MSTE B-E

Question 1

In a lottery the total prize money available was a million dollars, paid out in prizes which
were powers of $11 viz., $1, $11, $121, etc. Noe more than 6 people received the same prize.
How many prize winners were there, and how was the money distributed?

A. 10
B. 20
C. 30
D. 40

Answer 1

B

Question 2

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. Age = 2 and 20 , St. No. = 71
B. Age = 1 and 18, St. No = 73
C. Age = 1 and 19, St. No. = 72
D. Age = 1 and 18, St. No. = 72

Answer 2

D

Question 3

Dr. Reed, arriving late at the lab one morning, pulled out his watch 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. Gains 60/143 minutes
B. Loses 60/143 minutes
C. Gains 60/144 minutes
D. Gains 60/142 minutes

Answer 3

A

Question 4

A salesman visits ten cities arranged in the form of a circle, spending a day in each. He
proceeds clockwise from one city to the next, except whenever leaving the tenth city. How
many days must elapse before his location is completely indeterminate, i.e., when he could
be in any one of the ten cities?

A. 82
B. 83
C. 84
D. 85

Answer 4

B

Question 5

A man walks one mile south, one mile west, and then one mile north ending where he
began. From how many points on the surface of the earth can such a journey be made?
(There are more than 1)

A. 0
B. 1
C. Infinite
D. None of the above

Answer 5

C

Question 6

How many colors are necessary for the squares of a chessboard in order to assure that a
bishop cannot move from one square to another of the same color?

A. 8
B. 9
C. 10
D. 11

Answer 6

A

Question 7

Six boys on a hockey team pick a captain by forming a circle and counting out until only
one remains. Joe is given the option of deciding what number to count by. If he is second
in the original counting order what number should he choose?

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

Answer 7

B

Question 8

Six grocers in a town each sell a different brand of tea in four ounce packets at 25 cents
per packet. One of the grocers gives short weight, each packet of his brand weighing only
3 ¾ ounces. If I can use a balance for only one weighing, what is the minimum amount I
must spend to be sure of finding the grocer who gives short weight?

A. 3.6 dollars
B. 3.7 dollars
C. 3.8 dollars
D. 3.9 dollars

Answer 8

B

Question 9

On a certain day, our parking lot contains 999 cars, no two of which have the same 3- digit
license number. After 5:00 p.m. what is the probability that the license numbers of the
first 4 cars to leave the parking lot are in increasing order of magnitude?

A. 4!
B. 5!
C. 3!
D. 6!

Answer 9

A

Question 10

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. 358
B. 359
C. 360
D. 361

Answer 10

D

Question 11

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. 5.2 = 20
B. 5.3 = 20
C. 5.4 = 20
D. 5.4 = 21

Answer 11

C

Question 12

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. 99 yards
B. 100 yards
C. 101 yards
D. 102 yards

Answer 12

B

Question 13

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. one acre
B. two acre
C. three acre
D. four acre

Answer 13

A

Question 14

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. 2x10
B. 4x6
C. 3x10
D. 5x7

Answer 14

B or C

Question 15

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. 21 inches
B. 22 Inches
C. 23 inches
D. 24 inches

Answer 15

D

Question 16

The Sultan arranged his wives in order of increasing seniority and presented each with a
golden ring. Next, every 3rd wide, starting with the 2nd, was given a 2nd ring; of these
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. 9840 wives
B. 9841 wives
C. 9842 wives
D. 9843 wives

Answer 16

C

Question 17

The undergraduate of a School of Engineering wished to form ranks for a parade. In ranks
of 3 abreast, 2 m2n 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. 1151
B. 1152
C. 1154
D. 1155

Answer 17

C

Question 18

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. No of Person = 2 ; No of Passage = 5
B. No of Person = 3 ; No of Passage = 4
A. No of Person = 2 ; No of Passage = 4
A. No of Person = 3 ; No of Passage = 5

Answer 18

A

Question 19

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. 99
B. 100
C. 101
D. 102

Answer 19

B

Question 20

A certain magic square contains nine consecutive 2-digit numbers. The sum of the
numbers in any line is equal to one of the numbers in the square with the digits reversed.
This is still the case if 7 is added to each entry. What is the number in the center square?

