GRE Sample
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Vocabulary
Builder
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GRE Sample
EFFECTIVE WAYS OF LEARNING VOCABULARY
Do you remember the popular scene from the movie ‘V for Vendetta’ where the protagonist utters
a dialogue with a deluge of words starting with ‘V’? Would you really enjoy the scene if you did not
understand a word he said? You would rather take him for a crazy person like the lady in the scene
does.
What should you do to get equipped with enough vocabulary to probably give an exemplary speech
or watch and enjoy a vivified movie full of complex vocabulary or write a flowery love letter to your
beloved one?
Here are few ways that people suggest to build good vocabulary.
1. Flash cards.
2. Word lists.
3. Contextual vocabulary.
4. Reading books/ novels/ newspapers/ magazines.
5. Watching movies.
6. Dictionary.
7. Conversing a lot in English.
8. Playing Scrabble.
9. Solving Crosswords.
10. Dumb charades.
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But seriously, do you think you can learn vocabulary by mugging up all the words in the dictionary or
having a dictionary every time you read a small essay in a magazine?
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At Abhyaas, we believe in four very powerful techniques to learn vocabulary. Let’s try to see what
they are and learn to implement them in our pursuit of a better vocabulary.
1.
2.
3.
4.
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Etymology, Root Words, Prefixes and Suffixes.
Contextual Vocabulary.
Visual Vocabulary.
Word Bridges.
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GRE Sample
ETYMOLOGY, ROOT WORDS, PREFIXES AND SUFFIXES
Etymology deals with the origin of the words. One of the most effective ways to learn vocabulary is
to understand the roots of the word. Each word has a root which can be either a prefix or a suffix.
These roots are derived from various languages like the Greek, Latin, French and even our own
Sanskrit. Each root gives you the hint (or in some cases story behind the word) to guess what the
meaning of a particular word could be. Below given is a list of few root words and the words that
originate from them.
ambi
:
ante
:
anti
:
auto
:
bene
:
brevis :
bellum :
bi
:
biblios :
bio
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:
circum :
credo :
dis(dif,di) :
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eu
:
extra
:
both
ambiguous, ambidextrous, ambivalent
before
antedate, anteroom
against
antipathy, antagonist
self
autocrat, autobiography
well
beneficent, benevolent, benefactor
short
brevity, abridge, abbreviate
war, rebellious
belligerent, bellicose
two
binoculars, bicameral, bigamy
a book
bibliophile, bibliomaniac, bibliography
life
biology
around
circumspect, circumnavigate, circuitous
belief
credulous, credible
apart
disjoin, differ
well
eulogy, euphony, eugenics
beyond, outside of
extravagant, extraordinary, extrapolate
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GRE Sample
STORIES BEHIND FEW WORDS AND PHRASES
Hazard: The word comes from the Arabic al-zahr, which means the dice. In the Western Europe
the term came to be associated with a number of games using dice, which were learned during the
crusades whilst in the Holy Land. The term eventually took on the connotation of danger because,
from very early on, game suing dice were associated with the risky business of gambling and con
artists using corrupted dice.
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Alcohol: The word comes from the Arabic al-kuhl, which originally meant a very fine powder of
black lead which was used for eye makeup. It was obtained by the process of distillation or very
high refining and thus alcohol which is one of the very refined products was thus named.
Hobson’s choice: Tobias Hobson was a Cambridge stable manager who lent horses. He insisted
that the customers take the horses in the stall closest to the door or take none at all. Hence, the
meaning of Hobson’s choice is almost no choice at all.
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Henry Ford almost gave no choice to his customers. When he introduced the first set of ford cars,
he said to the customers, “You can get a car of any colour as long as it is black”. Isn’t that a
quintessential example of Hobson’s choice?
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Hat trick: The term originated from the most famous sport in our country, cricket. In England,
when the bowler took three wickets in three successive balls, a hat was presented by the club
commemorating the effort. The same spread into different sports.
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Villain: Would you believe that the roots of the word villain are from the word village? Seems, odd
right? Long ago, in England, there was a distinct separation of the class and the common folk. The
people who worked in the fields, the villagers, were thought of as beneath the nobility and were
associated with theft from the noble. Hence, a sense of bad person came to be associated with the
people from villages. While in the present context, villains are no longer considered to be people
from the villages, the association of the person being bad remained with the word.
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Tongue in cheek: The commonly used phrase meaning ‘to speak insincerely’, comes from the
habitual gesture of Old ages where it was a practice to signal disregard for someone or something by
making a bulge in your cheek using your tongue.
