.
37.
38.
39.
40.
C
A
D
C
B
B
A
C
B
A
41. D
42. D
PART III:
1.c
2.b
3.c
4.c
5.a
6.b
7.a
8.b
9.b
10.a
11.d
12.b
13.b
14.c
15.d
16.b
17.d
18.a
19.b
20.a
21.c
22.a
23.a
24.a
25.a
Part IV
ANSWER KEY
1 B
2 C
3 B
4 B
5 B
6 C
7 B
8 C
9 C
10 B
11 C
12 B
13 A
14 C
15 D
PART V
answer key:
1. d
4. b
2. a
5. d
3. b
6. a
7. a
8. d
9. a
10. d
11. a
12. c
13.d
14.d
15. d
178 | L E T - R e v i e w e r – G e n e r a l E d u c a t i o n
PART VI
Answer key:
1.
2.
3.
4.
5.
6.
7.
d
c
d
a
d
b
c
PART VII
1. E
2. A
3. E
4. B
5. E
6. A
7. C
8. B
9. C
10. B
41.
42.
43.
44.
45.
46.
47.
48.
49.
50.
A
B
A
D
E
A
E
D
C
A
8.
9.
10.
11.
12.
13.
14.
11.
12.
13.
14.
15.
16.
17.
18.
19.
20.
C
C
C
A
B
D
B
B
A
E
c
d
d
b
15.
16.
17.
18.
19.
20.
e
a
b
21. D
22. D
23. E
24.D
25. E
26. B
27. C
28. D
29. A
30. E
31.
32.
33.
34.
35.
36.
37.
38.
39.
40.
a
d
e
a
b
b
B
A
B
A
B
C
C
C
B
D
51. D
52. B
53. D
54. C
55. C
56. A
57. C
58.D
PART VIII
Answer key:
1. C
3. A
2. C
4. B
5. D
6. B
7. B
8. B
|LET-Reviewer – General Education
9. B
10. A
179
ENGLISH
PART I
1. A
2. A
3. A
4. B
5. A
6. B
7. A
8. C
9. B
10. A
11.
12.
13.
14.
15.
16.
17.
18.
19.
20.
B
A
A
B
A
B
D
C
B
C
21.
22.
23.
24.
25.
26.
27.
28.
29.
30.
B
D
B
C
D
B
A
B
B
A
31.C
32.C
33. C
34. C
35. C
36. A
37. D
38. C
39. C
40. A
41.
42.
43.
44.
45.
46.
47.
48.
49.
50.
D
A
A
D
D
D
C
A
B
C
51.
52.
53.
54.
55.
56.
57.
58.
59.
60.
B
A
C
C
B
C
B
A
C
B
61.
62.
63.
64.
65.
66.
67.
68.
69.
70.
B
A
D
C
C
A
B
A
C
A
71.
72.
73.
74.
75.
76.
77.
78.
79.
80.
81.
82.
83.
84.
85.
86.
87.
88.
89.
90.
D
B
C
B
C
C
C
A
D
A
91. C
92. A
93. A
94. B
95. C
96. D
97. D
98. A
99. A
100. C
101.
102.
103.
104.
105.
106.
107.
108.
109.
110.
A
D
B
C
B
B
A
D
B
A
B
B
C
C
C
D
D
B
B
A
111.
112.
113.
114.
115.
116.
117.
118.
119.
120.
A
D
B
C
B
A
A
C
B
A
121. B
122. A
180 | L E T - R e v i e w e r – G e n e r a l E d u c a t i o n
PART II
1. c
2. d
3. c
4. a
5. b
6. b
7. d
8. c
9. a
10. c
11.
12.
13.
14.
15.
16.
17.
18.
19.
20.
d
d
a
a
b
a
a
b
c
b
11.
12.
13.
14.
15.
16.
17.
18.
19.
20.
c
d
b
a
b
b
c
c
d
c
21.
22.
23.
24.
25.
26.
27.
28.
29.
30.
11. a
12. b
13. c
14. b
15. c
16. a
17. b
18. b
19. b
20.a
21.
22.
23.
24.
25.
PART III
1. a
2. b
3. a
4. b
5. a
6. b
7. a
8. a
9. a
10.b
b
a
b
b
b
b
b
c
b
b
PART IV
ANSWER KEY
1. b
2. b
3. b
4. c
5. b
6. c
7. d
8. c
9. d
10. c
c
a
b
d
d
|LET-Reviewer – General Education
181
PART V
1. C
2. D
3. C
4. B
5. D
6. D
7. A
8. A
9. A
10. C
11.
12.
13.
14.
15.
16.
17.
18.
19.
20.
C
A
B
D
A
C
C
C
B
A
21.
22.
23.
24.
25.
26.
27.
28.
29.
30.
C
B
D
D
C
B
A
A
A
D
31.
32.
33.
34.
35.
36.
37.
38.
39.
40.
B
B
C
A
D
B
C
D
C
C
41.
42.
43.
44.
45.
46.
47.
48.
49.
50.
A
D
B
D
C
A
D
A
D
B
51.
52.
53.
54.
55.
56.
57.
58.
59.
60.
A
D
D
D
A
C
D
C
B
D
61. A
62. D
63. B
64. B
65.A
66. D
67. C
68. A
69. B
70. D
71.
72.
73.
74.
75.
76.
77.
78.
79.
80.
B
C
D
B
C
D
B
A
D
D
81.
82.
83.
84.
85.
86.
87.
88.
89.
90.
B
C
A
B
D
D
D
C
C
C
91. C
92. D
93. D
94. A
95. A
96. D
97. B
98. B
99. C
100. A
101.
102.
103.
104.
105.
106.
107.
108.
109.
110.
111.
112.
113.
114.
115.
116.
117.
118.
119.
120.
131. A
132. C
133. D
141. C
142. C
143. D
121. A
122. B
123. C
D
B
D
D
A
B
B
B
B
A
D
B
C
A
D
C
D
C
C
C
151. D
152. A
153. C
182 | L E T - R e v i e w e r – G e n e r a l E d u c a t i o n
124.
