MSTE - LOOKSFAM
1.
2.
A Toyota Land Cruiser drives east from point A at 30 kph. Another car,
Ford Expedition, starting from B at the same time, drives S30°W toward
A at 60 kph. B is 30 km from A. How fast in kph is the distance between
two cars changing after 30 minutes?
(Ans. 60 kph)
7.
A lighthouse shows successive one-second flashes of red, white,
green, green, white, red. A second lighthouse does the same, only with
two-second flashes. The six-second sequence of the first lighthouse is
repeated steadily, as is the twelve-second sequence of the other
lighthouse. What fraction of the time do the two lights show the same
color if the given sequences start at the same time?
(Ans. 1/6)
In a room 40 feet long, 20 feet wide, and 20 feet high, a bug sits on an
end wall at a point one foot from the floor, midway between the
sidewalls. He decides to go on a journey to a point on the other end wall
which is one foot from the ceiling midway between the sidewalls. Having
no wings, the bug must make this trip by sticking to the surfaces of the
room. What is the shortest route that the bug can take?
(Ans. 58 ft)
8.
Near the town Lunch, Nebraska there is a large triangular plot of land
bounded by three straight roads which are 855, 870, and 975 yards long
respectively. The owner of the land, a friend of mine, told me that he had
decided to sell half the plot to a neighbor, but that buyer had stipulated
that the seller of the land should erect the fence which was to be a
straight one. The cost of fences being high, my friend naturally wanted
the fence to be as short as possible. What is the minimum length the
fence can be?
(Ans. 600 yards)
9.
A coffee pot with a circular bottom tapers uniformly to a circular top
with radius half that of the base. A mark halfway up the side says “2
cups”. Where should the “3 cups” mark go?
(Ans. About 2% of the way down from the tip of the pot.)
3.
In Bristol, 90% of the citizens drink tea, 80% drink coffee, 70% drink
whiskey, and 60% drink gin. No one drinks all four beverages. What
percent of Bristol's citizens drink liquor?
(Ans. 100%)
4.
Smith and Jones, both 50% marksmen, decide to fight a duel in which
they exchange alternate shot until one is hit. What are the odds in favor
of the man who shoot first?
(Ans. 2/3)
5.
6.
A coin is so unbalance that you are likely to get two heads in two
successive throws as you are to get tails in one. What is the probability
of getting heads in a single throw?
(Ans. 0.618)
A farmer owned a square field measuring exactly 2261 m on each
side. 1898 m from one corner and 1009 m from an adjacent corner
stands Narra tree. A neighbor offered to purchase a triangular portion of
the field stipulating that a fence should be erected in a straight line from
one side of the field to an adjacent side so that the Narra tree was part
of the fence. The farmer accepted the offer but made sure that the
triangular portion was a minimum area. What was the area of the field
the neighbor received and how long was the fence?
(Ans. A=939,120 m2 and L=2018 m)
10. On what days of the week can the first day of a century fall? (The first
day of the twentieth century was Jan. 1, 1901)
(Ans. Monday)
11. Specialized Bolt has decided to build a new plant that is very similar to
its existing plant. The plant will be used to produce 5,000 units if the
part. The loss due to scrap is exposed to be 2.5%. The company that
sell the raw materials to the XYZ Company will buy back any scrap or
MSTE - LOOKSFAM
waste for Php0.95 per cubic inch. The recovery cost is Php0.20 per
cubic inch. Approximately 15% of the waste is not recovered for resale.
Historical data show that on January 1,1987, the cost of this material
was Php1.45 per cubic inch, in a quantity of 8,000 inches^3. On March
1, 1988, the unit cost of 3,000 inches^3 was Php1.89 per cubic inch. For
the past 4 years we will assume that the inflation rates have remained
stable at an annual rate of 12% and that the date when the material is
to be purchased is February 1, 1990. The approximate capital cost of
the existing facility which was purchased recently was Php12,000 and
its production capacity is 20 units per day. Capital cost can be estimated
with It=1.12, approximately 0.35 hr is necessary to produce each unit.
This time was achieved over a production of 3,500 units per hour,
including benefits. Time is 1-hour part factory burden is 40% of direct
material. Estimate the parts manufacturing cost from the information
given.
(Ans. Php69,048)
12. An icicle forming from a dripping gutter is in the shape of a cone five
times as long as it is wide (at the top). A few hours later it has doubled
in length and the generating angle has also doubled. How does its
present weight compare with its previous weight?
(Ans. 33 times)
13. The north-south streets of a grid have block lengths of 140 m and the
east-west streets have block lengths of 240 m. Desired speed of
progressions are 50 km/h east west. Determine the actual speed of
progression for two-way progression in both orientation of the grid.