Let the cat out of the bag: To let the cat out of the bag is to reveal a secret. In olden days, artful
traders substituted a pig suckling with a cat and placed that in a bag so that the customer would not
notice it. If the cat jumped out of the bag, then the secret was out.
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GRE Sample
CONTEXTUAL VOCABULARY
Contextual Vocabulary: As the name suggests it is about understanding the meaning of a word
based on the context.You can guess the meaning of the word based on some clues.
Example : The couple finally secured a table at the popular, crowded restaurant.
What comes into your mind when you think of the word secured ?
Secured first rank
obtained
Secured 100 marks
scored
Is your house secure? insured/safe
Is the car door secure? locked
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But in the above example we are talking about “secured a table” which means the couple was finally
able to get a table and sit and have food.
Clue: Since the words have multiple meanings -understand the meaning based on the
given situation.
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Example : The king’s laws were often arbitrary; in other words, he made rules based on how he felt
at the moment.
“in other words” connects "arbitrary" and "he is making rules based on what he felt at the moment."
Clue: Look for a word that is synonym to the given unknown word.
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Example : David was very outgoing as opposed to his coy older sister.
As opposed to means David’s character is opposite to that of his sister.
David is outgoing. His sister is not outgoing. So, coy means not outgoing.
Clue: Look for a word that is an antonym to the given unknown word.
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Example : Abhishek had to duck under the doorway as he walked into the room.
We know the word duck means a bird. We also know duck out in cricket.
But what does to duck here mean ?
We can infer that Abhishek is very tall and he has to bend under the doorway
Clue: A meaning may not be explicitly given, you have to infer it.
Understand the meaning of the italic word in the following sentences.
• The fisherman cast his line.
• The members of the cast took a bow.
• They put a cast on my broken arm.
• The yard is littered with shells cast off by - the cicadas.
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GRE Sample
ABDICATE: Abdicate the throne. Abdicate mains to relinquish throne formally (It can never
happen in the current politics). It is similar to give up. Antonyms will be related to take.
Hand over
Renounce
Relinquish
Abdicate
Seize
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Usurp
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Besiege(to try
for a long time)
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ABHOR: I abhor that man. You can never imagine humans without likes and dislikes. Abhor
means to detest, hate, reject. Antonyms will be related to like. You should understand the intensity
variation between dislike and hate.
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Abominate
(very
strong)
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Strong
dislike
Despise
Detest
Loathe
Odious
Aversion
(mild)
Hate
Abhor
Relish
Like
Approve
Adore
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Love
GRE Sample
THE HIGH IMPACT WORD LIST
Word
Meaning
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ABACUS (n)
a frame with balls for calculating
ABATE (v)
to lessen, to subside
* * ** * * * * ** * * * * ** * * * * ** * * * * ** * * * * ** * * * * ** * * * * ** * * * * ** * * * * ** * * * * ** * *
Usage: Though the current storm abated, the tourists feared the impending one.
***************************************************************
ABDICATION (n)
giving up control or authority
ABERRATION (n)
abnormality
ABET (v)
help or encourage to do something wrong
ABEYANCE (n)
suspended action
ABHOR (v)
to hate
***************************************************************
Usage: She loves dogs, but she abhors cats.
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ABIDE (v)
to endure, be faithful
ABJURE (v)
promise or swear to give up
*****************************************************************
Usage: After the chowri-chora incident, Gandhji abjured his non-cooperation movement.
*****************************************************************
ABRADED (v)
rubbed off, worn away by friction
ABROGATE (v)
nullify by authority
ABSCOND (v)
run away to avoid arrest
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Usage: The police are after the accountant who absconded with money from the bank.
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ABSTRUSE (adj)
difficult to under stand
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Usage: Geometry is not rocket science. Why do you find it so abstruse?
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ABUT (v)
border on
ABYSMAL (adj)
so deep as to be immeasurable
ACARPOUS (adj)
effete, no longer fertile, worn out
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Usage: The villagers despised her for being an acarpous woman.
*****************************************************************
ACCLAIMED (v)
welcomed with shouts and approval
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GRE Sample
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GRE
Verbal Ability
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GRE Sample
INTRODUCTION TO GRE VERBAL SECTION
Introduction to the Verbal Reasoning measure:
The Verbal reasoning measure assesses:
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Your ability to analyze and evaluate written material and synthesize information obtained
from it.
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Analyze relationship among the component parts of a sentence.
·
Recognize relationships among words and concepts.
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Verbal reasoning questions appear in several formats. Each of which is discussed later in this section.
About half the measure requires you to read the passage and answer questions on those passages.
The other half requires you to read, interpret and complete existing sentences, group of sentences,
or paragraphs. Most, but not all, of the questions are standard multiple-choice questions, the different
response patterns are:
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Select the correct option
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Select multiple correct options
·
Select the correct sentence from the paragraph
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The number of choices varies depending on the type of question.
