MSTE B-E 2

Question 1

Venusian batfish come in three sexes, which are
indistinguishable (except by Venusian batfish). How
many live specimens must our astronauts bring home in
order for the odds to favor the presence of a “mated
triple” with its promise of more little batfish to come?

A. Five specimens (50/81)
B. Five specimens (50/86)
C. Five specimens (50/85)
D. Five specimens (50/84)

Answer 1

A.

Question 2

In a carnival game, 12 white balls and 3 black balls are
put in an opaque bottle, shaken up, and drawn out one
at a time. The player gets 25 cents for each white ball
which emerges before the first black ball. If he pays one
dollar to play, how much can he expect to win (or lose)
on each game.

A. Average gain of a quarter a game
B. Average loss of a quarter a game
C. Average loss of two quarters a game
D. Average win of a quarter a game

Answer 2

B.

Question 3

In the binary system there are only two positive integers
containing no digit more than once, namely 1 and 10.
How many are there in base ten?

A. 8,677,960 integers
B. 7,677,690 integers
C. 8,776,690 integers
D. 8,677,690 integers

Answer 3

D.

Question 4

In the final seconds of the game, your favorite N.B.A.
team is behind 117 to 118. Your center attempts a shot
and is fouled for the 2nd time in the last 2 minutes as
the buzzer sounds. Three to make two in the penalty
situation. Optimistic? Note: the center is only a 50% free
thrower. What are your team’s overall chances of
winning?

A. 12/16 (75%)
B. 11/16 (69%)
C. 11/15 (73.3%)
D. 10/16 (62.5%)

Answer 4

B.

Question 5

One of a pair of dice is loaded so that the chance of a 1
turning up is 1/5, the other faces being equally likely. Its
mate is loaded so that the chance of a 6 turning up is
1/5, the other faces being equally likely. How much does
this loading increase the probability of throwing a 7 with
the two dice?

A. 1/750
B. 1/350
C. 1/550
D. 1/650

Answer 5

A.

Question 5

A sharp operator makes the following deal. A player is
to toss a coin and receive 1, 4, 9, … n^2 dollars if the
first head comes up on the first, second, third, … n-th
toss. The sucker pays ten dollars for this. How much can
the operator expect to make if this is repeated a great
many times?

A. 8
B. 7
C. 6
D. 10

Answer 5

C.

Question 5

If all the 720 permutations of the digits 1 through 6 are
arrange in numerical order, what is the 417th term?

A. 432615
B. 423451
C. 435261
D. 432516

Answer 5

D.

Question 5

The local weather forecaster says, “no rain” and his
record is 2/3 accuracy of prediction. But the Federal
Meteorological Service predicts rain, and their record is
3/4. With no other data available, what is the chance of
rain?

A. 1/5
B. 4/5
C. 5/5
D. 3/5

Answer 5

D.

Question 6

In 1969, the World Series began in the stadium of
American League pennant winner. Assume the
contenders are evenly matched. What is the probability
that the series ended where it began?

A. 3/8
B. 4/8
C. 5/8
D. 6/8

Answer 6

C.

Question 7

In a carnival game 5 balls are tossed into a square box
divided into 4 square cells, with baffles to insure that
every ball has an equal chance of going in any cell. The
player pays $1 and receives $1 for every cell which is
empty after the 5 balls are thrown. How much does the
operator expect to make per game?

A. 4¢
B. 5¢
C. 6¢
D. 3¢

Answer 7

A.

Question 8

Having lost a checker game, a specialist in learning
programs threw one of the red checkers out the window.
His wife reboxed the 12 black pieces and 11 red pieces
one at a time in random fashion. The number of black
checkers in the box always exceeded the number of
reds. What was the a priori probability of this
occurrence.

A. 1/22
B. 1/23
C. 1/24
D. 1/25

Answer 8

B.

Question 9

To stimulate his son in the pursuit of partial differential
equations, a math professor offered to pay him $8 for
every equation correctly solved and to fine him $5 for
every incorrect solution. At the end of 26 problems,
neither owed any money to the other. How many did the
boy solve correctly?

A. 15 problems
B. 9 problems
C. 12 problems
D. 10 problems

Answer 9

D.

Question 10

An expert on transformer design relaxed one Saturday
by going to the races. At the end of the first race, he had
doubled his money. He bet $30 on the second race and
tripled his money. He bet $54 on the third race and
quadrupled his money. He bet $72 on the fourth race
and lost it, but still had $48 left. With how much money
did he start?