Round the cycle to the nearest 5 s. Hint: Convert desired speeds of
progression to m/s and determine cycle lengths, C=2NL/s.
(Ans. 50.4 km/h NS, 43.2 km/h EW)
14. A proposed new bus route is expected to require 8 new buses and to
operate a total of 560,000 vehicle kilometers (veh-km) per year and
29,000 vehicle-hours (veh-hr) per year. Buses cost $200,000 each,
have a 10-year life, and a salvage value after 10 years of $25,000 each.
Operating costs include labor costs (wages, benefits, etc.) at
$45.00/veh-h, maintenance costs at $0.16/veh-km, and cost of fuel, oil,
tires, etc. at $0.38/veh-km. Calculate the life cycle cost (present value)
of adding this route and operating it for 10 years, assuming an annual
interest rate of 7.5 percent.
(Ans. $11,920,257)
15. There are nine cities which served by two competing airlines. One or the
other airline (but not both) has a flight between every pair of cities. What
is the minimum number of triangular flights (i.e. trips from A to B to C
and back to A on the same airline)?
(Ans. 12)
16. You and a friend spot a lose $20 bill simultaneously and agree to an
auction in which you write down your bids and compare them. High
bidder gets the $20 and pays the other the amount of the higher bid. Tie
bidders split the $20. How much do you bid?
(Ans. $9.99)
17. The local weather forecaster says “no rain” and his record is 2/3
accuracy of prediction. Bu the Federal Meteorological Service Predicts
rain and their record is 3/4. With no other data available, what is the
chance of rain?
(Ans. 3/5)
18. Two wheels in the same plane are mounted on shaft 13 in. apart. A
belt goes around both wheels to transmit power from one to the other.
The radii of the two wheels and the length of the belt not in contact with
the wheels at any moment are all integers. How much larger is one
wheel than the other?
(Ans. 5 inches)
19. Three hares are standing in a triangular filed which is exactly 100 yards
on each side. One hare stands at each corner; and simultaneously all
three set off running. Each hare runs after the hare in the adjacent
MSTE - LOOKSFAM
corner on his left, thus following a curved course which terminates in the
middle of the filed, all three hares arriving there together. The hares
obviously ran at the same speed, but just how far did they run?
(Ans. 100 yards)
26. A neat computer programmer wears a clean shirt every day. If he
drops of his laundry and picks up the previous week’s load every
Monday night, how many shirts must he own to keep him going?
(Ans. 15)
20. What is the longest 6’ wide shuffle board court which will fit in a 20’30’
rectangular room?
(Ans. 30 7/8 feet)
27. No factorial can end in five zeros. What is the next smallest number
of zeros in which a factorial cannot end?
(Ans. 11)
21. A one-acre filed in the shape of a right triangle has a post at the midpoint
of each side. A sheep is tethered to each of the side posts and a goat to
the post on the hypotenuse. The ropes are just long enough to let each
animal reach the two adjacent vertices. What is the total area the two
sheep have to themselves, i.e., the area the goat cannot reach?
(Ans. 1 acre)
28. Very few people are aware of the growth pattern of Jack’s beanstalk.
On the first day it increased its height by ½, on the second day by 1/3,
on the third day by ¼, and so on. How long did it take to achieve it
maximum height (100 times its original height)?
(Ans. 198 days)
22. A spider and a fly are located at opposite vertices of a room of
dimensions 1, 2, and 3 units. Assuming that the fly is too terrified to
move, find the minimum distance the spider must crawl to reach the fly?
(Ans. √18)
23. What is the least number of links that must be disengaged from a 23link chain so that any number of links from 1 to 23 can be obtained by
taking one or more of the pieces?
(Ans. 2)
24. Assuming the sun rises at 6:00 a.m., sets at 6:00 p.m., and moves at a
uniform rate, how can a lost boy scout determine south by means of a
watch on a cloudless day?
(Ans. Align the hour hand, with the sun’s azimuth, and south will
be midway between the hour hand and 12.)
25. There are three families, each with two sons and two daughters. In
how many ways can all these young people be married?
(Ans. 80)
29. The passengers on an excursion bus consisted of 14 married couple,
8 of whom brought no children, and 6 of whom brought 3 children
apiece. Counting the driver, the bust had 31 occupants. How is this
possible?
(Ans. Included among the 18 children were 8 married couples)
30. A hospital nursery contains only two baby boys; the girls have not yet
been counted. At 2:00 p.m. a new baby is added to the nursery. A baby
is then selected at random to be the first to have its footprint taken. It
turns out to be a boy. What is the probability that the last addition to the
nursery was a girl?
