Looksfam Set 1 - Litton

Question 1

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. His survival probability is enhanced about .4 by spinning.
b. His survival probability is enhanced about .2 by spinning.
c. His survival probability is enhanced about .3 by spinning.
d. His survival probability is enhanced about .1 by spinning

Answer 1

d. His survival probability is enhanced about .1 by spinning

Question 2

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 a win at tic-tac-toe?

a. 3/21
b. 5/21
c. 2/21
d. 4/21

Answer 2

c. 2/21

Question 3

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. 2/5
b. 4/5
c. 1/5
d. 3/5

Answer 3

d. 3/5

Question 4

Six boys on a hockey team pick a captain by forming a circle and counting out until the 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. 10
b. 8
c. 7
d. 9

Answer 4

a. 10

Question 5

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. 22/23
b. 3/23
c. 1/23
d. 19/23

Answer 5

c. 1/23

Question 6

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. four
b. six
c. three
d. five

Answer 6

d. five

Question 7

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. Brian is not loved by Gwen, and the boy who is loved by Helen does not love Gwen, who loves Alan?

a. Chrysler loves Alan
b. Faye loves Alan
c. Gwen loves Alan
d. Eve loves Alan

Answer 7

c. Gwen loves Alan

Question 8

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. 6!
b. 3!
c. 4!
d. 5!

Answer 8

c. 4!

Question 9

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? (past board
exam)

Answer 9

Align the hour hand, with the sun’s azimuth, and south will be midway between the hour hand and12.

Question 10

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? (past
board exam)

Answer 10

Two. The 4th and the 11th.

Question 11

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. 0.681
c. 0.816
d. 0.861

Answer 11

a. 0.618

Question 12

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. 65₵
b. 95₵
c. 85₵
d. 75₵

Answer 12

b. 95₵

Question 13

A hospital nursery contains only two baby boys; the girls have not yet been counted. At 2:00 pm, 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. 4/5
b. 2/5
c. 1/5
d. 3/5

Answer 13

b. 2/5

Question 14

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. 3
b. 2.5
c. 2
d. 1.5

Answer 14

d. 1.5

Question 15

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

Answer 15

5/8

Question 16

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 1/4, and so on. How long did it take to achieve its maximum height (100 times its original height)?

a. 201 days
b. 200 days
c. 199 days
d. 198 days

Answer 16

d. 198 days

Question 17

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. 1/8
b. 1/7
c. 1/6
d. 1/9

Answer 17

c. 1/6

Question 18

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. 8
c. 15
d. 7

Answer 18

c. 15

Question 19

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. 2.6 dollars
b. 4.2 dollars
c. 5.1 dollars
d. 3.7 dollars

Answer 19

d. 3.7 dollars

Question 20

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 14 children were 8 married couples.
b. Included among the 18 children were 10 married couples.
c. Included among the 18 children were 8 married couples.
d. Included among the 18 children

Answer 20

c. Included among the 18 children were 8 married couples.

Question 21

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 shots first?

a. 3/4
b. 2/3
c. 1/2
d. 1/3

Answer 21

b. 2/3

Question 22

In the final seconds of the game, your favorite NBA 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. about 65%
b. about 69%
c. about 72%
d. about 75%

Answer 22

b. about 69%

Question 23

A hunter wished to take his one-piece rifle on a train but the conductor refused to permit it in the coach and the baggage man could not take any article whose greatest dimension exceeded 1 yard. The length of the rifle was 1.7 yards. What could the hunter do?

a. He could put his gun diagonally in a cubical box, 2 yards on a side.
b. He could put his gun diagonally in a cubical box, 1 yard on a side.

Answer 23

b. He could put his gun diagonally in a cubical box, 1 yard on a side.

Question 24

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. 15 and 17 would be in the third group and 16 in the second
b.
c. 15 and 16 would be in the third group and 17 in the second
d. 16 and 17 would be in the third group and 15 in the second

Answer 24

c. 15 and 16 would be in the third group and 17 in the second

Question 25

A gambler devised a game to be played with a friend. He bet ½ 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 he bet was for ½ 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
b. He gained
c. Break even
d. He lost, even if they played only twice, or four times, or six, or …

Answer 25

d. He lost, even if they played only twice, or four times, or six, or …

Question 26

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

a. 1, 2, 3
b. 2, 1, and 3

Answer 26

b. 2, 1, and 3

Question 27

What letters follow OTTFFSSE_

a. D
b. N
c. E
d. O

Answer 27

b. N

Question 28

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

a. 432615
b. 432516
c. 432651
d. 432561

Answer 28

a. 432615

Question 29

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. one part in 750
b. one part in 720
c. one part in 360
d. one part in 380

Answer 29

a. one part in 750

Question 30

There are four volumes on an encyclopedia on a shelf, each volume containing 300 pages, (that is, numbered 1 to 600), but these have been placed on 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. 450
b. 500
c. 400
d. 600

Answer 30

b. 500

Question 31

Dr. Furbisher LaRouche, the noted mathematician, was shopping at a hardware store and asked the price of certain articles. The salesman replied, “One would cost 10 cents, eight would cost 10 cents, seventeen would cost 20 cents, one hundred and four would cost 30 cents, seven hundred and fifty six would also cost 30 cents, and one thousand and seventy two would cost 40 cents.” What was Dr. LaRouche buying?

a. Dr. LaRouche was buying numbers (for doors, gates, etc.) and the price was 10 cents per digit.
b.
c. Dr. LaRouche was buying numbers (for doors, gates, etc.) and the price was 8 cents per digit.
d.