A. 28$
B. 29$
C. 38$
D. 39$

Answer 10

B.

Question 11

Between Sing-Sing and Tarry-Town,
I met my worthy friend, John Brown,
And seven daughters, riding nags,
And everyone had seven bags.
In every bag were thirty cats,
And every cat had forty rats,
Besides a brood of fifty kittens.
All but the nags were wearing mittens!
Mittens, kittens - cats, rats - bag, nags - Browns,
How many were met between the towns?

A. 764,488
B. 746,488
C. 766,488
D. 744,488

Answer 11

A.

Question 12

Dr. Reed, arriving late at the lab one morning, pulled out
his watch and said, “I must have it seen to. I have
noticed that the minute and the hour hand are exactly
together every sixty-five minutes.” Does Dr. Reed’s
watch gain or lose, and how much per hour?

A. 60/143 minutes
B. 61/143 minutes
C. 60/144 minutes
D. 60/142 minutes

Answer 12

A.

Question 13

At this moment, the hands of a clock in the course of
normal operation describe a time somewhere between
4:00 and 5:00on a standard clock face. Within one hour
or less, the hands will have exactly exchanged
positions; what time is it now?

A. 4:25.85
B. 4:26.95
C. 4:26.58
D. 4:26.85

Answer 13

D.

Question 14

Two men are walking towards each other at the side of
a railway. A freight train overtakes one of them in 20
seconds and exactly ten minutes later meets the other
man coming in the opposite direction. The train passes
this man in l8 seconds. How long after the train has
passed the second man will the two men meet?
(Constant speeds are to be assumed throughout.)

A. 5563 seconds
B. 5562 seconds
C. 5662 seconds
D. 5560 seconds

Answer 14

B.

Question 15

[NOV 2023] Using the French Tricolor as a model, how
many flags are possible with five available colors if two
adjacent rows must not be colored the same?

A. 45 flags
B. 55 flags
C. 50 flags
D. 40 flags

Answer 15

C.

Question 16

A cubic box with sides ‘a’ feet long is placed flat against
a wall. A ladder ‘p’ feet long is placed in such a way that
it touches the wall as well as the free horizontal edge of
the box. If a = 1 and p = sqrt(15), calculate at what height
the ladder touches the wall from the floor

A. 3.63 or 1.38 feet
B. 3.62 or 1.38 feet
C. 3.83 or 1.38 feet
D. 3.39 or 1.38 feet

Answer 16

A.

Question 17

[NOV 2017] 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 at two steps per second, reaching the top in
32 steps. How many steps are there in the escalator?

A. 90 steps
B. 80 steps
C. 70 steps
D. 50 steps

Answer 17

B.

Question 18

Citizens of Franistan pay as much income tax
(percentagewise) as they make rupees per week. What
is the optimal salary in Franistan?

A. 60 rupees
B. 55 rupees
C. 70 rupees
D. 50 rupees

Answer 18

D.

Question 19

There are nine cities which are 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)?

A. 13 triangular flights
B. 11 triangular flights
C. 10 triangular flights
D. 12 triangular flights

Answer 19

D.

Question 20

Two snails start from the same point in opposite
directions toward two bits of food. Each reaches his
destination in one hour. If each snail had gone in the
direction the other took, the first snail would have
reached his food 35 minutes after the second. How do
their speeds compare?

A. The first snail traveled at three-fourths the speed
of the second
B. The first snail traveled at two-thirds the speed of the second.
C. The first snail traveled at three-fifths the speed of the second.
D. The first snail traveled at four-thirds the speed of the second.

Answer 20

A.

Question 21

A necklace consists of pearls which increase uniformly
from a weight of 1 carat for the end pearls to a weight of
100 carats for the middle pearl. If the necklace weighs
altogether 1650 carats and the clasps and string
together weigh as much (in carats) as the total number
of pearls, how many pearl does the necklace contain?

A. 33 pearls
B. 32 pearls
C. 34 pearls
D. 31 pearls

Answer 21

A.

Question 22

A pupil wrote on the blackboard a series of fractions having positive integral terms and connected by signs which were either all * or all X, although they were so carelessly written it was impossible to tell which they were. It still wasn't clear even though he announced the result of the operation at every step. The third fraction had denominator 19. What was the numerator? A. 26 B. 24 C. 25 D. 23

Answer 22

C.