A. 5pi
B. 17
C. 100
D. 25

Answer 20

B

Question 21

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 18 seconds. How long after the train
has passed the second man will the two men meet? (Constant speeds are to be assumed
throughout.)

A. 5562
B. 136
C. 169
D. 83

Answer 21

A

Question 22

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 direction the other took, the
first snail would have reached his food 35 minutes after the second. How do their speeds
compare?

A. 1/2
B. 3/4
C. 2/3
D. 1

Answer 22

B

Question 23

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. 0.514
B. 25
C. 35
D. 24

Answer 23

B

Question 24

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

Answer 24

B

Question 25

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. Thee 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 be he expect to win)
or lose) on each game?

A. Loss 24 cents/game
B. Gains 25 cents/game
C. Loss 25 cents/game
D. Loss 24 cents/game

Answer 25

C

Question 26

There are four volumes of an encyclopedia on a shelf, each volume containing 300 pages,
(that is, numbered 1 to 600), but these have been placed n the shelf in random order. A
bookworm starts at the first page of Vol. 1 and eats his way through to the last page of Vol.
4. What is the expected number of pages (excluding covers) he has eaten through?

A. 5562
B. 100
C. 500
D. 700

Answer 26

C

Question 27

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. 6
B. 23
C. 4
D. 8

Answer 27

C

Question 28

Dr. Fubisher LaRouche, the noted mathematician, was shoping at a hardware store and
asked the price of certain articles. The salesman replied. “One would cost 10 cents, eight
would ost 10 cents, seventeen would cost 20 cents, one hundred and four would cost 30
cents, seven hundred and fifty-six would aslo cost 30 cents, and one thousand and seventytwo would cost 40 cents.” What was Dr. LaRouche buying?

A. 20 cent/number
B. 15 cent/number
C. 25 cent/number
D. 10 cent/number

Answer 28

D

Question 29

In a memorable game with the Podunk Polecats, the Mudville Mets established a record.
They received the maximum number of walks possible in one inning in which one player
(who happened to ne the Mighty Casey) was up three times and accounted for all three
outs. How many walks did Podunk allow in that tedious half-inning?

A. 10
B. 20
C. 30
D. 40

Answer 29

C

Question 30

In the game “subtract-a-square,” a positive integer is written down and two players
alternately subtract squares from it with the restriction that the remainder must never be
less than zero. The player who leaves zero wins. What square should the first player
subtract if the original number is 29?

A. 9
B. 10
C. 11
D. 12

Answer 30

A

Question 31

Maynard’s Grandfather Clock is driven by two weights, one for the striking mechanism
which strikes the hours only, and the other for the time mechanism. When he hears the
clock strike his bedtime, he immediately winds the clock and retires. After winding, the
weighs are exactly opposite each other. The weighs are again opposite every six hours
thereafter. What is Maynard’s bedtime?

A. 6pm or 7am
B. 9pm or 3am
C. 9pm or 2am
D. 3pm or 9am

Answer 31

B

Question 32

In a fast Major League baseball game, pitcher Hi N. Outside managed to get by possible.
He played the entire game, which was not called prior to completion. How many pitches
did he make?

A. 23 pitches
B. 24 pitches
C. 25 pitches
D. 26 pitches

Answer 32

C

Question 33

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?

A. 1/2
B. 2/5
C. 2/3
D. 3/4

Answer 33

B

Question 34

If two marbles are removed at random from a bag containing lack and white marbles, the
chance that they are both white is 1/3. If 3 are removed at random, the chance that they
all are white is 1/6. How many marbles are there of each color?