Structure of Verbal Reasoning measure:
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The test has 2 sections of Verbal each of approximately 20 Questions per section. Time for each
section is 30 mins. The directions at the beginning of the section specifies, the number of questions
and time allowed for the section.
There will also be an unidentified unscored section which may be based on Verbal or Quant with
approximately 20 Questions and 30 - 35 mins per section.
Verbal/Quant/unscored sections may appear in any order.
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GRE Sample
SENTENCE EQUIVALENCE
Strategies for Sentence Equivalence
Sentence Equivalence questions test your ability to understand the sentence using a variety of clues
provided by syntax and grammar to recognize the overall meaning of a sentence. The clues can be
punctuation marks, conjunctions etc. You need to choose two words that best complete the blank.
Consider each answer choice carefully and decide which of the two choices complete the sentence
in a way that gives the sentence a logically satisfactory meaning that is same and allows it to be read
as a stylistically integrated whole. Remember that both the words should produce sentences that
mean the same thing.
Approaches to crack the questions
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1. Fill the blanks with your own words
Before reading the answer choices, you may find it helpful to fill in the blanks with a word or
words of your own that complete the meaning of the sentence. Then examine the answer choices
to see if one of them parallels your own completion of the sentence.
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Example: Our bookshelves at home display a range of books on wide-ranging subjects and in
many languages, reflecting the ____ tastes of our family members.
A. anomalous
D. arcane
B. limited
E. furtive
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C. diverse
F. eclectic
The sentence speaks about wide range of books. Thus, the family must have wide ranging
tastes. The blank takes in a word which indicates variety. So from the given options eclectic
which means taking things from a wide range of sources, must be the answer. So ‘eclectic’ and
‘diverse’ will be the answer (anomalous = abnormal; arcane = esoteric; furtive = stealthy)
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2. Read the sentence and understand the mood or tone
Adjectives and Adverbs in a sentence will help you to understand the mood or tone. For example,
Melancholy, dull, gloomy express a negative mood. Excited, enthusiastic etc express a positive
and happy tone. So, if you pay attention on words you can understand whether the tone is
sad, happy, sarcastic, ironic etc.
Example: Dejected by having performed poorly in the final match, Venniza began to question
her abilities. Her self confidence was _________
A. appeased
D. elevated
B. destroyed
E. sustained
C. placated
F. down
The word ‘dejected’ implies a negative tone. So the blank also indicates that her self confidence
is down. So ‘down’ and ‘destroyed’ will be the most suitable answers.
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GRE Sample
TEXT COMPLETION
Text completion questions test your ability to read, interpret, evaluate and reason from the content
you have read and guess the remaining information in the paragraph.
These questions will have one to five lines; and one to three blanks. If it has one blank then there will
be five options. Else for each blank there will be three options. You are required to construct a
meaningfully coherent paragraph.
Approaches to crack the questions
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1. Read through the passage to get an overall sense of it.
Certain keywords in a sentence give you an idea about the author’s tone, mood and style of
writing and helps you to make the correct guess for the possible answer.
Example: Women squat, heads covered, beside huge piles of limp fodder and __________ oil
lamps, and just above all the cows in the three towns converge upon this spot. Sinners, supplicants
and yes, even scallywags hand over a few coins for a crack at redemption and handful of grass.
A. shining
B. bright
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C. sputtering
D. effulgent
E. radiant
The words ‘squat’ , ‘beside limp fodder’ , ‘ sinners’, ‘redemption’ indicate a negative dull tone.
So shining, bright, radiant, effulgent do not fit. Sputtering is to make a noise as if spitting (light
popping sound of flame which is dying out).(Effulgent=radiant, refulgent)
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2. Think up your own words to fill the blanks
As human beings we have a natural tendency to force ourself to accept a particular option as an
answer, our inclination towards a word may not be correct. So first start with reading the paragraph,
guess the words in the blanks and then proceed to the options.
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Example: In parts of the Arctic, the land grades into the land fast ice so _______ that you can
walk off the coast and not know you are over the hidden sea.
A. permanently
B. imperceptibly
C. irregularly
D. precariously
E.slightly
The words ‘so’ ‘walk off coast’ gives you the clue. The ice on the sea is frozen and you can
walk on it without realizing the same. The word in the blank could be related to not knowingly.
So imperceptibly is the answer.(precariously = dangerously, not safe)
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GRE Sample
READING COMPREHENSION
Reading comprehension (RC) questions measure your ability to read with understanding, insight and
discrimination. This type of question explores your ability to analyze a written passage from several
perspectives. These include your ability to recognize both explicitly stated elements in the passage
and assumptions underlying statements or arguments in the passage as well as the implications of
those statements or arguments.