Question 23

Jai Alai balls come in boxes of 8 and 15; so that 38 balls (one small box and two large) can be bought without having to break open a box, but not 39. What is the maximum number of balls which cannot be bought without breaking boxes? A. 96 balls B. 98 balls C. 91 balls D. 97 balls

Answer 23

D.

Question 24

A parking lot charges X for the first hour or fraction of an hour and 2/3 of X for each hour or fraction thereafter. Smith parks 7 times as long as Jones but pays only 3 times as much. How long did each park? (The clock registers only 5-minute intervals.) A. Jones parked for 0.4 hour and Smith for 3.4 hours. B. Jones parked for 1.5 hours and Smith for 2.5 hours. C. Jones parked for 0.3 hour and Smith for 3.3 hours. D. Jones parked for 0.5 hour and Smith for 3.5 hours.

Answer 24

D.

Question 25

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? A. 27% B. 24% C. 25% D. 26%

Answer 25

C.

Question 26

What is the millionth term of the sequence 1, 2, 2, 3, 3, 3, 4, 4, 4, 4, … in which each positive integer n occurs in blocks of n terms? A. 1,413 B. 1,414 C. 1,444 D. 1,414.5

Answer 26

B.

Question 27

The teacher marked the quiz on the following basis: one point for each correct answer, one point off for each question left blank and two points off for each question answered incorrectly. Pat made four times as many errors as Mike, but Mike left nine more questions blank. If they both got the same score, how many errors did each make? A. Pat made eight errors and Mike made two errors. B. Pat made nine errors and Mike made one error. C. Pat made eight errors and Mike made four errors. D. Pat made seven errors and Mike made three errors.

Answer 27

A.

Question 28

A student, just beginning the study of logarithms, was required to evaluate an expression of the form of (log A)/(log B). He proceeded to cancel common factors in both numerator and denominator, (including the “factor” log), and arrived at the result 2/3. Surprisingly, this was correct. What were the values of A and B? A. A = 8/4, B = 28/8 B. A = 9/4, B = 28/8 C. A = 9/5, B = 26/8 D. A = 9/4, B = 27/8

Answer 28

D.

Question 29

[MAY 2017] There are four towns at the corners of a square. Four motorists set out, each driving to the next (clockwise) town, and each man but the fourth going 8 mph faster than the car ahead – thus the first car travels 24 mph faster than the fourth. At the end of one hour the first and third cars are 204, and the second and fourth 212 (beeline) miles apart. How fast is the first car traveling and how far apart are the towns? A. 50 mph, 180 miles B. 49 mph, 180 miles C. 48 mph, 180 miles D. 50 mph, 182 miles

Answer 29

A.

Question 30

Solve the equation sqrt(x + sqrt(x + sqrt(x + … = sqrt(x sqrt(x sqrt x … where both members represent infinite expressions. A. x = 1 or 2 B. x = -1 or 2 C. x = 0 or 2 D. x = 0 or 1

Answer 30

C.

Question 31

[APR 2023] A pencil, eraser and notebook together cost $1.00. A notebook costs more than two pencils, and three pencils cost more than four erasers. If three erasers cost more than a notebook, how much does each cost? A. P = $25, E = $19, N = $54 B. P = $26, E = $18, N = $56 C. P = $26, E = $19, N = $55 D. P = $25, E = $18, N = $55

Answer 31

C.

Question 32

A forgetful physicist forgot his watch one day and asked an E.E. on the staff what time it was. The E.E. Iooked at his watch and said: “The hour, minute, and sweep second hands are as close to trisecting the face as they ever come. This happens only twice in every 12 hours, but since you probably haven't forgotten whether you ate lunch, you should be able to calculate the time.” What time was it to the nearest second? A. 2:54:35 or 9:5:25 B. 2:55:45 or 9:6:35 C. 2:55:35 or 9:6:25 D. 2:53:35 or 9:4:25

Answer 32

A.

Question 33

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? A. 13 faces B. 14 faces C. 12 faces D. 15 faces

Answer 33

B.

Question 34

[NOV 2017] A new kind of atom smasher is to be composed of two tangents and a circular arc which is concave towards the point of intersection of the two tangents. Each tangent and the arc of the circle is 1 mile long. What is the radius of the circle? A. 1437.40 feet B. 1438.45 feet C. 1436.45 feet D. 1437.45 feet

Answer 34

D.