(Ans. 2/5)
31. Mr. Field, a speeder, travels on a busy highway having the same rate
of traffic flow in each direction. Except for Mr. Field, the traffic is moving
at the legal speed limit. Mr. Field passes one car for every nine which
he meets from the opposite direction. By what percentage is he
exceeding the speed limit?
(Ans. 25%)
MSTE - LOOKSFAM
32. A necklace consists of pearls which increase uniformly from a weight
of 1 carat for the end pearl to a weight of 100 carats for the middle pearl.
If the necklace weighs altogether 1650 carats and the clasp and string
together as much (in carat) as the total number of pearls, how many
pearls does the necklace contain?
(Ans. 33)
33. Dr. Irving Weiman, who is always in a hurry, walks up an up-going
escalator at the rate of one step per second. Twenty steps bring him to
the top. Next day he goes up to two steps per second, reaching the top
in 32 steps. How many steps are there in the escalator?
(Ans. 80)
34. The faces of a solid figure are all triangles. The figure has nine
vertices. At each of six of these vertices, four faces meet, and at each
of the other three vertices, six faces meet. How many faces does the
figure have?
(Ans. 14)
35. Between Kroflite and Beeline are five other towns. The seven towns
are an integral number of miles from each other along a straight road.
The towns are so spaced that if one knows the number of miles a person
has traveled between any two towns he can determine the particular
town uniquely. What is the minimum distance between Kroflite and
Beeline to make this possible?
(Ans. 25 miles)
36. The estimated cycle time for a wheel scraper is 6.5 min. Calculate the
number of pushers required to serve a fleet of nine scrapers using single
pushers. Determine the result for both backtrack and chain-loading
methods.
(Ans. 2 and 3)
37. Given the following information on a shovel/truck operation, calculate
the number of trucks theoretically required and the production of this
combination. Shovel production at 100% efficiency = 283 BCM/h Job
efficiency = 0.75 Truck capacity = 15.3 BCM Truck cycle time, excluding
loading = 0.5h
(Ans. 11 trucks and 212 BCM/h)
38. Determine the design lateral force for the slab form 152 mm thick,
6.1 m wide, and 30.5 m long shown in Figure 5. The slab is to be poured
in one pour. Assume concrete density is 2403 kg/m3 and that the
formwork weighs 0.72 kPa.
(Ans. 1.46 kN/m)
39. A jaw crusher is producing 227 t/h of crushed gravel and discharging it
onto a three-screen deck. The top screen in the deck is a 38-mm screen.
The gradation of crusher output shows 100% passing 76 mm, 92%
passing 38 mm, and 80% passing 19 mm. Material weight is 1842
kg/m3. Find the minimum size of the 38-mm screen to be used. Check
both total screen load and screen passing capacity.
(Ans. 2.9 m2)
40. To compress 2.8 m3 of free air per minute from atmospheric (0.101
N/mm2) to (0.7 N/mm2) indicated on the gauge (i.e. 8.01 bar absolute)
requires a compressor with theoretical power value: 𝑃𝑜𝑤𝑒𝑟 = 103 ×
0.101 × (𝑣1 / 60) log𝑒 𝑝2 / 0.101𝑘𝑊
(Ans. 9.7 kW or 13.1 HP)
41. The density of air decreases with increasing altitude and this for a
compressor operated above sea level, k should be reduced. For
example, to compress 2.8 m 3 of air per minute from 0.05 N/mm2
(atmospheric pressure) to 0.801 N/mm2 (absolute pressure) requires a
compressor with a power value of 𝑃𝑜𝑤𝑒𝑟 = 103 × 𝑝1 × (𝑣1 / 60) log𝑒 𝑝2
/ 𝑝1
(Ans. 6.47 kW)
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42. A copper wire has a nominal breaking strength of 300 MPa and a
reduction of area of 77%. Calculate the true tensile strength (breaking
load/true area).
(Ans. 1300 MPa)
43. A copper wire has a nominal breaking strength of 300 MPa and a
reduction of area of 77%. Calculate the true strain 𝜖𝑡𝑟 at the point of
fracture. (The instantaneous strain 𝑑𝜖 is equal to 𝑑𝑙/𝑙).
(Ans. 1.47 or 147%)
alighting passengers use the back door. Fare collection is exact fare and
farebox, but no single coin. Assume clearance time is 15 s, and that the
maximum allowable probability of bus queuing is 1 percent. The stop is
a near-side stop at an intersection with g/C ratio of 0.50. How many
berths are required?
(Ans. 2)
44. An aluminum wire is stressed 34.5 MPa in tension. What temperature
increase is required to change its length by the same amount?
(Ans. 22°C)
49. The number of hours daylight, D(t) at a particular time of the year can
be approximated by D(t) = for t days and t = 0 corresponding to January
1. The constant K determines the total variation in day length and
depends on the latitude of the locale. When is the day length the
longest, assuming that it is NOT a leap year?