There will be around 10 passages throughout your exam. The topics will be varied. These questions
may have one option or more than one option correct. You will also be asked to highlight a particular
line in the paragraph that explains the given question.
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Let’s understand what can hinder your performance and what can boost your performance in RC.
How to improve reading
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To perform better in RC you have to read a lot and across various topics.
Reading speed is very important because the faster you read the less time you consume from the
total exam time. It also helps you to focus better and avoid distractions.
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Note: Reading fast alone is not sufficient, you have to be an active and effective reader.
Factors influencing Reading Speed:
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a. Eye span & fixation points
b. Vocalization & Sub vocalization
c. Mouse / Hand pointers
d. Regression
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a. Eye span & fixations: Eye-span is referred to the amount of text someone takes in at one
glance. The period of time during which an eye rests on a word is called fixation.
A speed reader reads many words in one fixation and moves on very quickly to the next set of
words.
Read the passage given below and realize the variation your reading speed.
As a child at the age of three, my sister and I had pictures taken together. My sister
and I are ten months and three weeks apart. In this special family picture
we look
identical.
Our big, dark blue and brown eyes
and smile resemble two
calm
little girls, enjoying the moment with peaceful smiles on our faces. In our long, dark
red and blue dresses we sit straight up in front of a warm red fireplace surrounded by green plants.
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GRE Sample
SE CLASS EXERCISE 4
1. If at all there’s one thing he can be ridiculed for, it’s for making some ______________bad
choices in his career that have resulted in some great flops of the millennium, but tell me of one
good actor who’s not made bad acting choices and I’ll take all my words back.
A. artificially
B. monumentally
C. enormously
D. trivially
E. arduously
F. implicitly
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2. The ________ little fact that the new age directors are only self-aggrandizing, over-exaggerated
pompous clones with neither the vision nor the courage to make movies that don’t play to the
gallery, prohibits us from expecting something new or sensible from a movie, how much ever
hyped it is.
A. irksome
B. wrenching
C. nascent
D. imposing
E. interesting
F. vexing
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3. As an austerity measure, a _________of up-market party hosts who regularly hold parties at
the festival, have decided not to hold lavish bashes this year.
A. minuscule
B. zealot
C. slew
D. volume
E. paltry
F. sheaf
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4. The pictures and videos from Abu Ghraib did bring home what was happening there in a way
that nothing else could have done, and promoted a great wave of _________ and humanitarian
concern that helped to get the place closed down.
A. revulsion
B. benevolence
C. aversion
D. turpitude
E. anachronism
F. sympathy
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5. Though James Oliver entered with the __________ conviction that he would make it big in
Hollywood, he realized within a short while that American entertainment is a cut-throat business.
A. sophisticated
B. naive
C. guileless
D. professional
E. cynical
F. uninhibited
6. She gasped when she saw that her parents’ home was _________with ketchup, chocolate
syrup and eggs.
A. florid
B. ornate
C. deluded
D. splattered
E. adorned
F. dabbled
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GRE Sample
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Analytical Writing Assessment
(AWA)
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GRE Sample
INTRODUCTION
The Analytical Writing Assessment (AWA) is one of the most neglected yet one of the most important
sections of the GRE Exam. The GRE AWA section has two tasks. One task tests your ability to
express your views on an issue. You will have two options to choose from. The second task tests
your ability to think critically and analyze a logically flawed argument. Both the tasks are for 30 mins.
The AWA section has scores ranging from 0 to 6, 6 being the highest. A well written and coherent
essay with relevant examples would get a score of no less than 4.5. Papers awarded 6’s are
considered to be outstanding, 5’s are strong, 4’s are adequate, 3’s are limited, 2’s are seriously
flawed, and 1’s are fundamentally deficient.
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Your Issue and Argument scores are combined into one average score that is reported to the colleges.
Although you can view your math and verbal scores at the test center shortly after the test, your
analytical writing score will not be available until 10–15 days after the test.
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The best part of good preparation for the AWA section is that it also helps in your TOEFL exam
which invariably every one of you will be taking as part of your admission process.
It is our endeavor that all the students take the AWA section seriously and score a minimum of 3.5,
which is a cutoff for few of the very good colleges in the United States of America.
The GRE AWA tests your skills on
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Ability to articulate complex ideas clearly and effectively
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Ability to examine claims and accompanying evidence
•
Ability to support ideas with relevant reasons and examples
•
Ability to sustain a well-focused, coherent discussion
•
Ability to control the elements of standard written English.