125.
126.
127.
128.
129.
130.
D
A
B
C
C
C
B
134.
135.
136.
137.
138.
139.
140.
A
A
D
C
D
C
D
144.
145.
146.
147.
148.
149.
150.
161.
162.
163.
164.
165.
166.
167.
168.
169.
170.
B
D
C
A
C
D
A
B
D
B
171.
172.
173.
174.
175.
176.
177.
178.
179.
180.
C
A
A
A
C
D
D
A
C
C
181.
182.
183.
184.
185.
186.
187.
188.
189.
190.
D
C
C
B
A
A
C
B
C
D
191.
192.
193.
194.
195.
196.
197.
198.
199.
200.
D
C
B
D
D
A
D
D
D
C
211.
212.
213.
214.
215.
216.
217.
218.
219.
220.
B
C
A
D
A
C
C
C
B
C
221.
222.
223.
224.
225.
226.
227.
228.
229.
230.
D
D
D
C
D
A
D
D
A
B
231.
232.
233.
234.
235.
236.
237.
238.
239.
240.
A
C
C
A
A
C
C
B
C
B
201.
202.
203.
204.
205.
206.
207.
208.
209.
210.
C
D
D
B
C
A
C
B
A
C
241.
242.
243.
244.
D
D
C
A
245.
246.
247.
248.
A
A
D
D
B
D
C
C
B
C
D
154.
155.
156.
157.
158.
159.
160.
C
D
B
D
A
D
B
249. C
250. C
|LET-Reviewer – General Education
183
VOCABULARY
1. acclimate
POS: Verb
MEAN: adjust to new
surroundings
Correct: A
2. accolade
POS: Noun
MEAN: Praise
Correct: D
3. accommodations
POS: Noun
MEAN: lodging
Correct: D
4. accompany
POS: Verb
MEAN: go with
Correct: D
5. accomplish
POS: Verb
MEAN: Achieve
Correct: C
7. accord
POS: Noun
MEAN: Agreement
Correct: C
8. account
POS: Noun
MEAN: a listing of personal
or business funds in a bank
Correct: B
9. accountant
POS: Noun
MEAN: a person who takes
care of financial matters
Correct: B
10. accrue
POS: Verb
MEAN: accumulate
Correct: D
11. achieve
POS: Verb
MEAN: Accomplish
Correct: B
12. achievement
POS: Noun
MEAN: Accomplishment
Correct: A
6. accomplishment
POS: Noun
MEAN: Achievement
Correct: D
13. acknowledge
POS: Verb
MEAN: confirm
Correct: C
184 | L E T - R e v i e w e r – G e n e r a l E d u c a t i o n
14. acquaintance
POS: Noun
MEAN: a person of casual
relationship
Correct: C
21. adamant
15. acquire
POS: Verb
MEAN: buy, get
Correct: D
22. addendum
16. acquisition
POS: Noun
MEAN: purchase
Correct: B
17. acting
POS: Adjective
MEAN: temporary
Correct: B
18. activate
POS: Verb
MEAN: make operational
Correct: A
19. actuarial
POS: Adjective
MEAN: insurance
Correct: B
20. acumen
POS: Noun
MEAN: Insight
Correct: B
POS: Adjective
MEAN: firm, insistent
Correct: B
POS: Noun
MEAN: an added part
Correct: D
23. address
POS: Noun
MEAN: location
Correct: D
24. addressee
POS: Noun
MEAN: person receiving a
delivery
Correct: A
25. adjourn
POS: Verb
MEAN: end, finish
Correct: B
26. adjuster
POS: Noun
MEAN: estimator of damage
Correct: C
27. administration
POS: Noun
MEAN: management
Correct: A
|LET-Reviewer – General Education
185
28. administrator
POS: Noun
MEAN: Manager
Correct: D
35. affirmative
POS: Adjective
MEAN: positive
Correct: C
29. advance
POS: Noun
MEAN: Loan of money
Correct: B
36. affix
POS: Verb
MEAN: position, place, write
Correct: A
30. adverse
POS: Adjective
MEAN: bad
Correct: C
37. affluent
POS: Adjective
MEAN: wealthy
Correct: B
31. advertisement
POS: Noun
MEAN: Commercial
enticement
Correct: B
38. afford
POS: Verb
MEAN: have the financial
means
take a dangerous financial
risk
Correct: D
32. advertising
POS: Adjective
MEAN: marketing
Correct: A
33. advice
POS: Noun
MEAN: recommendation
Correct: C
34. affiliate
POS: Noun
MEAN: partner
Correct: C
39. agency
POS: Noun
MEAN: company that
represents another
Correct: C
40. agent
POS: Noun
MEAN: Person that
represents clients
Correct: D
186 | L E T - R e v i e w e r – G e n e r a l E d u c a t i o n
41. aggressive
POS: Adjective
MEAN: bold, not passive
Correct: D
MEAN: spending amount
permitted
Correct: D
48. allowance
42. agreement
POS: Noun
MEAN: Compact of
concurrence
Correct: D
POS: Noun
MEAN: spending amount
Correct: C
49. alter
43. allegation
POS: Noun
MEAN: claim
Correct: D
44. alliance
POS: Noun
MEAN: partnership
Correct: B.”
POS: Verb
MEAN: change
Correct: B
50. alternate
POS: Noun
MEAN: a second choice
Correct: A
45. ally
POS: Noun
MEAN: partner
Correct: C
46. allocation
POS: Noun
MEAN: expenditures
Correct: B
47. allotment
POS: Noun
|LET-Reviewer – General Education
187
MATHEMATICS
PART I
1. If the first positive even integer is 2x + 6, then find the
next three positive even integers.
a.
b.
c.
d.
2x + 3, 2x + 4, 2x + 5
2x + 6, 2x + 7, 2x + 8
2x + 8, 2x + 10, 2x + 12
2x + 4, 2x + 2, 2x
The answer is letter C. Finding the INTEGERS,
remember the following terms when dealing with number
problems.
