MSTE B-E 2 Flashcards
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)
A.
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
B.
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
D.
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%)
B.
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
A.
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
C.
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
D.
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
D.
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
C.
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¢
A.
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
B.
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
D.
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$
B.
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
A.
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
A.
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
D.
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
B.
[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
C.
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
A.
[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
B.
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
D.
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
D.
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.
A.
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
A.
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
C.
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
D.
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.
D.
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%
C.
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
B.
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.
A.
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
D.
[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
A.
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
C.
[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
C.
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
A.
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
B.
[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
D.
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
B.
[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
A.
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
B.
[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
A.
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
C.
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
A.
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
C
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
B.
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
A.
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
D.
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
C.
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
B.
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
D.
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
C.
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
B.
[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
D.
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
A.
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
A.
[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
C.
[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
C.
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
B.
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
C.
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
A.
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
D.
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
C.
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
A.
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
B.
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
B.
[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
A.
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
B.
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
D.
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
A.
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
B.
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
B.
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
C.
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
A.
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
A.
If THAT = (AH)(HA), what is THAT?
A. 6785
B. 6786
C. 6776
D. 6796
B.
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
D.
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
A.
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
A.
What is the remainder upon dividing 5^999,999 by 7?
A. 4
B. 6
C. 8
D. 12
B.
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
B.
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))
C.
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
A.
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
C.
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
B.
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
A.
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
A.
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
C.
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
B.
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
A.
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
A.
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
C.
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
C.
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
A.
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
B.
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
B.
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
A.
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)
D.
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
A.
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
A.