A. 3 whites, 2 black
B. 4 whites, 3 black
C. 5 white, 4 black
D. 6 white, 4 black

Answer 34

D

Question 35

A chemist has three large test tubes and a beaker with 54 c.c. of elixir. Using the test tubes
and ingenuity only, how can he retain 50 c.c. in the beaker?

A. 30
B. 40
C. 50
D. 60

Answer 35

C

Question 36

A neat computer programmer wears a clean shirt every day. If he drops off his laundry and
picks up the previous week’s load every Monday night, how many shirts must he own to
keep him going?

A. 14
B. 13
C. 15
D. 16

Answer 36

C

Question 37

A sharp operator makes the following deal. A player is to toss a coin and receive 1, 4, 9, …..
n2 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 repeated a great
many times?

A. 3 dollars/game
B. 4 dollars/game
C. 5 dollars/game
D. 6 dollars/game

Answer 37

B

Question 38

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. 30
D. 31

Answer 38

B

Question 39

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

A. 10 rupees
B. 90 rupees
C. 50 rupees
D. 100 rupees

Answer 39

C

Question 40

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 clasp and string together weigh as much (in carats) as the total number of
pearls, how many pearls does the necklace contain?

A. 33 pearls
B. 34 pearls
C. 35 pearls
D. 32 pearls

Answer 40

A

Question 41

. 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 = 4, Mike = 2
B. Pat = 8, Mike = 2
C. Pat = 2, Mike = 4
D. Pat = 2, Mike = 8

Answer 41

B

Question 42

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 No. = 205, No. of houses = 204
B. House No. = 204, No. of houses = 205
C. House No. = 208, No. of houses = 204
D. House No. = 204, No. of houses = 208

Answer 42

D

Question 43

Four players played a hand of hearts at $1 a point (pairwise payoffs). Dave lost $10 to Arch,
$12 to Bob, and $20 to Chuck. How many hearts did poor Dave take in?

A. 1
B. 2
C. 3
D. 4

Answer 43

D

Question 44

. All the members of a fraternity play basketball while all but one play ice hockey; yet the
number of possible basketball teams (5 members) is the same as the number of possible
ice hockey teams (6 members). Assuming there are enough members to form either type
of team, how many are in the fraternity?

A. 10
B. 15
C. 20
D. 25

Answer 44

B

Question 45

A game of super-dominoes is played with pieces divided into three cells instead of the
usual two, containing all combinations from triple blank to triple six, with no duplications.
For example, the set does not include both 1 2 3 and 3 2 1 since these are merely reversals
of each other. (But, it does contain 1 3 2.) How many pieces are there in a set?

A. 136
B. 163
C. 196
D. 169

Answer 45

C

Question 46

. 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. 17
B. 18
C. 19
D. 20

Answer 46

B

Question 47

A circle of radius 1 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. 5pi
B. 4pi
C. 3pi
D. 6pi

Answer 47

A

Question 48

Max and his wife Min each toss a pair of dice to determine where they will spend their
vacation. If either of Mins dice displays the same number of spots as either of Max’s, she
wins and they go to Bermuda. Otherwise, they go to Yellowstone. What is the chance they’ll
see “Old Faithful” this year?

A. 0.541
B. 0.514
C. 0.154
D. 0.451

Answer 48

B

Question 49

How many three-digit telephone area codes are possible given that: (a) the first digit must
not be zero or one; (b) the second digit must be zero or one; (c) the third digit must not be
zero; (d) the third digit may be one only if the second digit is zero?

A. 163
B. 136
C. 169
D. 196

Answer 49

B

Question 50

Rigorously speaking, two men are “brothers- in-law” if one is married to the full sister of
the other. How many men can there be with each man a brother-in-law of every other
man?

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

Answer 50

A

Question 51

A forgetful physicist forgot his watch one day and asked an E.E. on the staff what time it
was. The E.E. looked 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. 2:45:53 and 9:50:52
B. 2:54:35 and 9:05:25
C. 2:55:25 and 9:50:35
D. 2:54:55 and 9:45:25

Answer 51

B

Question 52

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. 1.5
B. 2
C. 2.5
D. 3

Answer 52

C

Question 53

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 = 8, Field goal = 11
B. Free throw = 11, Field goal = 8
C. Free throw = 8, Field goal = 18
D. Free throw = 18, Field goal = 11

Answer 53

A

Question 54

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 traveled when he
gets there?