CONSECUTIVE
INTEGERS:
Let x be the first integer
Let x + 1 be the 2nd integer
Let x + 2 be the 3rd integer
Let x + 3 be the 4th integer
and so on…
CONSECUTIVE ODD/EVEN
INTEGERS:
Let x be the first integer
Let x + 2 be the 2nd integer
Let x + 4 be the 3rd integer
Let x + 6 be the 4th integer
and so on…
FOR ODD and EVEN integers, we add 2 for the next
integer, so if the first positive EVEN integer is 2x + 6, then
the next positive even integers would be
188 | L E T - R e v i e w e r – G e n e r a l E d u c a t i o n
2x +6 + 2 = 2x + 8
= 2x + 12
2x + 8 + 2 = 2x + 10
2x + 10 + 2
2. If 4x – 7 is the first odd integer, then find the 7th even
integer after it.
a.
b.
c.
d.
4x – 6
4x – 5
4x + 6
4x + 5
The answer is letter D. Finding the INTEGERS,
remember the following terms when dealing with number
problems.
CONSECUTIVE INTEGERS:
Let
Let
Let
Let
x
x
x
x
be the first integer
+ 1 be the 2nd integer
+ 2 be the 3rd integer
+ 3 be the 4th integer
and so on…
CONSECUTIVE ODD/EVEN
INTEGERS:
Let x be the first integer
Let x + 2 be the 2nd integer
Let x + 4 be the 3rd integer
Let x + 6 be the 4th integer
and so on…
FOR ODD and EVEN integers, we add 2 for the next
integer, so if the first ODD integer is 4x – 7 , then the next
odd integers would be
4x
4x
4x
4x
4x
4x
– 7 + 2 = 4x – 5
– 5 + 2 = 4x – 3
– 3 + 2 = 4x – 1
– 1 + 2 = 4x + 1
+ 1 + 2 = 4x + 3
+ 3 + 2 = 4x + 5
2ND
3RD
4TH
5TH
6TH
7TH
3. If x + y = 17, then find (x + y)² = _________.
a. 289
b. 34
c. 49
d. 389
The answer is letter A. Since x + y = 17, squaring both
sides we have
(𝑥 + 𝑦 )2 = 172
(𝑥 + 𝑦 )2 = 289
4. If 3x – 18y = - 21, then x – 6y = ________.
a.
b.
c.
d.
7
-7
-63
63
The answer is letter B. As you noticed,
3x – 18y = - 21
3(x – 6y) = - 21
x – 6y = - 7
factor by a common factor which is 3
divide both sides by 3
simplify
5. If (x – y)² = 49, then x² - 2xy + y² = __________.
a.
b.
c.
d.
89
49
13
7
The answer is letter B. Just expand (x - y)²
(x – y)² = (x – y)(x – y) = x² - 2xy + y² which is also equal to 49
6. If x – 2y = 14, then x² = ____________.
a.
b.
c.
d.
y² + 56y +196
y² + 6y +6
4y² + 6y +16
4y² + 56y +196
190 | L E T - R e v i e w e r – G e n e r a l E d u c a t i o n
The answer is letter D. Manipulating the equation,
x – 2y = 14
x = 14 + 2y
𝑥 2 = (14 + 2𝑦)2
𝑥 2 = (14 + 2𝑦)(14 + 2𝑦)
𝑥 2 = 196 + 28𝑦 + 28𝑦 + 4𝑦 2
𝑥 2 = 196 + 56𝑦 + 4𝑦 2
7. If x² - y² = 264 and x - y = 6 then x + y = __________.
a.
b.
c.
d.
32
44
9
81
The answer is letter B. This is a special product
question. Remember this
𝑥 2 − 𝑦 2 = (𝑥 + 𝑦)(𝑥 − 𝑦)
6
𝑥 2 − 𝑦 2 = 264
(𝑥 + 𝑦)(𝑥 − 𝑦) = 264
(𝑥 + 𝑦)(6) = 264
factor
substitute 6 for x – y because x – y =
(𝑥 + 𝑦) = 44
𝑑𝑖𝑣𝑖𝑑𝑒 𝑏𝑜𝑡ℎ 𝑠𝑖𝑑𝑒𝑠 𝑏𝑦 6
8. If the
two.
a.
b.
c.
d.
first integer is 2x + 1, then find the sum of the next
x-5
x+5
4x + 5
4x - 5
The answer is letter C. Finding the INTEGERS,
remember the following terms when dealing with number
problems.
CONSECUTIVE INTEGERS:
CONSECUTIVE ODD/EVEN
INTEGERS:
Let
Let
Let
Let
x
x
x
x
be the first integer
+ 1 be the 2nd integer
+ 2 be the 3rd integer
+ 3 be the 4th integer
and so on…
Let
Let
Let
Let
x
x
x
x
be the first integer
+ 2 be the 2nd integer
+ 4 be the 3rd integer
+ 6 be the 4th integer
and so on…
For integers, we add 1 for the next integer, so if the first
integer is 2x + 1, then the next two integers would be
2x +1 + 1 = 2x + 2
2x + 2 + 1 = 2x + 3
Their sum is
2x + 2 + 2x + 3
=
4x + 5
9. The product of the first two of the seven consecutive
positive odd integers is 99. Find the sum of the fifth and the
seventh integers.
a.
b.
c.
d.
76
38
93
8
The answer is letter B. Finding the INTEGERS,
remember the following terms when dealing with number
problems.