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The crux of the GRE AWA is about constructing an essay with coherent ideas. Before we go into the
detailed discussion of what are the strategies to be used to construct a well written issue or an
argument. Let us first see few tips to write a very good essay.
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GRE Sample
ESSAY WRITING BASICS
The scorers/evaluators/readers of your essays have a huge task of reviewing hundreds of essays of
fellow GRE test takers. So you should make a conscious effort of writing a captivating essay. But
how do you write a captivating essay? Are there any rules that make your essay stand out in a lot?
Having good knowledge of various topics, and to go with it, there are a few tips or strategies that
you can use to construct a well written essay.
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1. Have a good beginning.
What better than having a gripping start to a story? As we mentioned earlier, the scorers have a
tedious task of reviewing hundreds of essays. So when you make your essay start in an interesting
way, it always captivates the attention of the scorers. You can start your essays with a quote or
an anecdote. An anecdote is a short story about a particular topic. You can also pose a question
to keep the reader engaged, so that he keeps reading to find an answer.
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2. Do not maintain the same tone all throughout your essay. Bring in some rhythm and cadence to
your writing.
It is always better to use transitional words and phrases and figurative speech in your essay.
Transitional words and phrases are helpful not only in linking your ideas between sentences, but
also in providing cohesiveness from paragraph to paragraph. In addition to, furthermore, it is
evident that, however, on the contrary, sadly enough, as a result, vicariously, in the hind sight etc
are examples of transitional phrases and words. Usage of figurative speech like hyperbole,
simile, metaphor etc makes your essay flowery.
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3. Maintain consistency in person. Based on the topic of the essay choose a person and stick to
the same.
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4. Avoid redundancy. Never belabor or beat around the bush while writing about a topic. You can
sometimes restate to emphasize, make sure that it never is tautological.
5. Avoid grammatical mistakes. You will lose marks for improper usage of words and word forms.
So, if you are not sure about the usage of a particular word, try to find a replacement for that.
6. The GRE AWA exam has a simple word processor. It does not have a spell check. So when you
practice for your AWA section, practice in notepad rather than Microsoft word. Avoid incorrect
spellings which would certainly have a negative impact on your score.
7. Use proper punctuation. Improper usage of punctuation could completely change the meaning
of the sentence.
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GRE Sample
ANALYTICAL WRITING
The Analytical Writing measure assesses your critical thinking and analytical writing skills. It assesses
your ability to articulate and support complex ideas, construct and evaluate arguments, and sustain
a focused and coherent discussion. It does not assess specific content knowledge.
The Analytical Writing measure consists of two separately timed analytical writing tasks:
•
a 30-minute “Analyze an Issue” task
•
a 30 minute “Analyze an Argument” task
Overview of the Analytical Writing Measure
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The Issue task presents an opinion on an issue of broad interest followed by specific instructions
on how to respond to that issue. You are required to evaluate the issue, considering its complexities,
and develop an argument with reasons and examples to support your views.
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The Argument task presents a different challenge from that of the Issue task: it requires you to
evaluate a given argument according to specific instructions. You will need to consider the logical
soundness of the argument rather than to agree or disagree with the position it presents.
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The two tasks are complementary in that one requires you to construct your own argument by
taking a position and providing evidence supporting your views on the issue, whereas the other
requires you to evaluate someone else’s argument by assessing its claims and evaluating the evidence
it provides.
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Preparing for the Analytical Writing Measure:
The basic guidelines one must keep in mind before approaching the ‘Writing’ tasks are: (these
guidelines will hold good for both the tasks)
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1. For every point you make in a GRE essay, always provide a reason and/or an example to
support that point. (This is the cardinal rule for writing GRE essays)
2. Use transition words and phrases to help the reader follow the flow of your discussion eg. inaddition, moreover, furthermore, finally etc..
3. Try to include brief introductory and concluding paragraphs, which are consistent with each
other and with the paragraphs in the body of your essay. Such lines will help your essay appear
well-organized.
4. Compose your introductory remarks last — after you’ve completed the rest of your essay.
Why? Your essay might evolve different from your initial thesis; if you’ve composed your
introduction first, you might need to rewrite it.
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GRE Sample
ANALYZE - ISSUE TASK
The ‘Analyze an Issue’-task assesses your ability to think critically about a topic of general interest
according to specific instructions and to clearly express your thoughts about it in writing. Each issue
topic makes a claim that test takers can discuss from various perspectives and apply to many
different situations or conditions. The issue statement is followed by specific instructions. Your
task is to present a case for your own position on the issue according to the specific instructions.