A. North Pole, sqrt 2x10^7
B. North Pole, sqrt 7x10^2
C. North Pole, sqrt 3x10^2
D. North Pole, sqrt 2x10^3

Answer 54

A

Question 55

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. 19.7 miles
B. 16.7 miles
C. 17.9 miles
D. 17.7 miles

Answer 55

C

Question 56

The Ben Azouli are camped at an oasis 45 miles west of Taqaba. They decided to dynamite
the Trans-Hadramaut 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. 1
B. 2
C. 3
D. 4

Answer 56

B

Question 57

A student beginning the study of Trigonometry came across an expression of the form sin
(X + Y). He evaluated this as sin X + sin Y. Surprisingly he was correct. The values of X
and Y differed by 10˚; what were these values, assuming that 0˚ < X < Y < 360˚?

A. x = 165, y = 175
B. x = 175, y =185
C. x = 185, y = 175
D. x = 175, y = 165

Answer 57

B

Question 58

Dad and his son have the same birthday. One the last one, Dad was twice as old as Junior.
Uncle observed that this was the ninth occasion on which Dad’s birthday age has been an
integer multiple of Junior’s. How old is Junior?

A. Junior = 36, Dad = 72
B. Junior = 34, Dad = 72
C. Junior = 35, Dad = 71
D. Junior = 36, Dad = 73

Answer 58

A

Question 59

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 towns uniquely. What is the minimum distance between Kroflite and Beeline to
make this possible?

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

Answer 59

B

Question 60

There are three families, each with two sons and two daughters. In how many ways can all
these young people be married?

A. 75
B. 85
C. 90
D. 80

Answer 60

D

Question 61

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% freethrower. What are your team’s overall chances of winning?

A. 96%
B 36%
C. 69%
D. 63%

Answer 61

C

Question 62

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. 4 inches
B. 3 inches
C. 5 inches
D. 6 inches

Answer 62

C

Question 63

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. Boys = 3, Girls = 2
B. Boys = 4, Girls = 2
C. Boys = 3, Girls = 5
D. Boys = 2, Girls = 4

Answer 63

D

Question 64

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. Adam = 40x47 ; Brown = 30x63 ; Clark = 30x64
B. Adam = 40x46 ; Brown = 30x63 ; Clark = 30x64
C. Adam = 40x48 ; Brown = 32x60 ; Clark = 30x64
D. Adam = 40x48 ; Brown = 30x64 ; Clark = 32x60

Answer 64

C

Question 65

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

A. 4:27.853
B. 4:25.853
C. 4:26.853
D. 4:28.853

Answer 65

C

Question 66

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 = 1,466,690 ; Dimension = (1080x1358) ; (1163x1260) ; (970x1512)
B. Area = 1,469,960 ; Dimension = (1086x1348) ; (1160x1260) ; (970x1512)
C. Area = 1,465,960 ; Dimension = (1086x1348) ; (1160x1260) ; (970x1512)
D. B. Area = 1,469,960 ; Dimension = (1080x1348) ; (1163x1260) ; (970x1521)

Answer 66

A

Question 67

Rufus T. Flypaper drives two miles to work every
morning- Very precise, he knows he must average 30
mph to arrive on time. One morning a woman driver
impedes him for the first mile, cutting his average to only
l5 mph. He quickly calculated his proper speed for the
rest of his trip to arrive on time. Assume that his car
could do 120 mph. Could he arrive on time?

A. No; he has already used 3 minutes, the time that
he has to go the whole 4 miles.
B. No; he has already used 2 minutes, the time that
he has to go the whole 4 miles.
C. Yes; he has already used 4 minutes, the time that
he has to go the whole 2 miles.
D. No; he has already used 4 minutes, the time that
he has to go the whole 2 miles.