CONSECUTIVE INTEGERS:
Let
Let
Let
Let
x
x
x
x
be the first integer
+ 1 be the 2nd integer
+ 2 be the 3rd integer
+ 3 be the 4th integer
and so on…
CONSECUTIVE ODD/EVEN
INTEGERS:
Let x be the first integer
Let x + 2 be the 2nd integer
Let x + 4 be the 3rd integer
Let x + 6 be the 4th integer
and so on…
192 | L E T - R e v i e w e r – G e n e r a l E d u c a t i o n
FOR ODD and EVEN integers, we add 2 for the next
integer, so if the first ODD integer is 4x – 7 , then the next
odd integers would be
x
x
x
x
x
x
x
+
+
+
+
+
+
2
4
6
8
10
12
1ST
2ND
3RD
4TH
5TH
6TH
7TH
The product of the first two integers is 99.
x(x + 2) = 99
𝑥 2 + 2𝑥 = 99
expand
𝑥 2 + 2𝑥 − 99 = 0
transpose 99
(𝑥 + 11)(𝑥 − 9) = 0
factor
𝑥 + 11 = 0
𝑥−9=0
equate each factor to zero
𝑥 = −11
𝑥=9
simplify
Disregard -11 because we are ask of the POSITIVE
integers.
x
x
x
x
x
x
x
+
+
+
+
+
+
2
4
6
8
10
12
9
11
13
15
17
19
21
So the sum of the 5th and the 7th integers is 17 + 21 =
38
10. What is the slope of the line perpendicular to 3x + 2y =
6.
a.
b.
c.
d.
2
2/3
-3/2
-2
The answer is letter C. Change the given equation into
slope-intercept form y = mx + b, where m is the slope.
3x + 2y = 6
2y = -3x + 6
2
−3
6
y= 2x+2
2
y=
−3
2
x+3
The slope 𝑚 =
transpose 3x
divide both sides by 2
simplify
−3
2
11. What is the slope of the line parallel to 2x – 3y = 8.
a.
b.
c.
d.
2/3
3/2
-3/2
-2
The answer is letter A. Change the given equation into
slope-intercept form y = mx + b, where m is the slope.
Parallel lines have the same slope.
2x – 3y = 8
– 3y = -2x + 8
−3
−2
8
y
=
x
+
−3
−3
−3
2
8
y = 3x− 3
transpose 2x
divide both sides by -3
simplify
2
The slope 𝑚 = 3
12. The
a.
b.
c.
d.
inverse of the function f(x) = 7x + 4 is ___________.
f -1(x) = (y – 4)/7
f-1(x) = (x + 4)/7
f-1(x) = (y + 4)/7
f-1(x) = (x – 4)/7
The answer is letter D. Finding the inverse,
f(x) = 7x + 4
194 | L E T - R e v i e w e r – G e n e r a l E d u c a t i o n
y = 7x + 4
x = 7y + 4
x – 4 = 7y
𝑥−4
7𝑦
=
7
7
𝑥−4
7
f(x) = y
interchange the x and the y
transpose 4
divide both sides by 7
=𝑦
simplify
𝑥−4
= f-1(x)
f-1(x) = y
7
13. If 3x + 2 is the 6th integer, then the sum of the 9th and
the 11th integers is _______________.
a.
b.
c.
d.
6x - 33
6x + 33
6x + 12
6x -23
The answer is letter C. Finding the INTEGERS,
remember the following terms when dealing with number
problems.
CONSECUTIVE INTEGERS:
Let
Let
Let
Let
x
x
x
x
be the first integer
+ 1 be the 2nd integer
+ 2 be the 3rd integer
+ 3 be the 4th integer
and so on…
CONSECUTIVE ODD/EVEN
INTEGERS:
Let x be the first integer
Let x + 2 be the 2nd integer
Let x + 4 be the 3rd integer
Let x + 6 be the 4th integer
and so on…
For integers, we add for the next integer, so if the 6th
integer is 3x + 2 , then the next integers would be
3x + 2
3x + 3
3x + 4
3x + 5
3x + 6
3x + 7
6th
7th
8th
9th
10th
11th
the sum of the 9th and the 11th integers is
3x + 5 + 3x + 7 = 6x + 12
14.Find the value of the expression 4a + 2x + d when a = 7,
x = -2 and d = 4.
a.
b.
c.
d.
23
28
56
78
The answer is letter B. Substituting the values on the
given expression,
4a + 2x + d = 4(7) + 2(-2) + 4 = 28 – 4 + 4 = 28
15. If (a + b)² =
________________.
a.
b.
c.
d.
64,
and ab
=
3, then a²
+
76
58
82
13
The answer is letter B. Expanding the equation,
(a + b)² = 64
(a + b)(a + b) = 64
a² + ab + ab + b² = 64
a² + 3 + 3 + b² = 64
a² + 6 + b² = 64
a² + b² = 64 – 6
a² + b² = 58
16. Find the sum of the first 22 positive odd integers.
196 | L E T - R e v i e w e r – G e n e r a l E d u c a t i o n
b² =
a.
b.
c.
d.
564
648
253
484
The answer is letter C. The first 22 positive integers
are (1, 2, 3,…, 21, 22)
Getting the sum,
𝑛
(𝑡ℎ𝑒 𝑓𝑖𝑟𝑠𝑡 𝑡𝑒𝑟𝑚 + 𝑡ℎ𝑒 𝑙𝑎𝑠𝑡 𝑡𝑒𝑟𝑚)
2
22
(1 + 22)
𝑆22 =
2
𝑆22 = 11(23)
𝑺𝟐𝟐 = 𝟐𝟓𝟑
𝑆𝑛 =
17. Find the sum of the first 100 positive even integers.
a.
b.
c.
d.
10,100
9,550
9,505
10,500
The answer is letter A. The first 100 positive even
integers are (2, 4,…, 198, 200).
There are 100 integers from 2 to 200. Getting the sum,
𝑛
(𝑡ℎ𝑒 𝑓𝑖𝑟𝑠𝑡 𝑡𝑒𝑟𝑚 + 𝑡ℎ𝑒 𝑙𝑎𝑠𝑡 𝑡𝑒𝑟𝑚)
2
100
(2 + 200)
𝑆100 =
2
𝑆100 = 50(202)
𝑺𝟏𝟎𝟎 = 𝟏𝟎, 𝟏𝟎𝟎
𝑆𝑛 =
18. Find the sum of the first 50 positive even integers.
a. 3,500
b. 2,550
c. 3,550
d. 2,500
The answer is letter B. The first 50 positive even
integers are (2, 4,…, 98, 100).