Before beginning your written response, be sure to read the issue and instructions carefully and think
about the issue from several points of view, considering the complexity of ideas associated with
those views. Then, make notes about the position you want to develop and list the main reasons and
examples that you could use to support that position.
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It is important that you address the central issue according to the specific instructions. Each task is
accompanied by one of the following sets of instructions.
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Specifications for the Issue Task Essay:
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Write a response in which you discuss the extent to which you agree or disagree with the
statement and explain your reasoning for the position you take. In developing and supporting
your position, you should consider ways in which the statement might or might not hold true and
explain how these considerations shape your position.
•
Write a response in which you discuss the extent to which you agree or disagree with the
recommendation and explain your reasoning for the position you take. In developing and
supporting your position, describe specific circumstances in which adopting the recommendation
would or would not be advantageous and explain how these examples shape your position.
•
Write a response in which you discuss the extent to which you agree or disagree with the claim.
In developing and supporting your position, be sure to address the most compelling reasons
and/or examples that could be used to challenge your position.
•
Write a response in which you discuss which view more closely aligns with your own position
and explain your reasoning for the position you take. In developing and supporting your position,
you should address both of the views presented.
•
Write a response in which you discuss the extent to which you agree or disagree with the claim
and the reason on which that claim is based.
•
Write a response in which you discuss your views on the policy and explain your reasoning for
the position you take. In developing and supporting your position, you should consider the
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GRE Sample
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GRE
Quantitative Ability
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GRE Sample
INTRODUCTION TO GRE MATH SECTION
Format
The GRE Math section consists of the following types of questions:
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Quantitative Comparison
Standard Multiple Choice with one correct answer
Multiple choice with more than one correct answer
Numeric Entry Questions
Data Interpretation and Data Analysis based Questions.
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You will also be provided with an on screen calculator to solve the problems. Most of the questions do not involve difficult calculations, so dont get into the habit of using the calculator just
because it's available. Use it for calculations you know are tedious and time consuming.
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The GRE Math part has two sections, each section has approximately 20 questions and you are
given 35 minutes to answer each section. You can score anything between 130-170 points (as
opposed to 200-800, in the previous pattern), in one point increments. If you do not attempt any
question at all, you will be given NS, meaning No Score.
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NUMBER SYSTEMS
Do you go numb when you see questions on number system? Do you get scared when somebody
asks you the last digit of 2376 raised to the power of 2376? Do you fail to see the rationale behind
denoting a rational number in terms of decimals and percentages?
Let’s unravel the mysteries behind these seemingly threatening questions. In fact we will go ahead
and make number systems your favourite topic by the end of this chapter.
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What do you understand by the term ‘number’ ? (It is certainly not the comparative degree of
numb :)
A number is a symbol that represents a particular quantity. Different number systems have different
ways of representing these symbols. The most commonly used number system is the Arabic number
system which has numbers like 1, 23, 45, 678 etc. You must have read other forms of representations like the Roman system where English letters are used as symbols to represent numbers. For
example, X, VI, C, LX etc.
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While, there exist various number systems we primarily work on the Arabic system which is the
most popularly followed system.
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Let us dig deep into this system and learn more about numbers.
On a broad scale, numbers can be divided into two categories, the real and the imaginary.
Real numbers: Real numbers are those numbers which can be represented on the number line. A
number line is a line containing all the positive and negative numbers ranging from negative infinity to
the positive infinity. Numbers like -4.5, 67/89, 9 etc are real numbers.
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-5 -4
-3
-2
-1
0
1
2
3
4
5
Imaginary numbers: Imaginary numbers, on the contrary, cannot be represented on the number
line. For example numbers like - 1 , - 2 etc are imaginary..
Real numbers can be further be divided into two parts. They are the Rational numbers and
irrational numbers.
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Integers
Real
Numbers
Rational
Numbers
Whole
Numbers
Natural
Numbers
Fractions
Irrational
Numbers
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The figure represented above is the Number tree. You can see how different numbers have been
evolved from the others and the various classifications are also provided.
Example 1: Which of the following numbers is a prime number?
A. 234
B. 675
C. 123
D. 631
E. 290
Solution: As mentioned earlier, except 2 all other even numbers are composite. So, options A and
E are eliminated straight away. The number in the option B ends with 5 and thus has 5 as a factor.
So, option B is ruled out.
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123 is divisible by 3, so the only number left is 631. Thus the answer is (D).
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Alternative method: Checking whether all the numbers from 1 to 631 are factors of 631 are not
is a tedious process and might take ages. God bless mathematicians as they gave us an easier way
to find whether a number is a prime number or not.
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Check whether any of the numbers from 2 to the 631 (nearest value = 26) divides the number 631
or not. If any of these numbers divides the number then it is not a prime number. In this case none of
them divides 631 completely, so 631 is the answer.