Question 34

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. A. Sqrt(16) units B. Sqrt(18) units C. Sqrt(19) units D. Sqrt(18.5) units

Answer 34

B.

Question 35

[NOV 2017] 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? A. 58 feet B. 57 feet C. 56 feet D.55 feet

Answer 35

A.

Question 36

A circle of radius I inch is inscribed in an equilateral triangle. A smaller circle is inscribed at each vertex, tangent to the circle and two sides of the triangle. The process is continued with progressively smaller circles. what is the sum of the circumference of all circles. A. 7π B. 5π C. 4π D. 9π

Answer 36

B.

Question 37

[NOV 2023] A farmer owned a square field measuring exactly 2261 yards on each side. 1898 yards from one corner and 1009 yards from an adjacent corner stood a beech 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 beech tree was part of the fence. The farmer accepted the offer but made sure that the triangular portion was of minimum area. What was the area of the field the neighbor received, and how long was the fence? A. 939,120 square yards, 2018 yards B. 939,100 square yards, 2019 yards C. 938,120 square yards, 2018 yards D. 939,110 square yards, 2016 yards

Answer 37

A.

Question 38

A man leaves from the point where the prime meridian crosses the equator and moves forty-five degrees northeast by geographic compass which always points toward the north geographic pole. He constantly corrects his route. Assuming that he walks with equal facility on land and sea, where does he end up and how far will he have travelled when he gets there? A. 10^7 sqrt(3) meter B. 10^7 sqrt(1.5) meter C. 10^7 sqrt(2) meter D. 10^7 sqrt(5) meter

Answer 38

C.

Question 39

Near the town of 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 the 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? A. 600 yards B. 800 yards C. 700 yards D. 900 yards

Answer 39

A.

Question 40

Three hares are standing in a triangular field 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 corner on his left, thus following a curved course which terminates in the middle of the field, all three hares arriving there together. The hares obviously ran at the same speed, but just how far did they run? A. 400 yards B. 300 yards C. 100 yards D. 200 yards

Answer 40

C

Question 41

Scalene triangle ABC, which is not a right triangle, has sides which are integers. If sin A = 5/13, find the smallest values for its sides, i.e., those values which make the perimeter a minimum. A. a = 26, b = 17, c = 39 B. a = 25, b = 16, c = 39 C. a = 24, b = 15, c = 39 D. a = 25, b = 15, c = 40

Answer 41

B.

Question 42

A one-acre field 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? A. 1 acre B. 1.5 acre C. 2 acre D. 2.5 acre

Answer 42

A.

Question 43

A divided highway goes under a number of bridges, the arch over each lane being in the form of a semi-ellipse with the height equal to the width. A truck is 6 ft. wide and 12 ft. high. What is the lowest bridge under which it can pass? A.12 ft. 5 in. high B. 13 ft. 3 in. high C. 13 ft. 6 in. high D. 13 ft. 5 in. high

Answer 43

D.

Question 44

A cowboy is five miles south of a stream which flows due east. He is also 8 miles west and 6 miles north of his cabin. He wishes to water his horse at the stream and return home. What is the shortest distance he can travel and accomplish this? A. 17.8 miles B. 17.7 miles C. 17.9 miles D. 17.95 miles

Answer 44

C.

Question 45

While still at a sizable distance from the Pentagon building, a man first catches sight of it. Is he more likely to be able to see two sides or three? A. Equal probability of 1/4 B. Equal probability of 1/2 C. Equal probability of 2/3 D. Equal probability of 3/4

Answer 45

B.

Question 46

A pirate buried his treasure on an island, a conspicuous landmark of which were three palm trees, each one 100 feet from the other two. Two of these trees were in a NS line. The directions for finding the treasure read: “Proceed from southernmost tree 15 feet due north, then 26 feet due west.” Is the treasure buried within the triangle formed by the trees? A. The treasure lies inside. B. The treasure lies nearby. C. The treasure lies beyond. D. The treasure lies outside

Answer 46

D.

Question 47

An Origami expert started making a Nani-des-ka by folding the top left corner of a sheet of paper until it touched the right edge and the crease passed through the bottom left corner. He then did the same with the lower right corner, thus making two slanting parallel lines. The paper was 25 inches long and the distance between the parallel lines was exactly 7/40 of the width. How wide was the sheet of paper? A. 23 in B. 23.5 in C. 24 in D. 24.5 in

Answer 47

C.