(Ans. June 20)
45. The true density of a concrete to which an air entraining agent was
added is 2.80 g/cm3. However, a dry core (15.24 cm x 10.16 cm) of this
concrete weigh only 2.982 kg. The same core weighs 3.08 kg when
saturated with water. What are the percents of the open and closed
pores?
(Ans. 27.9 v/o and 5.9 v/o)
50. The number of hours daylight, D(t) at a particular time of the year can
be approximated by D(t) = for t days and t = 0 corresponding to January
1. The constant K determines the total variation in day length and
depends on the latitude of the locale. When is the day length the
shortest, assuming that it is NOT a leap year?
(Ans. December 20)
46. The true density of a concrete to which an air entraining agent was
added is 2.80 g/cm3. However, a dry core (15.24 cm x 10.16 cm) of this
concrete weigh only 2.982 kg. The same core weighs 3.08 kg when
saturated with water. What are the bulk and apparent densities?
(Ans. 2.41 g/cm3 and 2.62 g/cm3)
51. Labor laws in Erewhon require factory owners to give every worker a
holiday whenever one of them has a birthday and to hire without
discrimination on the grounds of birthdays. Except for these holidays,
they work a 365-day year. The owners want to maximize the expected
total number of man-days worked per year in a factory. How many
workers do factories have in Erewhon?
(Ans. 364)
47. An electrical porcelain product has only 1 v/o porosity as sold. It had
27 v/o porosity after pressing and drying, but before sintering. How much
linear shrinkage occurred during sintering?
(Ans. 9.7 l/o)
48. A bus route on a city street is scheduled for 2-min headways. On the
average, 7 passengers per bus board at a particular stop and 10
passengers alight. All boarding passengers use the front door and all
52. A spider eats three flies a day. Until he fills his quota, he has an even
chance of catching a fly that attempts to pass. A fly is about to make the
attempt. What are the chances of survival, given that five flies have
already made the attempt today?
(Ans. 3/4)
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53. In a little-known work, the famous geometer of Skalenos proves the
following theorem: “The square of the side opposite the Fandangle is
equal to the sum of the squares of the other two sides added to the
product of those two sides multiplied by the square root of two.” What is
a Fandangle?
(Ans. 135°)
54. Assume that a single depth charge has a probability of ½ of sinking a
submarine, ¼ of damage and ¼ missing. Assume also that two
damaging explosions sink the sub. What is the probability that 4 depth
charges sink the sub?
(Ans. 251/256)
55. A billiard table is in the form of an ellipse with one axis two feet longer
than the other. A ball is stuck from one focus and after bounding against
two cushions returns to its starting point. At the halfway point in its trip,
the ball is eight feet from the source. How big is the table?
(Ans. 15 ft and 17 ft)
56. Data over the last 5 years indicate that for each fatality, there are 40
nonfatal injury accidents ($15,000 present cost each) and 300 property
damage accidents ($2000 present cost each). What is the breakeven
value of a statistical life (VSL) needed to justify a highway project if I am
8%? The death rate on a particular three-lane road is 8 per 100 million
vehicle-miles. Adding a lane would reduce this to 5 per 100 million, and
other accidents would be reduced proportionately. The lane would cost
$1.5M per mile to build, and annual maintenance would be 3% of the
first cost. Assume that the lane would last 40 years. The road carries
10,000 vehicles per day.
(Ans. $359.8K)
57. Calculate the benefit/cost ratio for a highway project with the following
benefits and costs. The project life is 40 years, the interest rate is 10%,
and the project’s right-of-way is worth $5M in 40 years.
(Ans. 1.23)
58. Rosenberg Engineering has offices in northern California, where a
heat pump can be used for cooling in the summer and heating in the
winter. Replacing their current system will cost $1500 in May and $500
in June. Starting in July, it will save them $200 per month for the summer
months (June–August), $100 for the fall and spring months, and $150
for the winter months (November–March). What is the payback period
for the heat pump?
(Ans. 15 ¼ months)
59. The roof and ceiling of a commercial building will be insulated by
blown-in insulation, which can be specified in 1-inch-depth increments.
The minimum amount of insulation that will meet code is 6 inches, and
the maximum amount that will fit is 12 inches. What is the optimal depth
of this insulation? The firm uses an interest rate of 8% and a 30-year
building life. The installed cost of the insulation for the 10,000-squarefoot ceiling is $1.75 per cubic foot. Thicker insulation will reduce the
capacity of the HVAC equipment and the annual heating and cooling
costs. With 6 inches of insulation, the annual bill for heat gains and
losses through the roof will be $1200.
(Ans. 8’’)