1) A, B, and C participate in a track meet, consisting of at least three event. 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 occured in any event? a) A won the pole vault b) B won the pole vault c) C won the pole vault d) Cannot be determined 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) the ages must be 1, 18, and 72 b) the ages must be 1, 17, and 82 c) ages must be 2, 17, and 81  d) ages must be 2, 18 and 71 3) [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) 40x84, 23x60, 30x46 c) 40x46, 30x60, 32x64 d) 40x64, 32x46, 30x60  4) 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) H = 60, D = 39, P = 1 b) H = 1, D = 60, P = 39 c) H = 39, D = 1, P = 60 d) H = 1, D = 39, P = 60 5) Every year an 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) 8 years b) 7 years c) 9 years d) 6 years 6) 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) 3 in. b) 5 in. c) 8 in. d) 11 in. 7) 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) 2.5 in. b) 5.5 in. c) 3.5 in. d) 4.5 in. 8) 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 is 36 and Dad is 72  b) Junior is 18 and Dad is 54 c) Junior is 12 and Dad is 48 d) Junior is 9 and Dad is 45 9) 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) 1451 b) 1145 c) 1154 d) 1514 10) What is the remainder upon dividing 5^(999,999) by 7? a) 5 b) 6 c) 7 d) 8 11) 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 is 204 and there are 288 houses  b) House number is 240 and there are 288 houses c) House number is 244 and there are 288 houses d) House number is 200 and there are 288 houses 12) [NOV 2022] On 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 b) Tuesday c) Thursday d) Saturday 13) The Sultan arranged his wives in order of increasing seniority and presented each with a golden ring. Next, every 3rd wife, 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) 9284 b) 9248 c) 9842 d) 9824 14) [APRIL 2024/MAY 2017] A ball is dropped from a height of 10 feet. It rebounds one-half the distance on each bounce. What is the total distance it travels? a) 25 ft b) 30 ft c) 35 ft d) 40 ft 15) Obviously the smaller the compounding period, the greater the interest. How much does one dollar amount to after one year at 100% per annum interest, compounded continuously, i.e., instantaneously? a) $1.72 b) $2.17 c) $2.71 d) $1.27 16) 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) the complete box has dimensions in the ratio 6:3:1 b) the complete box has dimensions in the ratio 6:4:3 c) the complete box has dimensions in the ratio 6:5:2 d) the complete box has dimensions in the ratio 6:4:1 17) 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) 0 b) $2.50 c) $5.00 d) $7.50 18) 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 + 1/4 + … 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) 4/3 b) 3/4 c) 3/2 d) 2/3 19) 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) 2.3 miles b) 1.2 miles c) 3.2 miles d) 2.1 miles 20) 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 8 errors and Mike made 2 errors b) Pat made 2 errors and Mike made 8 errors c) Pat made 6 errors and Mike made 4 errors d) Pat made 4 errors and Mike made 6 errors 21) A teenager wants to go out 2 consecutive nights out of a 3-day weekend. Permission for each night is obtained (or denied) by asking either Father or Mother. Father is known to be more likely to grant permission. However, if the same parent is asked on 2 consecutive days, the answers are never the same 2 days running. Whom should he ask first? a) Father b) Mother c) Do not attempt d) Father and Mother 22) Hard Knox College is a member of a six-school basketball league in which every pair of schools plays each other twice. The other five schools ended the season with respective league records of .200, .300, .500, .600, and .800. How did Hard Knox make out? a) .300 b) .600 c) .800 d) .500 23) 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 all are white is 1/6. How many marbles are there of each color? a) w= 6, b= 4 b) w= 6, b= 6 c) w= 4, b= 6 d) w= 4, b= 4 24) 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) 0.816 b) 0.681 c) 0.861 d) 0.618 25) 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 .2 by spinning b) his survival probability is enhanced about .4 by spinning c) his survival probability is enhanced about .3 by spinning d) his survival probability is enhanced about .1 by spinning 26) [MAY 2019] 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) 16 b) 12 c) 10 d) 14 27) 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) 25 b) 29 c) 21 d) 33 28) [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 8 married couples  b) included among the 18 children were 6 married couples c) included among the 18 children were 5 married couples d) included 18 among the 18 children were 7 married couples 29) 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) 34 b) 52 c) 25 d) 43 30) [NOV 2021] 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) 500 yd b) 550 yd c) 600 yd d) 650 yd

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