Answer 67

D

Question 68

Stations A and B are 120 miles apart on a single-track
railroad. At the same time that a train leaves A for B at
25 mph, a train leaves B for A at 15 mph. Just as the
first train leaves A, a South American botfly flies from
the front of the engine straight toward the other train at
100 mph. On meeting the second train it immediately
turns back and flies straight for the first train. It continues
to fly back and forth with undiminished speed until it is
crushed in the eventual collision. How far had the fly
flown?

A. 400 miles
B. 300 miles
C. 500 miles
D. 600 miles

Answer 68

B

Question 69

Maynard’s Grandfather Clock is driven by two weights,
one for the striking mechanism which strikes the hours
only, the other for the time mechanism. When he hears
the clock strike his bedtime, he immediately winds the
clock and retires. After winding, the weights are exactly
opposite each other. The weights are again opposite
every six hours thereafter. What is Maynard’s bedtime?

A. 9 p.m. or 3 a.m.
B. 3 p.m. or 9 a.m.
C. 9 p.m. or 2 a.m.
D. 3 p.m. or 3 a.m.

Answer 69

A

Question 70

Two squares are removed from opposite corners of a
checkerboard leaving 62 squares. Can the
checkerboard be filled with 31 dominoes, each domino
covering two adjacent squares?

A. yes
B. no
C. maybe
D. none of the above

Answer 70

B

Question 71

[MAY 2017] 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?

A. Align the minute hand with the sun’s azimuth, and
south will be midway between the hour hand and
12.
B. Align the hour hand with the sun’s azimuth, and
south will be midway between the hour hand and
12.
C. Align the hour hand with the sun’s azimuth, and
south will be midway between the hour hand and
11.
D. Align the hour hand with the sun’s azimuth, and
south will be midway between the hour hand and
10.

Answer 71

B

Question 72

What letter follows OTTFFSSE_?

A. L
B. M
C. N
D. O

Answer 72

C

Question 73

The numbers are divided into three groups as follows:
0, 3, 6, 8, 9, … in the first group, 1, 4, 7, 11, 14, … in the
second group and 2, 5, 10, 12, 13, … in the third. In
which groups would 15, 16 and 17 be placed?

A. 16 and 15 in the third group, 17 in the second
group
B. 17 and 16 in the third group, 15 in the second
group
C. 15 and 16 in the third group, 17 in the second
group
D. 17 and 15 in the third group, 16 in the second
group

Answer 73

C

Question 74

In a fast Major League baseball game, pitcher Hi N.
Outside managed to get by with the minimum number
of pitches possible. He played the entire game, which
was not called prior completion. How many pitches did
he make?

A. 26
B. 27
C. 28
D. 29

Answer 74

C

Question 75

Determine the next three terms of the sequence 12, 1,
1, 1, …

A. 2, 1, and 4
B. 2, 0, and 3
C. 2, 4, and 3
D. 2, 1, and 3

Answer 75

D

Question 76

[MAY 2017] What is the least number of links that must
be disengaged from a 23-link chain so that any number
of links from 1 to 23 can be obtained by taking one or
more of the pieces?

A. Two (4th and 11th chain)
B. Two (5th and 11th chain)
C. Two (4th and 10th chain)
D. Two (5th and 10th chain)

Answer 76

A

Question 77

The set A contains the integers 0, 4, 5, 9, 11, 12, 13, 14,
19, … The set B contains 1, 2, 3, 6, 7, 8, 10, 15, 16, 17,
18, … Place the 20 and 21 in their proper sets.

A. 21 is in A, 20 is in B
B. 20 is in A, 21 is in B
C. 22 is in A, 21 is in B
D. 21 is in A, 21 is in B

Answer 77

B

Question 78

How many colors are necessary for the squares of a
chessboard in order to assure that a bishop cannot
move from one square to another of the same color?

