# GMAT Quantitative University of Management Development Institute of Singapore (MDIS) 2017

Subject: ; Class: ; with 37 questions; test in 75 minutes; update 26/10/2017
 Time 75 minutes Time to take the test Start exam Click button start to test. Guide to the test Subjects Gmat test Update 26/10/2017 Class Level 3 Number of questions 37 View 934 Tested 0

Question 1.

A gambler began playing blackjack with $110 in chips. After exactly 12 hands, he left the table with$320 in chips, having won some hands and lost others. Each win earned $100 and each loss cost$10. How many possible outcomes were there for the first 5 hands he played? (For example, won the first hand, lost the second, etc.)

 (A) 10 (B) 18 (C) 26 (D) 32 (E) 64

Question 2.

In a 4 person race, medals are awarded to the fastest 3 runners. The first-place runner receives a gold medal, the second-place runner receives a silver medal, and the third-place runner receives a bronze medal. In the event of a tie, the tied runners receive the same color medal. (For example, if there is a two-way tie for first- place, the top two runners receive gold medals, the next-fastest runner receives a silver medal, and no bronze medal is awarded). Assuming that exactly three medals are awarded, and that the three medal winners stand together with their medals to form a victory circle, how many different victory circles are possible?

 (A) 24 (B) 52 (C) 96 (D) 144 (E) 648

Question 3.

The organizers of a week-long fair have hired exactly five security guards to patrol the fairgrounds at night for the duration of the event. Exactly two guards are assigned to patrol the grounds every night, with no guard assigned consecutive nights. If the fair begins on a Monday, how many different pairs of guards will be available to patrol the fairgrounds on the following Saturday night?

 (A) 9 (B) 7 (C) 5 (D) 3 (E) 2

Question 4.

Larry, Michael, and Doug have five donuts to share. If any one of the men can be given any whole number of donuts from 0 to 5, in how many different ways can the donuts be distributed?

 (A) 21 (B) 42 (C) 120 (D) 504 (E) 5040

Question 5.

How many different combinations of outcomes can you make by rolling three standard (6-sided) dice if the order of the dice does not matter?

 (A) 24 (B) 30 (C) 56 (D) 120 (E) 216

Question 6.

A certain league has four divisions. The respective divisions had 9, 10, 11, and 12 teams qualify for the playoffs. Each division held its own double-elimination tournament -- where a team is eliminated from the tournament upon losing two games -- in order to determine its champion. The four division champions then played in a single-elimination tournament -- where a team is eliminated upon losing one game -- in order  todetermine the overall league champion. Assuming that there were no ties and no forfeits, what is the maximum number of games that could have been played in order to determine the overall league champion?

 (A) 79 (B) 83 (C) 85 (D) 87 (E) 88

Question 7.

You have a bag of 9 letters: 3 Xs, 3 Ys, and 3 Zs. You are given a box divided into 3 rows and 3 columns for a total of 9 areas. How many different ways can you place one letter into each area such that there are no rows or columns with 2 or more of the same letter? (Note: One such way is shown below.)

 X Y Z Y Z X Z X Y
 (A) 5 (B) 6 (C) 7 (D) 12 (E) 18

Question 8.

Eight women of eight different heights are to pose for a photo in two rows of four. Each woman in the second row must stand directly behind a shorter woman in the first row. In addition, all of the women in each row must be arranged in order of increasing height from left to right. Assuming that these restrictions are fully adhered to, in how many different ways can the women pose?

 (A) 2 (B) 14 (C) 15 (D) 16 (E) 18

Question 9.

You have a six-sided cube and six cans of paint, each a different color. You may not mix colors of paint. How many distinct ways can you paint the cube using a different color for each side? (If you can reorient a cube to look like another cube, then the two cubes are not distinct.)

 (A) 24 (B) 30 (C) 48 (D) 60 (E) 120

Question 10.

A group of four women and three men have tickets for seven adjacent seats in one row of a theatre. If the three men will not sit in three adjacent seats, how many possible different seating arrangements are there for these 7 theatre-goers?

 (A) 7! – 2!3!2! (B) 7! – 4!3! (C) 7! – 5!3! (D) 7 × 2!3!2! (E) 2!3!2!

Question 11.

Anthony and Michael sit on the six-member board of directors for company X. If the board is to be split up into 2 three-person subcommittees, what percent of all the possible subcommittees that include Michael also include Anthony?

 (A) 20% (B) 30% (C) 40% (D) 50% (E) 60%

Question 12.

A family consisting of one mother, one father, two daughters and a son is taking a road trip in a sedan. The sedan has two front seats and three back seats. If one of the parents must drive and the two daughters refuse to sit next to each other, how many possible seating arrangements are there?

 (A) 28 (B) 32 (C) 48 (D) 60 (E) 120

Question 13.