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Relation between Odd and Even numbers:
Odd + Even = Odd
Even + Odd = Odd
Odd + Odd = Even
Even + Even = Even
Oddeven = Odd
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Oddodd = Odd
Odd – Even = Odd
Even – Odd = Odd
Odd – Odd = Even
Even – Even = Even
Eveneven = Even
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Odd x Odd = Odd
Odd x Even =Even
Even x Odd= Even
Even x Even= Even
Evenodd = Even
GRE Sample
Concept of multiplying factor:
Consider the following example; Sachin scored 500 runs in IPL 2. He scored 10% more runs in IPL
3. What is the total number of runs he scored in IPL3 ?
The answer for this can be easily calculated by the principles discussed earlier in this chapter.
The total number of runs scored by sachin in IPL3 = 500 + (10/100) x 500 = 500 + 50 = 550.
The same can be done this way 500 + (10/100) x 500 = 500 (1+ 0.1)=500x1.1 = 550
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If we see clearly, we are multiplying the number of runs Sachin scored in IPL 2 by a factor 1.1 to get
the runs he scored in IPL 3. This factor of multiplication is called the multiplying factor.
The multiplying factor corresponding to an increase of x% is nothing but 1 + (x/100) and for a
decrease of x%, 1-(x/100)
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Multiplying Factor (M.F)
We could simply say, it is (1+ k), where k is percentage change expressed in decimal
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We have discussed earlier about how percentages, fractions/ratios, or decimals are inter-convertible and interchangeable. For easy calculations in GRE, it is advisable for the students to learn the
multiplication tables upto 20, squares upto 30 and cubes upto 20.
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Few of the very commonly used percentages and their corresponding fractional values are given.
1/2 = 50%
1/6 = 16.67%
2/5 = 40%
1/15 = 6.66%
7/8 = 87.5%
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1/3 = 33.33%
1/7 = 14.28%
3/5 = 60%
1/16 = 6.25%
1/20 = 5%
1/4 = 25%
1/8 = 12.5%
1/11 = 9.09%
3/8 = 37.5%
1/5 = 20%
1/9 = 11.11%
1/12 = 8.33%
5/8 = 62.5%
Example 2: If three fourth of students in the class have motor bikes and half of the bike owners
own a Hero Honda bike, what fraction of the class has Hero Honda bike? Also, represent the
same in terms of percentage.
Solution: The fraction of the class owning a Hero Honda bike = ¾ x ½ = 3/8
As mentioned above, the percentage equivalent to that is = 37.5 %.
The same problem can be solved using percentages instead of fractions. Try it for yourself.
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Harmonic Progression
If the reciprocals of a progression form an AP, then that progression is called a Harmonic
Progression.
The Harmonic mean of 2 numbers is given by HM= 2ab/a+b
For any two numbers a and b, AM  GM  HM
Some Important Formulae
n 
n( n  1)
2
n 2 
n( n  1)(2n  1)
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Example : The 20th term of the series 3, 5, 7, 9 …
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n3 
n 2 (n  1)2
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Solution: The above series is an arithmetic progression (AP). We can see that the common
difference of the above series is 2.
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Thus the 20th term of the series is given by, T20 = a + 19 × d
T20 = 3 + 19 × 2 = 3 + 38 = 41.
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GRE Sample
A polynomial of degree two is called a quadratic equation. A standard quadratic equation is of the
form ax2 + bx + c = 0, where a, b, c are all real and a  0. A quadratic equation has two roots.
The roots of the quadratic equation could be as follows
a. Real and different
b. Real and equal
c. Imaginary
The nature of roots of a quadratic equation ax2 + bx + c = 0 is governed by a value called the
discriminant (D). Discriminant is expressed as (b2 - 4ac). Shown below is the nature of roots based
on the discriminant value.
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D = b -4ac
If D = 0
(Rational and equal)
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D>0
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D is Perfect square
(Rational and unequal)
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If D < 0
(Roots are complex or imaginary)
D is not Perfect square
(Irrational conjugate pairs)
Example 1: What is the nature of roots of 3x2 - 5x + 3 = 0?
A. Real and equal
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B. Real and unequal
C. Rational
D. Imaginary
E. Irrational
Solution: To find the nature of the roots, we have to find the discriminant D = b2 - 4ac = (-5)2 +
4x3x3 = 25 - 36 = -9. If the discriminant value is negative, then the roots are complex or imaginary.
Roots of the Quadratic Equation
b  b 2  4ac
If ax + bx + c=0, then the roots of the quadratic equation are
2a
2
. The roots are commonly represented by  and  .