A. 7
B. 8
C. 9
D. 10

Answer 78

B

Question 79

A neat computer programmer wears a clean shirt every
day. If he drops off his laundry and picks up the previous
week’s load every Monday night, how many shirts must
he own to keep him going?

A. 14
B. 15
C. 16
D. 13

Answer 79

B

Question 80

[MAY 2019] The passengers on an excursion bus
consisted of 14 married couples, 8 of whom brought no
children, and 6 of whom brought 3 children apiece.
Counting the driver, the bus had 31 occupants. How is
this possible?

A. Included among the 18 children were 9 married
couples
B. Included among the 18 children were 7 married
couples
C. Included among the 18 children were 8 married
couples
D. Included among the 18 children were 6 married
couples

Answer 80

C

Question 81

Very few people are aware of the growth pattern of
Jack’s beanstalk. On the first day it increased its height
by 1/2, on the second day by 1/3, on the third day by
1/4, and so on. How long did it take to achieve its
maximum height (100 times its original height)?

A. 198 days
B. 199 days
C. 197 days
D. 196 days

Answer 81

A

Question 82

A jig-saw puzzle contains 100 pieces. A “move” consists
of connecting two clusters (including “clusters” of just
one piece.) What is the minimum number of moves
required to complete the puzzle.

A. 97
B. 98
C. 99
D. 100

Answer 82

C

Question 83

[NOV 2023] A novice librarian shelved a twelve-volume
set of encyclopedias in the following order from left to
right. Volume 8, 11, 5, 4, 9, 1, 7, 6, 10, 3, 12, and 2.
Using her system, where will the annual supplement,
Volume 13, go?

A. Between volumes 11 and 3
B. Between volumes 10 and 4
C. Between volumes 10 and 3
D. Between volumes 11 and 4

Answer 83

C

Question 84

With some sharp reasoning, you ought to be able to
determine the last member of the sequence for which
the first 20 members are: 11, 31, 71, 91, 32, 92, 13, 73,
14, 34, 74, 35, 95, 16, 76, 17, 37, 97, 38, 98, __?

A. 77
B. 78
C. 79
D. 76

Answer 84

C

Question 85

[NOV 2021] 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?

A. 1/5
B. 1/6
C. 1/7
D. 1/3

Answer 85

B

Question 86

Four players played a hand of hearts at $1 a point
(pairwise payoffs). Dave lost $10 to Arch, $12 to Bob,
and $20 to Chuck. How many hearts did poor Dave
take in?

A. 2 hearts and the queen of spades
B. 3 hearts and the queen of spades
C. 4 hearts and the queen of spades
D. 1 heart and the queen of spades

Answer 86

C

Question 87

On a certain campus liberal arts students always lie and
engineers always tell the truth. A stranger meets 3
students and asks the first if he is studying liberal arts.
The first answers the question, but the stranger doesn’t
hear him. The second student then says that the first
denied being a liberal arts student. Then the third
student says that the first is really a liberal arts student.
How many are Iiberal arts students? Can we decide
which?

A. 1, the first
B. 2, the first
C. 3, the first
D. 4, the first

Answer 87

A

Question 88

Four boys, Alan, Brian, Charles, and Donald, and four
girls, Eve, Fay, Gwen, and Helen are each in love with
one of the others, and, sad to say, in no case is their
love requited. Alan loves the girl who loves the man who
loves Eve. Fay is loved by the man who is loved by the
girl loved by Brian. Charles loves the girl who loves
Donald. If Brian is not loved by Gwen, and the boy who
is loved by Helen does not love Gwen, who loves Alan?

A. Eve loves Alan
B. Brian loves Alan
C. Helen loves Alan
D. Gwen loves Alan

Answer 88

D

Question 89

A canoe is floating in a swimming pool. Which will raise
the level of the water in the pool higher, dropping a
penny into the pool or into the canoe? Or does it make
any difference?

A. Dropping it into the canoe will lessen the water level
lower.
B. Dropping it into the canoe will raise the water level
higher.
C. Dropping it into the canoe will lessen the water level
higher.
D. Dropping it into the canoe will raise the water level
lower.