Question 48

The Ben Azouli are camped at an oasis 45 miles west of Taqaba. They decide to dynamite the TransHadramaut railroad joining Taqaba to Maqaba, 60 miles north of the oasis. If the Azouli can cover 18 miles a day, how long will it take them to reach the railroad? A. One day B. Two days C. One and a half days D. Two and a half days

Answer 48

B.

Question 49

[NOV 2017] A cross section through the center of a football is a circle x inches in circumference. The football is x – 8 inches long from the tip to tip and each seam is an arc of a circle ¾ if x inches in diameter. Find x. A. 19.69 in B. 20.65 in C. 20.68 in D. 20.69 in

Answer 49

D.

Question 50

A yang, ying, and yung is constructed by dividing a diameter of a circle, AB, into three parts by points C and D, then describing on one side of AB semicircles having AC and AD as diameters and on the other side of AB semicircles having BD and BC as diameters. Which is larger, the central portion or one of the outside pieces? A. All three are the same size B. All three are different sizes C. Two are the same size D. None are the same size

Answer 50

A.

Question 51

A diaper is in the shape of a triangle with sides 24, 20 and 20 inches. The long side is wrapped around the baby’s waist and overlapped two inches. The third point is brought up to the center of the overlap and pinned in place. The pin is to go through three thicknesses of material. What is the area in which the pin may be placed? A. 2.5 square in B. 2.5 square ft C. 2.6 square in D. 2.7 square in

Answer 51

A.

Question 52

[NOV 2016] 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? What is the capacity of the pot? A. 2% of the way down from the top, 3 1/4 cups B. 2% of the way down from the top, 3 1/2 cups C. 2% of the way down from the top, 3 1/37 cups D. 2% of the way down from the top, 3 cups

Answer 52

C.

Question 53

[MAY 2018] 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? A. Almost 32 times B. Almost 30 times C. Almost 33 times D. Almost 31 times

Answer 53

C.

Question 54

There is one flag at the entrance to a racetrack and another inside the track, half a mile from the first. A jockey notes that no matter where he is on the track, one flag is 3 times as far away as the other. How long is the track? A. 1980π² B. 1980π C. 1981π D. 1970π

Answer 54

B.

Question 55

What is the longest 6' wide shuffleboard court which will fit in a 20’ x 30’ rectangular room? A. 30.8750 B. 30.9 C. 30.875 D. 30.8755

Answer 55

C.

Question 56

Find the smallest number (x) of persons a boat may carry so that (n) married couples may cross a river in such a way that no woman ever remains in the company of any man unless her husband is present. Also find the least number of passages (y) needed from one bank to the other. Assume that the boat can be rowed by one person only. A. n = 2, x = 2, y = 5 B. n = 2, x = 3, y = 5 C. n = 2, x = 2, y = 4 D. n = 3, x = 2, y = 5

Answer 56

A.

Question 57

A, B, and C participate in a track meet, consisting of at least three events. A certain number of points are given for first place, a smaller number for second place, and a still smaller number for third place. A won the meet with a total score of 14 points; B and C are tied for second with 7 points apiece. B won first place in the high jump. Who won the pole vault assuming no ties occurred in any event? A. A won the long jump B. B won the pole vault C. A won the triple jump D. A won the pole vault

Answer 57

D.

Question 58

Find the simplest solution in integers for the equation (1/x^(2)) + (1/y^(2)) = (1/z^(2)). A. x = 15, y = 20, z = 11 B. x = 14, y = 20, z = 12 C. x = 15, y = 20, z = 12 D. x = 15, y = 19, z = 13

Answer 58

C.

Question 59

Maynard the Census Taker visited a house and was told, “Three people live there, The product of their ages is 1296, and the sum of their ages is our house number.” After an hour of cogitation Maynard returned for more information. The house owner said, “I forgot to tell you that my son and grandson live here with me.” How old were the occupants and what was their street number? A. Ages: 1, 18, and 72 Street number: 91 B. Ages: 1, 18, and 73, Street number: 90 C. Ages: 1, 17, and 73, Street number: 93 D. Ages: 1, 19, and 72, Street number: 92

Answer 59

A.

Question 60

In Byzantine basketball there are 35 scores which are impossible for a team to total, one of them being 58. Naturally a free throw is worth fewer points than a field goal. What is the point value of each? A. Free throw: 9, Field goal: 12 B. Free throw: 8 Field goal: 11 C. Free throw: 7, Field goal: 11 D. Free throw: 7, Field goal: 10

Answer 60

B.