Sum of roots ( + )=
25
b
c
, Product of the roots ( )=
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GRE Sample
Graph of the curve y=x2
Graph of the curve y= -x2
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Graph of the curve y=(x+k)2
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Graph of the curve y= x2-k
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Graph of the curve y= x3
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Graph of the curve y= -x3
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Normal Distribution
Many natural processes yield data that have a relative frequency distribution shaped somewhat like
a bell as shown below with mean m and standard deviation d.
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Such data are said to be approximately normally distributed and have the following properties.
1. The mean, median, and mode are all nearly equal.
2. The data are grouped fairly symmetrically about the mean.
3. About two-thirds of the data are within 1 standard deviation of the mean.
4. Almost all of the data are within 2 standard deviations of the mean.
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As stated above, you can always associate a random variable X with a distribution of data by letting
X be a randomly chosen value from the distribution. If X is such a random variable for the distribution
above, we say that X is approximately normally distributed. Just as a data distribution has a mean
and standard deviation, the normal probability distribution has a mean and standard deviation. Also,
the properties listed above for the approximately normal distribution of data hold for the normal
distribution, except that the mean, median, and mode are exactly the same and the distribution is
perfectly symmetric about the mean.
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A normal distribution, though always shaped like a bell, can be centered around any mean and can
be spread out to a greater or lesser degree, depending on the standard deviation.
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MENSURATION & TRIGONOMETRY
1. Crafty Tara decides to make each of her friends a light box. To let the light out, she removes a
right triangle from each side of the box such that the area of each face of the box is the same.
What is the remaining surface area of the box if each edge of the box measures 4 feet and the
area of each triangle measures 6 square feet?
A. 60 sft
B. 55 sft
C. 50 sft
D. 28 sft
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2. The 25th Annual Go-Cart Race is just around the corner, and Dave needs to build a platform for
the winner. In honor of the tradition’s longevity, Dave wants the platform to be special. So, he will
cover all the exposed surfaces of his platform in red velvet. If the base step measures 15 feet by
7 feet by 1 foot, and each consecutive step is uniformly 1 foot from the edge of the last step, how
much exposed surface area must Dave cover?
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A. 340 sft
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B. 318 sft
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C. 254 sft
D. 328 sft
3. The area of the base of a tank is 100 sq. ft. It takes 20 seconds to fill the tank with water poured
at rate of 25 cubic feet per second. What is the height (in feet) of the rectangular tank?
A. 0.25
B. 0.5
C. 1
D. 5
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4. Water is poured into an empty cylindrical tank at a constant rate. In 10 minutes, the height of the
water increased by 7 feet. The radius of the tank is 10 feet. What is the rate at which the water
is poured in cubic feet per minute?
A. 11  /8
B. 11  /3
C. 7  /60
D. 70 
5. A closed rectangular tank contains a certain amount of water. When the tank is placed on its 3 ft
by 4 ft side, the height of the water in the tank is 5 ft. When the tank is placed on another side of
dimensions 4 ft by 5 ft, what is the height, in feet, of the surface of the water above the ground?
A. 2
B. 3
C. 5
D. 4
6. A, B, and C are three unequal faces of a rectangular tank. The tank contains a certain amount of
water. When the tank is based on the face A, the height of the water is half the height of the tank.
The dimensions of the side B are 3 ft × 4 ft and the dimensions of side C are 4 ft × 5 ft. What is
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22. The box-and-whisker plot below shows the amount of calories present in some bakery items.
• What is the IQR (Inter Quartile Range)?
• What is the average of the median and the lower quartile?
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• If the Lower and the Higher values increase by 50 calories each,what happens to the
median?
• In that case what happens to the lower quartile?
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• And the upper quartile?
23. The following box plot shows the weight of Rugby players (both Male & Female). Answer
the questions below.
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GRE Sample
Directions for questions 5 to 7: The information below shows the details of value of Indian Rupee
against the US Dollar from 09th July to 08th August, 2011. Answer the questions based on the
graph.
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5. On which day shown on the graph did the value of the US dollar increase against the Rupee by
the greatest amount?
A. July 10 B. July 14
C. July 21
D. July 23
E. Aug 4
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6. John had 100 dollars. The exchange rate converts the amount in US dollars to a number in Indian
Rupees by directly multiplying by the value of the exchange rate. By what amount did John’s
$100 increase in terms of Indian Rupees from July 9th to August 8th?
A. 5
B. 10
C. 15
D. 35
E. 55
7. On August 8th, the dollar value was approximately what percent of the dollar value on July
9th?
A. 1.28
B. 12.8
C. 101.07
D. 112.8
E. 128
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