Answer 31

a. Dr. LaRouche was buying numbers (for doors, gates, etc.) and the price was 10 cents per digit.

Question 32

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 there in the fraternity?

a.
b. The fraternity had 15 members could field 3,003 teams of either type.
c. The fraternity had 14 members could field 2,002 teams of either type.
d.

Answer 32

b. The fraternity had 15 members could field 3,003 teams of either type.

Question 33

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. The operator can expect to clear three dollars per game on the average
b. The operator can expect to clear five dollars per game on the average
c. The operator can expect to clear four dollars per game on the average
d. The operator can expect to clear six dollars per game on the average

Answer 33

c. The operator can expect to clear four dollars per game on the average

Question 34

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. Yes
b.
c. No; he has already used 4 minutes, the time that he has to go the whole 2 miles
d.

Answer 34

c. No; he has already used 4 minutes, the time that he has to go the whole 2 miles

Question 35

Mary Ann Moore’s father has a yacht and so has each of his four friends; Colonel Downing, Mr. Hall, Sir Barnacle Hood, and Dr. Parker. Each of the five also has one daughter of one of the others. Sir Barnacle’s yacht is the Gabrielle, Mr. Moore owns the Lorna; Mr. Hall the Rosalind. The Melissa, owned by Colonel Downing, is named after Sir Barnacle’s daughter. Gabrielle’s father owns the yacht which is named after Dr. Parker’s daughter. Who is Lorna’s father?

a. Dr. Parker
b. Mr. Hall
c. Chrysler Duaso
d. Colonel Downing

Answer 35

d. Colonel Downing

Question 36

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. 2/3
b. 16/52
c. 1/2
d. 0

Answer 36

d. 0

Question 37

Maynard’s Grandfather Clock is driven by two weighs, 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.
b.
c. The weights are opposite immediately after 3 and 9 o’clock, a.m. and p.m., so Maynard must retire
at 9 p.m. or 3 a.m.
d. The weights are opposite immediately after 4 and 10 o’clock, a.m. and p.m., so Maynard must retire
at 10 p.m. or 4 a.m

Answer 37

c. The weights are opposite immediately after 3 and 9 o’clock, a.m. and p.m., so Maynard must retire
at 9 p.m. or 3 a.m.

Question 38

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
b. 4
c. 3
d. 1

Answer 38

b. 4

Question 39

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

a. 80
b. 90
c. 68
d. 86

Answer 39

a. 80

Question 40

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. 5/256
b. 251/256
c. 215/256
d. 6/256

Answer 40

b. 251/256

Question 41

A game of super-dominoes is played with pieces divided into three cells instead of the unusual 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. 69 pieces
b. 96 pieces
c. 196 pieces
d. 169 pieces

Answer 41

c. 196 pieces

Question 42

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. 0.143
c. 0.134
d. 0.168

Answer 42

d. 0.168

Question 43

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 must not be zero; (d) the third digit may be one only if the second digit is zero.

a. 134 possible codes
b. 163 possible codes
c. 143 possible codes
d. 136 possible codes

Answer 43

d. 136 possible codes

Question 44

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 the boxes to give himself the best chance for survival?

a.
b. If the prisoner places one white ball in one box and the remaining balls (9 white and 10 black) other box, his chance of survival would be (1 + 9/19)/2 = 0.737 or 73%
c. If the prisoner places one white ball in one box and the remaining balls (9 white and 10 black) in the other box, his chance of survival would be (1 + 10/20)/2 = 0.75 or 75%
d. If the prisoner places one white ball in one box and the remaining balls (9 white and 10 black) in the
other box, his chance of survival would be (1 + 9/20)/2 = 0.725 or 72

Answer 44

b. If the prisoner places one white ball in one box and the remaining balls (9 white and 10 black) other box, his chance of survival would be (1 + 9/19)/2 = 0.737 or 73%

Question 45

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. An infinite series need not be the means of solution; a trivial means exists, 250 miles
b.
c. An infinite series need not be the means of solution; a trivial means exists, 300 miles
d.

Answer 45

c. An infinite series need not be the means of solution; a trivial means exists, 300 miles

Question 46

If 2 marbles are removed at random from a bag containing black and white marbles, the chance that they are both white is 1/3. If 3 are removed at random, the chance that they are all white is 1/6. How many marbles are there of each color?

a. w = 3 and b = 7
b. w = 6 and b = 4
c. w = 7 and b = 3
d. w = 4 and b = 6

Answer 46

b. w = 6 and b = 4

Question 47

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. His chance of accepting the lowest bid is easily seen to be 11/24. If he uses the lower of the two bids as his standard instead, then his chance is reduced to 10/24.

b. His chance of accepting the lowest bid is easily seen to be 10/24. If he uses the lower of the two
bids as his standard instead, then his chance is reduced to 11/24.

Answer 47

b. His chance of accepting the lowest bid is easily seen to be 10/24. If he uses the lower of the two
bids as his standard instead, then his chance is reduced to 11/24.

Question 48

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 to completion. How many pitches did he make?

a. 25
b. 24
c. 23
d. 22

Answer 48

a. 25