Question 61

Gherkin Gesundheit, a brilliant graduate mathematics student, was working on an assignment but, being a bit absent-minded, he forgot whether he was to add or to multiply the three different integers on his paper" He decided to do it both ways and, much to his surprise, the answer was the same. What were the three different integers? A. 1, 2, 5 B. 1, 2, 3 C. 1, 2, 4 D. 2, 3, 4

Answer 61

B.

Question 62

[NOV 2022] Three farmers, Adams, Brown and Clark all have farms containing the same number of acres. Adams' farm is most nearly square, the length being only 8 miles longer than the width. Clark has the most oblong farm, the length being 34 miles longer than the width. Brown's farm is intermediate between these two, the length being 28 miles longer than the width. If all the dimensions are in exact miles, what is the size of each farm? A. 40x48, 32x60, 30x64 B. 40x48, 31x60, 30x65 C. 41x48, 32x61, 29x64 D. 39x48, 33x60, 31x64

Answer 62

A.

Question 63

1960 and 1961 were bad years for ice cream sales but 1962 was very good. An accountant was looking at the tonnage sold in each year and noticed that the digital sum of the tonnage sold in 1962 was three times as much as the digital sum of the tonnage sold in 1961. Moreover, if the amount sold in 1960 (346 tons), was added to the 1961 tonnage, this total was less than the total tonnage sold in 1962 by the digital sum of the tonnage sold in that same year. Just how many more tons of ice cream were sold in 1962 than in the previous year? A. 360 tons B. 361 tons C. 362 tons D. 363 tons

Answer 63

B.

Question 64

Three rectangles of integer sides have identical areas. The first rectangle is 278 feet longer than wide. The second rectangle is 96 feet longer than wide. The third rectangle is 542 feet longer than wide. Find the area and dimensions of the rectangles. A. Area: 1,466,650 ft² Dimensions: 1081x1356, 1163x1261, 969x1513 B. Area: 1,467,000 ft² Dimensions: 1085x1350, 1160x1258, 975x1510 C. Area: 1,466,700 ft² Dimensions: 1082x1355, 1166x1262, 972x1510 D. Area: 1,466,640 ft2 Dimensions: 1080x1358, 1164x1260, 970x1512

Answer 64

D.

Question 65

When little Willie had sold all his lemonade, he found he had $7.95 in nickels, dimes, and quarters. There were 47 coins altogether and, having just started to study geometry, he noticed that the numbers of coins satisfied a triangle inequality, i.e., the sum of any two denominations was greater than the third. How many of each were there? A. D = 20, Q = 32, N = 4 B. D = 20, Q = 33, N = 4 C. D = 20, Q = 32, N = 5 D. D = 20, Q = 30, N = 3

Answer 65

A.

Question 66

There are 100 coins in a piggy bank totaling $5.00 in value, the coins consisting of pennies, dimes, and half dollars. How many of each are there? A. P = 59, D = 39, H = 1 B. P = 60, D = 39, H = 1 C. P = 60, D = 39, H = 2 D. P = 60, D = 38, H = 1

Answer 66

B.

Question 67

Every year engineering consultant pays a bonus of $300 to his most industrious assistant, and $75 each to the rest of his staff. After how many years would his outlay be exactly $6,000 if all but two of his staff had merited the $300 bonus, but none of them more than twice? A. Years: 7, Staff: 8 B. Years: 8 Staff: 7 C. Years: 8, Staff: 9 D. Years: 8, Staff: 6

Answer 67

B.

Question 68

In European countries the decimal point is often written a little above the line. An American, seeing a number written this way, with one digit on each side of the decimal point, assumed the numbers were to be multiplied. He obtained a two-digit number as a result but was 14.6 off. What was the original number? A. 5.3 B. 5.2 C. 5.4 D. 5.5

Answer 68

C.

Question 69

Two wheels in the same plane are mounted on shafts 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? A. 5 in B. 6 in C. 7 in D. 8 in

Answer 69

A.

Question 70

Five points are located in or on the perimeter of an equilateral triangle with 9-inch sides. If d is the distance between the closest pair of points, what is the maximum possible value of d? A. 4.5 in B. 4.55 in C. 4.3 in D. 4.4 in

Answer 70

A.