There are 50 integers from 2 to 100. Getting the sum,
𝑛
(𝑡ℎ𝑒 𝑓𝑖𝑟𝑠𝑡 𝑡𝑒𝑟𝑚 + 𝑡ℎ𝑒 𝑙𝑎𝑠𝑡 𝑡𝑒𝑟𝑚)
2
50
(2 + 100)
𝑆50 =
2
𝑆50 = 25(102)
𝑺𝟓𝟎 = 𝟐, 𝟓𝟓𝟎
𝑆𝑛 =
19. Find the sum of all positive even integers between 40 to
60 inclusive.
a.
b.
c.
d.
750
650
450
550
The answer is letter D. The positive even integers are
(40, 42,…, 58, 60).
There are 11 integers from 40 to 60. Getting the sum,
𝑛
(𝑡ℎ𝑒 𝑓𝑖𝑟𝑠𝑡 𝑡𝑒𝑟𝑚 + 𝑡ℎ𝑒 𝑙𝑎𝑠𝑡 𝑡𝑒𝑟𝑚)
2
11
(40 + 60)
=
2
11
(100)
=
2
𝑆𝑛 =
𝑆11
𝑆11
𝑺𝟏𝟏 = 𝟓𝟓𝟎
198 | L E T - R e v i e w e r – G e n e r a l E d u c a t i o n
20. Let f(x) = 3x² - 2x + 5 and g(x) = 2x + 1, find (f + g)(-2).
a.
b.
c.
d.
15
16
17
18
The answer is letter D. Add the functions,
f(x) + g(x) = 3x² - 2x + 5 + 2x + 1 = 3x² + 6 = 3(-2)² + 6 =
3(4) + 6 = 18
21. Let f(x) = 3x² - 5 and g(x) = 2x + 1, find (f • g)(-1).
a.
b.
c.
d.
2
18
11
6`
The answer is letter A. Multiply the functions,
f(x)•g(x) = (3x² - 5)(2x + 1) = 6𝑥 3 + 3𝑥 2 − 10𝑥 − 5
= 6(−1)3 + 3(−1)2 − 10(−1) − 5 = −6 + 3 + 10 − 5 = 2
22. The sale price of a camera after a 20% discount is 7,200.
What was the price before the discount?
a.
b.
c.
d.
5760
1,440
9,000
8,640
The answer is letter C. The price which is 7,200 is the result
when the original price is deducted with 20% of the original
price. This means that 7,200 is just 80% of the original
price. This is where we start solving the problem.
80%(original price) = 7,200
0.8(x) = 7,200
x = 7,200 ÷ 0.08
x = 9,000 is the original price
23. Which of the following is a real number?
a.
b.
c.
d.
a + bi, b ≠ 0
2 + 0i
2 + 3i
3 + 8i
The answer is letter B. Letter A has the imaginary part
of b, letter C has 3. Letter D has 8 imaginary part,
letter B has an imaginary part of 0 so it translates to 2
+ 0i = 2 which is a real number.
24. Which of the following is equal to zero?
a.
b.
c.
d.
4 – 4i
0 + 0i
0 – 3i
-3 + 3i
The answer is letter B.
25. How many multiples of 20 are there in the first 100
positive even integers inclusive?
a.
b.
c.
d.
10
5
7
9
The answer is letter A. The first 100 positive even
integers are
2, 4,…,198,200..
The multiple of 20 are 20, 40, 60, 80, 100,
120,140,160,180, 200
200 | L E T - R e v i e w e r – G e n e r a l E d u c a t i o n
There are 10 of them.
26. Which of the following is not a pure imaginary number?
a.
b.
c.
d.
0 – 3i
2 + 2i
8 – 11i
1 + 0i
The answer is letter D. Letter A has the imaginary part
of -3, letter B has the imaginary part of 2, letter C has
-11. Letter D has 0 imaginary part so it translates to 1
+ 0i = 1
27. Which of the following is not a complex number?
a.
b.
c.
d.
0 – 3i
2 + 2i
8 – 0i
0 + 4i
The answer is letter C. Letter A has the imaginary part
of -3, letter B has the imaginary part of 2, letter C has
0. Letter D has 4 imaginary part.
28. What is 104% of 740?
a.
b.
c.
d.
790.66
769.60
967.90
679.60
The answer is letter B. Change the percentage into
decimal number and multiply it to 740.
1.04(740) = 769.60
29. Express 2,600 in scientific notation.
a.
b.
c.
d.
2.6 x 10²
26 x 10²
2.6 x 10³
0.26 x 10³
The answer is letter C. there are 3 decimal places until
the first non-zero digit.
30. Express 0.00387 in standard form.
a.
b.
c.
d.
3.87 x 10²
3.87 x 10
3.87 x 10³
3.87 x 10−3
The answer is letter D. There are 3 decimal places until
the first non-zero digit.
31. Express 1.96 x 10−9 in expanded form.
a.
b.
c.
d.
0.00000000196
196,000,000
19,600,000
0.000000196
The answer is letter A. There are 9 decimal places until
the first non-zero digit.
32. The population of Manila in 2005 was 5.68 million. The
population in 2006 was lower by 325,000. What was the
population in 2006?
a. 5.355 million
202 | L E T - R e v i e w e r – G e n e r a l E d u c a t i o n
b. 5.553 million
c. 3.555 million
d. 5.535 million
The answer is letter A. Subtract 325,000 from 5.68
million.
33. How many grams are there in 2.03 kilograms?
a.
b.
c.
d.
203 grams
20,300 grams
2,030 grams
200,300 grams
The answer is letter C. There are 1000 grams in a
kilogram. Multiply them 1000 grams x 2.03 kg = 2,030
grams
34. Given that 32.6 x 145 = 4,727, find the exact value of
3.26 x 0.145.
a.
b.
c.
d.
4.727
47.27
472.7
0.4727
The answer is letter D.
35. Express 7/20 as percentage.
a.
b.
c.
d.
7%
35%
14%
28%
The answer is letter B. Divide it. The result is
multiplied by 100.
