MSTE

Question 1

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?

Answer 1

300 miles

Answer: 300 miles

Question 2

A man walks one mile south, one mile west, 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).

Answer 2

infinite

Answer: infinite

Question 3

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?

Answer 3

9 pm or 3 am

Answer : 9 pm or 3 am

Question 4

[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?

Answer 4

Align hour hand with the sun’s azimuth and south will be midway between the hour hand and 12

Answer: Align hour hand with the sun’s azimuth and south will be midway between the hour hand and 12

Question 5

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?

Answer 5

25

Answer: 25

Question 6

[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?

Answer 6

2

Answer: 2

Question 7

State University won their first football game of the season 17 to 0. Though they scored no safeties, they managed to score more points each quarter than they had scored in the previous quarter. What were State’s quarter scores?

Answer 7

0, 3,6,8

Answer: 0, 3,6,8

Question 8

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?

Answer 8

8

Answer: 8

Question 9

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?

Answer 9

15

Answer: 15

Question 10

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)?

Answer 10

198

Answer: 198

Question 11

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?

Answer 11

10

Answer: 10

Question 12

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?

Answer 12

99

Answer: 99

Question 13

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

Answer 13

between volume 10 and 3

Answer: between volume 10 and 3

Question 14

[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?

Answer 14

1/6

Answer: 1/6

Question 15

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?

Answer 15

Gwen

Answer: Gwen

Question 16

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?

Answer 16

Gwen

Question 17

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?

Answer 17

25 miles

Question 18

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?

Answer 18

$3. 7

Question 19

A man has red, gray and black flagstones for making a walk. He wants no two consecutive stones to be the same color, no consecutive pair of stones to have the same two colors in the same order, no repetition of three consecutive colors, etc. He starts out laying first a red stone, then a gray, and continues until he finishes laying the seventh stone. He then finds himself stymied and unable to use any stone for the eighth without repetition of some color pattern. What were the colors of the first seven stones?

Answer 19

R G R B R G R

Question 20

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?

Answer 20

Smith should leave two chains of 6 and 3 links

Question 21

[APRIL 2023/NOV 2016] In Bristol 90% of the citizens drink tea; 80% drink coffee; 70% drink whiskey; and 60% drink gin. No one drinks all four beverages. What percent of Bristol’s citizens drink liquor?

Answer 21

100%

Question 22

[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?

Answer 22

$9.99

Question 23

[NOV 2016] 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?

Answer 23

2/3

Question 24

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

Answer 24

1/24

Question 25

[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 hemisphere?

Answer 25

1.0

Question 26

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?

Answer 26

251/256

Question 27

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?

Answer 27

2/21

Question 28

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

Answer 28

80

Question 29

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.

Answer 29

136

Question 30

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 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?

Answer 30

500

Question 31

[MAY 2019] 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

Answer 31

Incomplete question

Question 32

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?

Answer 32

500

Question 33

With no other data available, what is the chance of rain?

Answer 33

3/5

[MAY 2019] 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.