Question 71

If THAT = (AH)(HA), what is THAT? A. 6785 B. 6786 C. 6776 D. 6796

Answer 71

B.

Question 72

A group of hippies are pondering whether to move to Patria, where polygamy is practiced but polyandry and spinsterhood are prohibited, or Matria, where polyandry is permitted, and polygamy and bachelorhood are proscribed. In either event the possible number of “arrangements” is the same. The girls outnumber the boys. How many are there? A. 3 girls and 2 boys B. 4 girls and 3 boys C. 4 girls and 1 boy D. 4 girls and 2 boys

Answer 72

D.

Question 73

Dad and his son have the same birthday. On the last one, Dad was twice as old as Junior. Uncle observed that this was the ninth occasion on which Dad's birthday age had been an integer multiple of Junior's. How old is Junior? A. Junior: 36 Dad: 72 B. Junior: 36, Dad: 71 C. Junior: 36, Dad: 70 D. Junior: 35, Dad: 72

Answer 73

A.

Question 74

The undergraduates of a School. of Engineering wished to form ranks for a parade. In ranks of 3 abreast, 2 men were left over; in ranks of 5, 4 over; in 7's,6 over; and 11's, 10 over. What is the least number of marchers there must have been? A. 1154 marchers B. 1155 marchers C. 1140 marchers D. 1153 marchers

Answer 74

A.

Question 75

What is the remainder upon dividing 5^999,999 by 7? A. 4 B. 6 C. 8 D. 12

Answer 75

B.

Question 76

A pet store offered a baby monkey for sale at $1.25. The monkey grew. Next week it was offered at $1.89, then $5.13, then $5.94, then $9.18. What will be the price of the monkey on the sixth week? A. $12.40 B. $12.42 C. $12.43 D. $12.45

Answer 76

B.

Question 77

Assume the universe is a billion billion light years in diameter and is packed solidly with matter weighing a billion billion tons per cubic inch and each gram of this matter contains a billion billion atoms. Also, every second during the past billion billion years, a billion billion similar universes were created- Without using any symbols and restricting yourself to a total of three digits, write a number that far exceeds the total atoms of all these universes. A. 9^(9^(3)) B. 9^(9^(6)) C. 9^(9^(9)) D. 9^(9^(12))

Answer 77

C.

Question 78

The sum of the digits on the odometer in my car (which reads up to 99999.9 miles) has never been higher than it is now, but it was the same 900 miles ago. How many miles must I drive before it is higher than it is now. A. 100 miles B. 200 miles C. 300 miles D. 400 miles

Answer 78

A.

Question 79

The first expedition to Mars found only the ruins of a civilization. The explorers were able to translate a Martian equation as follows: 5x^2 – 50x + 125 = 0, x = 5, x = 8. This was strange mathematics. The value x = 5 seemed legitimate enough but x = 8 required some explanation. If the Martian number system developed in a manner similar to ours, how many fingers would you say the Martians had? A. 15 fingers B. 12 fingers C. 13 fingers D. 10 fingers

Answer 79

C.

Question 80

A rectangular picture, each of whose dimensions is an integral number of inches, has an ordinary rectangular frame 1 inch wide. Find the dimensions of the picture if the area of the picture and the area of the frame are equal? A. 3x10 or 4x5 B. 3x10 or 4x6 C. 3x9 or 4x6 D. 3x9 or 4x5

Answer 80

B.

Question 81

My house is on a road where the numbers run 1, 2, 3, 4., - consecutively. My number is a three digit one and, by a curious coincidence, the sum of all house numbers less than mine is the same as the sum of all house numbers greater than mine. What is my number and how many houses are there on my road? A. House number: 204 Number of houses: 288 B. House number: 204, Number of houses: 290 C. House number: 204, Number of houses: 280 D. House number: 205, Number of houses: 289

Answer 81

A.

Question 82

The sum and difference of two squares may be primes: 4 – 1 = 3 and 4 + 1 = 5; 9 – 4 = 5 and 9 + 4 = 13, etc. Can the sum and difference of two primes be squares? If so, how many different primes is this possible? A. p = 2, q = 2 B. p = 2, q = 3 C. p = 2, q = 4 D. p = 2, q = 5

Answer 82

A.