7/20 = 0.35 x 100 = 35%
36. A man earns 15,000 per month. If he receives his
13th month pay and a bonus equivalent to 150% of his
monthly salary, calculate his total annual salary?
a.
b.
c.
d.
218,000
217,500
217,000
216,500
The answer is letter B.
13 months x 15,000 = 195,000
150% (15000) = 22,500
195000 + 22500 = 217,500
37. Given that 22.5 x 225 = 5,062.5, find the exact value of
0.225 x 2.25.
a.
b.
c.
d.
5.0625
50.625
0.50625
0.050625
The answer is letter C.
38. There are 6,000 people in a village. 30% of the people are
men, and 32% are women. What is the total number of
children in the village?
a.
b.
c.
d.
2,280
2,180
2,380
2,820
The answer is letter A. Take the number of women and
men,
Men
30%(6000) = 1800
204 | L E T - R e v i e w e r – G e n e r a l E d u c a t i o n
Women 32%(6000) = 1920
6000 – 1800 – 1920 = 2,280
39 A bike was bought at 3,250 pesos and sold at 20% profit.
What was the cost price of the bike?
a.
b.
c.
d.
3,700
3,800
3,900
4,000
The answer is letter C. The total price is 3250 which is
100% plus 20% of the price. So, The total price is
120% of the original price
120%(3250) =1.2(3250) =3,900
40. A jacket was sold at 550 pesos after a loss of 15%, what
was the cost price of the jacket?
a.
b.
c.
d.
647.50
647.60
647.06
647.40
The answer is letter C. Since 550 was sold after a loss
of 15%, therefore 550 is just 85% of the original price.
85% (x) = 550
x = 550 ÷ 0.85 = 647.06
41. If I paid 225 pesos for an article after a discount of 15%,
then what was the marked price?
a.
b.
c.
d.
264.71
274.73
284.75
294.77
The answer is letter A. Since 225 was sold after a loss
of 15%, therefore 225 is just 85% of the original price.
85% (x) = 225
x = 225 ÷ 0.85 = 264.71
42. A businessman bought a product for 1,600 and sold it at
6% profit. How much did he earn?
a.
b.
c.
d.
94
95
96
97
The answer is letter C.
6%(1600) =0.06(1600) = 96
43. A 650-peso polo shirt was sold at 18% discount plus 5%
sales tax. How much did the customer pay for the product?
a.
b.
c.
d.
559.85
559.25
559.90
559.65
The answer is letter D. Get the selling price plus 5% of
the selling price.
650 (18%) = 650(0.18) = 117
650 – 117 = 533
selling price
533(5%) = 533(0.05) = 26.65
The total price plus sales tax = 533 + 26.65 = 559.65
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44. A pair of shoes costs 1,250. How much will the
customer pay if there is a 10% discount to be deducted plus
12% VAT?
a.
b.
c.
d.
1,230
1,240
1,250
1,260
The answer is letter D. Get the selling price plus 5% of
the selling price.
1250 (10%) = 1250(0.1) = 125
1250 – 125 = 1125
selling price
1125(12%) = 1125(0.12) = 135
The total price plus sales tax = 1125 + 135 = 1,260
45. A finance company charges 5% annual simple interest
on a car loan of 750,000 pesos for five years. How much
interest is payable?
a.
b.
c.
d.
185,500
186,500
187,500
188,500
The answer is letter C. Take the 5% interest a year
then multiply it by 5.
750,000 (0.05) = 37,500 x 5years = 187,500
PART II
1. If the scores in mathematics test of 61 students are
arranged from the highest to the lowest, the 31st score is the
___________.
a. mode
b. median
c. mean
d. standard deviation
The answer is letter B. Remember that there are 30
scores (1~30) before 31th score and there are also 30 scores
(32~61) after it. Since the 31th score is the middlemost
datum, then it is the median of the set of data.
2. The vertex angle of an isosceles triangle is 45 degrees.
What is the measure of one of the base angles?
a. 64.5 degrees
b. 65.5 degrees
c. 66.5 degrees
d. 67.5 degrees
The answer is letter D. Take note that the total
internal angle measure of a triangle is 180 degrees. In the
question it says that the triangle is an isosceles triangle. In
an isosceles triangle, the two legs are congruent as well as
the base angles.
Too get X,
180 – 45 = 135
135 ÷ 2 = 67.5
45
X
X
208 | L E T - R e v i e w e r – G e n e r a l E d u c a t i o n
3. What number is next to the sequence 23450, 23850,
24250, 24650.
a. 24850
b. 24950
c. 25050
d. 25150
The answer is letter C. The next term is obtained by
adding 400 to the preceding term.
4. What value of x will make the proportion correct? 12:x =
2.4:5
a. 15
b. 20
c. 25
d. 30
The answer is letter C. In proportion, multiply the
means (x and 2.4) and equate it with the product of the
extremes (12 and 5).
x (2.4) = 12 (5)
2.4x = 60
x = 25
simplify
dividing both side by 2.4
5. There are 70 men in a committee consisting of 120
members. What is the ratio of women to the men?
a. 3:7
b. 4:5
c. 5:6
d. 5:7
The answer is letter D. the total members of the
committee is 120 of which 70 are men. So, 120 – 70 = 50.
There are 50 women.
The ratio of women to men is 50:70 or 5:7.
6. A letter is picked at random from the English alphabet.
What is the probability that the letter is contained in the
word “great”?
a. 4/26
b. 5/26
c. 5/13
d. 4/13
The answer is letter B. There are 26 letters in an
English alphabet. There are 5 letters in the word GREAT. So
the probability is 5/26.
7. A vehicle consumes 2.5 liters of gasoline to travel 30
kilometers. To the nearest tenth, how many liters of gasoline
will it take for the vehicle to travel 418 kilometers?
a. 31.83L
b. 32.83L
c. 33.83L
d. 34.83L
The answer is letter D. This is a ratio and proportion
problem, so to solve,
2.5 : 30 = x : 418
30x = 418(2.5)
30x = 1,045
x = 34.83
8. What is the equivalent fraction of the decimal 0.725?
a.
b.
c.
d.