Answer 89

B

Question 90

Five suspects were rounded up in connection with the
famous “Cock Robin Murder.” Their statements were as
follows: A: “C and D are lying.” B: “A and E are lying.” C:
“B and D are lying.” D: “C and E are lying.” E: “A and B
are lying.” Who is lying?

A. A is lying
B. B is lying
C. C is lying
D. D is lying

Answer 90

A

Question 91

Six grocers in a town each sell a different brand of tea
in four-ounce packets at 25 cents per packet. One of the
grocers gives short weight, each packet of his brand
weighing only 3 3/4 ounces. If I can use a balance for
only one weighing, what is the minimum amount I must
spend to be sure of finding the grocer who gives short
weight?

A. 3.5 dollars
B. 3.6 dollars
C. 3.7 dollars
D. 3.8 dollars

Answer 91

C

Question 92

A lamp has three on-off buttons, all of which must be on
for the lamp to light. A man wishes to turn on the lamp
at a moment when only the second switch is off. He
does not know this and proceeds to press the first
button. Getting no result, he presses the second and
eventually, on the seventh trial, (never repeating any onoff configuration), the lamp finally lights. In what order
did he press the buttons?

A. 1-3-3-2-1-2-3
B. 2-1-3-2-1-3-2
C. 1-2-3-2-1-2-3
D. 3-2-1-2-1-2-3

Answer 92

C

Question 93

A game proceeds as follows: Smith starts with a 10-link
chain and removes any single link, presenting Jones
either with a 9-link chain or two chains having a total of
9 links. Jones removes any one link from each of the
chains. Smith removes any one link from each of the
remaining chains and so on, until the winner removes
the last link or links. What should Smith do first?

A. Leave two chains of 6 and 3 links
B. Leave two chains of 3 and 6 links
C. Leave two chains of 9 and 6 links
D. Leave two chains of 6 and 9 links

Answer 93

A

Question 94

[APR 2023] 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
citizen drink liquor?

A. 90% drink liquor
B. 80% drink liquor
C. 100% drink liquor
D. 95% drink liquor

Answer 94

C

Question 95

[MAY 2017] You and a friend spot a loose $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?

A. $9.69
B. $9.79
C. $9.89
D. $9.99

Answer 95

D

Question 96

A gambler devised a game to be played with a friend.
He bet 1/2 the money in his pocket on the toss of a coin;
heads he won, tails he lost. The coin was tossed, and
the money handed over. The offer was repeated, and
the game continued. Each time the bet was for 1/2 the
money then in his possession. Eventually the number of
times he lost was equal to the number of times he won.
Quickly now! Did he gain, lose, or break even?

A. He lost
B. He gain
C. Break even
D. He won

Answer 96

A

Question 97

A prisoner is given 10 white balls, 10 black balls and two
boxes. He is told that an executioner will draw one ball
from one of the two boxes. If it is white, the prisoner will
go free; if it is black, he will die. How should the prisoner
arrange the balls in boxes to give himself the best
chance for survival?

A. 1 white ball in one box and the remaining balls in
the other box (77.3%)
B. 2 white ball in one box and the remaining balls in
the other box (73.7%)
C. 1 white ball in one box and the remaining balls in
the other box (73.7%)
D. 1 white ball in one box and the remaining balls in
the other box (70.7%)

Answer 97

C

Question 98

[NOV 2019] Smith and Jones, both 50% marksmen,
decide to fight a duel in which they exchange alternate
shots until one is hit. What are the odds in favor of the
man who shoots first?

A. 1/3
B. 2/3
C. 1/4
D. 1/2

Answer 98

B

Question 99

There are n points on a circle. A straight-line segment is
drawn between each pair of points. How many
intersections are there within the circle if no 3 lines are
collinear?