Question 83

In what days of the week can the first day of a century fall? (The first day of the twentieth century was Jan. 1, 1901) A. Monday, Wednesday, Friday, and Sunday only, The 21st century will start on a Tuesday B. Monday, Thursday, Friday, and Sunday only, The 21st century will start on a Thursday C. Monday, Tuesday, Thursday, and Saturday only The 21st century will start on a Monday D. Monday, Tuesday, Wednesday, and Friday only, The 21st century will start on a Wednesday

Answer 83

C.

Question 84

In the arithmetic of Puevigi, 14 is a factor of 41. What is the base of the number system? A. 10 B. 11 C. 12 D. 13

Answer 84

B.

Question 85

No factorial can end in five zeros. What is the next smallest number of zeros in which a factorial cannot end? A. 11 B. 13 C. 15 D. 17

Answer 85

A.

Question 86

Barnie Bookworm bought a thriller - found to his dismay, Just before the denouement a fascicle astray. Instead of counting one through ten, a standard cure for rages, He totaled up the number of the missing sheal of pages. The total was eight thousand and six hundred fifty-six. What were the missing pages? Try to find them just lor kicks A. Page 225-286 B. Page 224-285 C. Page 225-285 D. Page 226-287

Answer 86

A.

Question 87

The Sultan arranged his wives in order of increasing seniority and presented each with a golden ring. Next, every 3rd wife, starting the 2nd, was given a 2nd ring; of every 3rd one starting with the 2nd received a 3rd ring, etc. His first and most cherished wife was the only one to receive 10 rings. How many wives had the Sultan. A. 9,841 wives B. 9,843 wives C. 9,842 wives D. 9,000 wives

Answer 87

C.

Question 88

The alphametic LIX + LVI = CXV and X^2 = C involving Roman numerals is correct. It will still be correct if the proper Arabic numerals are substituted. Each letter denotes the same digit throughout, and no 2 letters stand for the same digit. Find the unique solution. A. 940 B.939 C. 938 D. 937

Answer 88

C.

Question 89

A ball is dropped from a height of 10 feet. It rebounds one-half the distance in each bounce. What is the total distance it travels? A. 30 feet B. 40 feet C. 50 feet D. 60 feet

Answer 89

A.

Question 90

A rectangular box without a top is to be made from a sheet of metal in the manner familiar to all calculus students, i.e., by cutting out squares from the corners and bending up the sides. The finished product is to have maximum volume and its dimensions are to be all integers" How will these dimensions compare if the metal cutout amounts to 10% of the original sheet? A. 6:2:1 B. 6:3:1 C. 6:3:2 D. 7:3:2

Answer 90

B.

Question 91

A student studying series starts with the familiar 1 + 1/2 + 1/4 + 1/8 + … and inserts terms midway between these, obtaining 1 + 3/4 + 1/2 + 3/8 + ¼ + … He divides this by 2, since, as he explains it. “There are now twice as many terms as before.” He repeats the process, interpolating terms between those already placed, again dividing by 2. If he continues this indefinitely, what limit will the series approach? A. 2/3 B. 3/2 C. 4/2 D. 3/1

Answer 91

B.

Question 92

Mr. X veers to the right when he walks. The curvature of his path is proportional to his latitude. He starts walking North from point A on the equator, in the area of a large level plain, and finds he Is proceeding East when he is one mile north of the equator. He continues walking and arrives back at the equator at point B. What is the straight-line distance from A to B? A. 2x = a trifle less than 1.2 miles B. 2x = a little less than 1.3 miles C. 2x = a trifle less than 1 mile D. 2x = a trifle less than 1.5 miles

Answer 92

A.

Question 93

Which contains more terms: the general polynomial of tenth degree in six variables or the general polynomial of sixth degree in ten variables? A. Both are equal (8,100 terms) B. Both are equal (8,010 terms) C. Both are equal (8,000 terms) D. Both are equal (8,008 terms)

Answer 93

D.

Question 94

A boat owner agrees to take a group on an outing at $4.50 apiece if the number of passengers is equal to or less than his break-even point. For each person above this he reduces the fare for all passengers 3 cents per person. If he has on board now the number of passengers that maximizes the total collected, what is the boat owner's profit? A. Zero B. One C. Five D. Two

Answer 94

A.

Question 95

The price per cubic inch for plantinum trays is the same as that per square inch for platinum sheets. A metal supply house has a square of platinum which will yield the same amount whether sold as a sheet or fashioned into a tray of maximum volume with the four cut-out corners sold as sheets. How big is the square? A. 1 foot B. 2 feet C. Half a foot D. One and a half feet

Answer 95

A.