2/29
29/40
30/40
29/30
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The answer is letter B. Changing a decimal number
into fraction is to remove the decimal point and divide the
number by a number with zeros which is determined by the
number of decimal places that the decimal number have.
0.725 has 3 decimal places and the number with three zeros
is 1000. So
0.725 =
29(25)
29(25)
725
29
=
=
=
1000
40
40(25)
40(25)
9. 24% of 6400 = _____
a. 1,236
b. 1,336
c. 1,436
d. 1,536
The answer is letter D. Translate the English sentence
into mathematical equation, we have
24% of 6,400 = x
0.24 of 6,400 = x
0.24 (6,400) = x
1,536 = x
10. What percent of 650 is 13?
a. 1%
b. 2%
c. 3%
d. 4%
The answer is letter B. In answering this type of
percentage problem (asking for percentage), just 13 by 650
(ALWAYS). Translating the sentence,
x% of 650 is 13.
x (650) = 13
of means multiplication, and is means
equals
x = 13 ÷ 650
x = 0.02
x% = 2%
dividing both sides by 650
simplify
multiply by 100 to get the percentage
11. What number is 70% of 3,400?
a. 2,180
b. 2,280
c. 2,380
d. 2,480
The answer is letter C. To answer this type of
percentage question,
Change the percentage into decimal number, then
multiply them.
x = 70% (3,400)
x = 0.7 (3,400)
x = 2,380
212 | L E T - R e v i e w e r – G e n e r a l E d u c a t i o n
12. What is the equivalent decimal form of 650/900?
a. 11/18
b. 17/18
c. 1/19
d. 13/18
The answer is letter D. Simplify the fraction into
simplest form. Determine the common factor of
both the numerator and the denominator and
cancel it. In this problem, the common factor is
50.
650
900
650÷50
13
= 900 ÷50 = 18
13. What is the sum of the factors of 24?
a. 60
b. 61
c. 62
d. 63
The answer is letter A. Identify all the factors of 24.
The factors of 24 are {1,2,3,4,6,8,12,24}, so
1
+ 2 + 3 + 4 + 6 + 8 + 12 + 24 = 60
14. The difference of two numbers is 40. Their sum is
80. Find the two numbers.
a.
b.
c.
d.
21 and 59
20 and 60
19 and 61
18 and 62
The answer is letter B. This is a number problem
and is being solved this way,
Let x be the 1st number
Let y be the 2nd number
The difference of two numbers is 40 == x – y = 40
Their sum is 80 == x + y = 80
Solving by elimination method,
x – y = 40
x + y = 80
2x = 120
x = 60
Solving for y when x = 60,
x + y = 80
60 + y = 80
y = 80 – 60
y = 20
214 | L E T - R e v i e w e r – G e n e r a l E d u c a t i o n
15. What is ½ of the 50% of 250?
a.
b.
c.
d.
62.5
72.5
52.5
82.5
The answer is letter A. Multiply all data given,
½ (50%)(250) = ½ (0.5)(250) = 62.50
16. What is the product of a number and its reciprocal?
a. 0
b. 1
c. 2
d. 3
The answer is letter B. To solve, let the number be x.
It’s reciprocal is 1/x
1
𝑥
𝑥
𝑥
𝑥 ( )= =1
17. What number completes the sequence?
320,440,560,______,800
a.
b.
c.
d.
580
600
640
680
The answer is letter D. each term is taken by adding
120 to the preceding term. So, 560 + 120 = 680
18. If a box contains 9 yellow, 5 black, and 14
green balls. Find the probability of getting green.
a. 0.35
b. 0.14
c. 0.5
d. 0.55
The answer is letter C. The total number of balls
is 28.
The probability =
𝑔𝑟𝑒𝑒𝑛
𝑡𝑜𝑡𝑎𝑙 𝑛𝑢𝑚𝑏𝑒𝑟 𝑜𝑓 𝑏𝑎𝑙𝑙𝑠
=
14
28
= 0.5
19. Which of the following must be true about the sum of
all the prime numbers between 20 and 30?
a. It is a prime number.
b. It is an odd number.
c. It is a factor of 156
d. It is a multiple of 5
e. It is a factor of 10
Answer is C
23 and 29 are the only prime numbers between 20 and
30
23+29=52
52 x 3 = 156
This shows that 52 is a factor of 156
216 | L E T - R e v i e w e r – G e n e r a l E d u c a t i o n
20. At a dinner party each table can seat eight people. If
100 people attend the party, what is the minimum
number of tables that are needed?
a. 12
b. 13
c. 14
d. 15
e. 16
Answer is B
Divide the number of people at the party by the number
of seats around each table
100÷ 8 = 12.5
Thirteen tables will be needed to seat all 100 people
21. What is the greatest integer that evenly divides both
48 and 64?
a. 12
b. 16
c. 24
d. 6
e. 8
Answer is B
The largest integer that evenly divides both 48 and 64 is
the GCF of the two numbers. The factors of 48 are
{1,2,3,4,6,8,12,16,24,48}
The factors of 64 are {1,2,4,8,16,32,64}. The GCF is 16
22. When x is divided by 8, the remainder is 3. What is
the remainder when 4x is divided by 8?
a. 1
b. 2
c. 3
d. 4
e. 5
Answer is D
Try an example. Choose 3 for x.
3 divided by 8 leaves a
remainder of 3. Multiply 3 × 4=12
12 divided by 8 leaves a remainder of 4
23. Let x, y, and z be positive integers such that y is a
multiple of x and z. All of the following statements are
true except for:
a. y z is a multiple of x
b. x is a factor of y
c. x z is a factor of y
d. z divides evenly into y
e. x divides evenly into y z
Answer is C
Note that this item asks for the choice that is NOT true
We know y is a multiple of x and z. That means y times
any number is also a multiple of x, so choice A must be true.
Also, because we know y is a multiple of x and z, this
means that x and z divide evenly into y, so choices B, D and
E are true.
The process of elimination leaves choice C.