A. nC2 or nP2 / 24
B. nC3 or nP3 / 24
C. nC4 or nP4 / 24
D. nC5 or nP5 / 24

Answer 99

C

Question 100

On a certain day, our parking lot contains 999 cars, no
two of which have the same 3-digit license number. After
5:00 p.m. what is the probability that the license
numbers of the first 4 cars to leave the parking lot are in
increasing order of magnitude?

A. 1/12
B. 1/16
C. 1/24
D. 1/32

Answer 100

C

Question 101

[NOV 2016] Three marksmen simultaneously shoot at
and hit a rapidly spinning spherical target. What is the
probability that the three points of impact are on the
same.

A. 1
B. 2
C. 3
D. 4

Answer 101

A

Question 102

Assume that a single depth charge has a probability of
1/2 of sinking a submarine, 1/4 of damage and 1/4 of
missing. Assume also that two damaging explosions
sink the sub. What is the probability that 4 depth
charges will sink the sub?

A. 253/256
B. 255/256
C. 249/256
D. 251/256

Answer 102

D

Question 103

What is the most likely distribution of the suits in a
hand at Bridge?

A. 4-4-3-2
B. 4-3-4-2
C. 4-2-3-4
D. 4-2-3-2

Answer 103

A

Question 104

An expert gives team A only a 40% chance to win the
World Series. Basing his calculation on this a gambler
offers 6 to 5 odds on team B to win the first game. Is his
judgment sound?

A. YES
B. NO
C. MAYBE
D. NONE OF THE ABOVE

Answer 104

A

Question 105

A coin is so unbalanced 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?

A. 0.618
B. 0.518
C. 0.816
D. 0.815

Answer 105

A

Question 106

Three dart players threw simultaneously at a tic-tac-toe
board, each hitting a different square. What is the
probability that the three hits constituted in a win at tictac-toe?

A. 4/21
B. 6/21
C. 2/21
D. 1/21

Answer 106

C

Question 107

Four swimming pool builders submit sealed bids to a
homeowner who is required by law to accept the last bid
that he sees, i.e., once he looks at a bid, he
automatically rejects all previous bids. He is not
required to open all the envelopes, of course. Assuming
that all four bids are different, what procedure will
maximize his chances of accepting the lowest bid. and
what will be the probability of doing so?

A. 10/24
B. 9/24
C. 11/24
D. 13/24

Answer 107

C

Question 108

Martian coins are 3-sided (heads, tails, and torsos),
each side coming up with equal probability. Three
Martians decided to go odd-man-out to determine who
pays a dinner check. (If two coins come up the same
and one different, the owner of the latter coin foots the
bill). What is the expected number of throws needed in
order to determine a loser?

A. 0.5 throws
B. 1.5 throws
C. 2.5 throws
D. 3.5 throws

Answer 108

B

Question 109

Six men decide to play Russian roulette with a six-gun
loaded with one cartridge. They draw for position, and
afterwards’ the sixth man casually suggests that
instead of letting the chamber rotate in sequence, each
man spin the chamber before shooting. How would this
improve his chances?

A. 0.4
B. 0.3
C. 0.2
D. 0.1

Answer 109

D

Question 110

A long shot poker player draws two cards to the five and
six of diamonds and the joker. What are his chances of
coming up with a pat hand? (straight or flush)

A. 0.186
B. 0.168
C. 0.861
D. 0.618

Answer 110

B

Question 111

In Puevigi, the game of craps is played with a referee
calling the point by adding together the six faces (three
on each die) visible from his vantage point. What is the
probability of making 16 the hard way? (That is, by
throwing two eights.)

A. 0
B. 1
C. 2
D. 3

Answer 111

A

Question 112

Max and his wife Min each toss a pair of dice to
determine where they will spend their vacation. If either
of Min’s dice displays the same number of spots as
either of Max’s, she wins, and they go to Bermuda.
Otherwise, they go to Yellowstone. What is the chance
they’ll see “Old Faithful” this year?

A. 0.468
B. 0.486
C. 0.684
D. 0.864

Answer 112

B

Question 113

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