Use an example to check this. Let x = 3, y = 12, and z = 6. y
is a multiple of x and z, but x z = 18 is not a multiple of y =
12
24. When a two-digit number is divided by 5 the remain-der
is 2. Which of the following statements must be true about
the two-digit number?
a. The sum of all the digits is odd
b. The digit in the one’s place is odd
c. The number is prime
d. The number is odd
e. The digit in the one’s place is prime
Answer is E
218 | L E T - R e v i e w e r – G e n e r a l E d u c a t i o n
The two-digit numbers that have a remainder of 2 when
divided by 5 are
{12,17, 22, 27, 32, 37, 42, 47, 52, 57, 62, 67, 72,
77,82,87, 92, 97}. Only choice E is always true, the one’s
digit is prime
Don’t be fooled because some of the answers are true
sometimes. For example, in choice (A) the sum of all digits is
odd.
This is true if the two-digit number is 32. The sum of the
digits 3 2 5 is odd. But choice (A) is not always true.
If the two digit number is 42, the sum of the digits 4 2
6 is not odd.
25. How many distinct composite numbers can be formed by
adding 2 of the first 5 prime numbers?
a. 3
b. 4
c. 5
d. 6
e. 7
The answer is A.
The first 5 prime numbers are {2,3,5,7,11}
Adding pairs of them, we have
2+3 = 5
2+11=13
2+5=7
2+7=9
3+5=8
3+7=10
3+11=14
5+7=12
5+11=16
7+11=18
5, 7, and 11 are prime numbers.
8, 9, 10, 12, 14, 16, and 18 are composite numbers
26. Alice is three more than twice Tom’s age. If Tom is 15
years old, how old is Alice?
a. 30
b. 31
c. 32
d. 33
The answer is letter D. Write an equation to describe the
relationship.
A be Alice’s age; T be Tom’s age: A = 3 + 2T
Substitute 15 for T and solve for A. 3 + 2(15)= 3 + 30 = 33
27. A store is having a sale on all items for 20% off the
original price. If x represents the original price of an item,
what expression represents the sale price of the item?
a. 0.20x
b. 0.08x
c. 0.8x
d. 0.02x
The answer is letter C. A 20% discount means an item
costs 80% of its original price.
0.80x
28. At the end of the school year, Anthony was 66
inches tall. When he came back from summer break for
school this year he was 6 feet tall. What percentage has
Anthony’s height increased since the end of last school year?
a. 0.99%
b. 9.99%
c. 9.09%
d. 99.9%
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The answer is letter C. First convert 6 feet into 72
inches. Therefore, Anthony went from 66 inches to 72
inches.
Divide the height difference by the original height.
Percent increase =
72−66
66
6
= 66≈ 9.09 %
29. On Tuesday Ray rode his bike 10 miles. On
Wednesday he increased Tuesday’s distance by 5 miles. On
Thursday he decreased Wednesday’s distance by 7 miles. On
Friday he increased Thursday’s distance by 12 miles. How
many total miles did Ray ride over the 4-day period?
A.
B.
C.
D.
E.
50
51
52
53
54
Answer: D
Days
Tuesday
Wednesday
Thursday
Friday
Total
Miles
10
10+5=15
15-7=8
8+12=20
10+15+8+20=53
30. 4 times x is equal to x increased by 6. x =
A. 1
B. 2
C. 3
D. 4
E. 5
Write an equation that describes the relationship. 4x
=x+6
Solve for x. 3x = 6 ⇒ x = 2
31. 2 times x plus 6 is equal to 5 times x less 3. x =
A. 1
B. 2
C. 3
D. 4
E. 5
Write an equation that describes the relationship. 2x
+ 6 = 5x – 3
Solve for x. 9 = 3x ⇒ 3 = x
32. 40% of the students in a class are female. If there are 10
females in the class, how many males are there in the class?
A.
B.
C.
D.
E.
5
10
15
20
25
Answer: C
Let x = total number of students in class.
Find the total number of students. 0.4x = 10 ⇒ x = 25
10 of the students are females, 25 − 10 = 15 of the
students are males
222 | L E T - R e v i e w e r – G e n e r a l E d u c a t i o n
33. Lindsey earns $15 hour for the first 40 hours she works
in a week and 50% more for every hour over 40. How many
hours did Lindsey work in a week, when she was paid
$937.50 before taxes?
A. 15hours
B. 30hours
C. 40hours
D. 45hours
E. 55hours
Answer: E
If Lindsey worked 40 hours, she would earn 40 × $15 =
$600.
So, $937.50 − $600 = $337.50 of her pay was from
overtime, when she earned $15 × 1.5 = $22.5 per hour.
That means she worked 337.5= 15 hours of overtime
She worked a total of 40 + 15 = 55 hours.
34. Tim earns $2,000 more a year than Pete. If Pete gets a
5% raise, their earnings would be equal. How much money
does Pete earn a year?
A.
B.
C.
D.
E.
35,000
40,000
45,000
50,000
55,000
Answer: C
Let t = Amount Tim earned.
Let p = Amount Pete earned.
Write two equations to represent the relationships
described in the problem.
t = p + 2,000 and t = 1.05 p.
Substitute 1.05p for t in the first equation.
1.05p = p + 2,000 ⇒ 0.05p = 2,000 ⇒ p = $40,000.
ANALOGY: SINGLE WORD APPROACH
1. c
2. c
3. b
4. a
5. d
6. d
7. b
8. b
9. d
10. d
11.
12.
13.
14.
15.
16.
17.
18.
19.
20.
d
d
c
d
d
c
a
d
d
a
21.
22.
23.
24.
25.
26.
27.
28.
29.
30.
a
c
b
d
d
a
c
d
d
b
31.
32.
33.
34.
35.
36.
37.
38.
39.
40.
b
a
a
c
a
b
b
b
a
a
224 | L E T - R e v i e w e r – G e n e r a l E d u c a t i o n
41.
42.
43.
44.
45.
46.
47.
48.
49.
a
c
b
c
c
c
d
d
b