Six mobsters have arrived at the theater for the premiere of the film “Goodbuddies.” One of the mobsters, Frankie, is an informer, and he's afraid that another member of his crew, Joey, is on to him. Frankie, wanting to keep Joey in his sights, insists upon standing behind Joey in line at the concession stand. How many ways can the six arrange themselves in line such that Frankie’s requirement is satisfied?

 (A) 6 (B) 24 (C) 120 (D) 360 (E) 720

Question 14.

A student committee that must consist of 5 members is to be formed from a pool of 8 candidates. How many different committees are possible?

 (A) 5 (B) 8 (C) 40 (D) 56 (E) 336

Question 15.

How many ways are there to award a gold, silver and bronze medal to 10 contending teams?

 (A) 10 × 9 × 8 (B) 10! / 3! 7! (C) 10! / 3! (D) 360 (E) 300

Question 16.

On Tuesday, Kramer purchases exactly 3 new shirts, 2 new sweaters, and 4 new hats, On the following day and each subsequent day thereafter, Kramer wears one of his new shirts together with one of his new sweaters and one of his new hats. Kramer avoids wearing the exact same combination of shirt, sweater, and hat for as long as possible. On which day is this no longer possible?

 (A) Tuesday (B) Wednesday (C) Thursday (D) Friday (E) Saturday

Question 17.

A certain stock exchange designates each stock with a one- , two-, or three-letter code, where each letter is selected from the 26 letters of the alphabet. If the letter may be repeated and if the same letters used in a different order constitute a different code, how many different stocks is it possible to uniquely designate with these codes?

 (A) 2951 (B) 8125 (C) 15600 (D) 15302 (E) 18278

Question 18.

A certain law firm consists of 4 senior partners and 6 junior partners. How many different groups of 3 partners can be formed in which at least one member of the group is a senior partner? (Two groups are considered different if at least one group member is different.)

 (A) 48 (B) 100 (C) 120 (D) 288 (E) 600

Question 19.

Pat will walk from intersection X to intersection y along route that is confined to the square grid of four streets and three avenues shown in the map above. How many routes from X to Y can Pat take that have the minimum possible length?

 (A) 6 (B) 8 (C) 10 (D) 14 (E) 16

Question 20.

A fair coin is flipped three times. What is the probability that the coin lands on heads exactly twice?

 (A) 1/8 (B) 3/8 (C) 1/2 (D) 5/8 (E) 7/8

Question 21.

There are 10 women and 3 men in room A. One person is picked at random from room A and moved to room B, where there are already 3 women and 5 men. If a single person is then to be picked from room B, what is the probability that a woman will be picked?

 (A) 13/21 (B) 49/117 (C) 15/52 (D) 5/18 (E) 40/117

Question 22.

If the probability of rain on any given day in Chicago during the summer is 50%, independent of what happens on any other day, what is the probability of having exactly 3 rainy days from July 4 through July 8, inclusive?

 (A) 1/32 (B) 2/25 (C) 5/16 (D) 8/25 (E) 3/4

Question 23.

In a shipment of 20 cars, 3 are found to be defective. If four cars are selected at random, what is the probability that exactly one of the four will be defective?

 (A) 170/1615 (B) 3/20 (C) 8/19 (D) 3/5 (E) 4/5

Question 24.

A certain bag of gemstones is composed of two-thirds diamonds and one-third rubies. If the probability of randomly selecting two diamonds from the bag, without replacement, is 5/12, what is the probability of selecting two rubies from the bag, without replacement?

 (A) 5/36 (B) 5/24 (C) 1/12 (D) 1/6 (E) 1/4

Question 25.

Triplets Adam, Bruce, and Charlie enter a triathlon. If there are 9 competitors in the triathlon and medals are awarded for first, second, and third place, what is the probability that at least two of the triplets will win a medal?

 (A) 3/14 (B) 19/84 (C) 11/42 (D) 15/28 (F) 3/4

Question 26.

Set S is the set of all prime integers between 0 and 20. If three numbers are chosen randomly from set S and each number can be chosen only once, what is the positive difference between the probability that the product of these three numbers is a number less than 31 and the probability that the sum of these three numbers is odd?

 (A) 1/336 (B) 1/2 (C) 17/28 (D) 3/4 (E) 301/336

Question 27.

A random 10-letter code is to be formed using the letters A, B, C, D, E, F, G, H, I and I (only the “I” will be used twice). What is the probability that a code that has the two I’s adjacent to one another will be formed?

 (A) 1/10 (B) 1/8 (C) 1/5 (D) 1/4 (E) 1/2

Question 28.

If p2 – 13p + 40 = q, and p is a positive integer between 1 and 10, inclusive, what is the probability that q < 0?

 (A) 1/10 (B) 1/5 (C) 2/5 (D) 3/5 (E) 3/10

Question 29.

A box contains three pairs of blue gloves and two pairs of green gloves. Each pair consists of a left-hand glove and a right-hand glove. Each of the gloves is separate from its mate and thoroughly mixed together with the others in the box. If three gloves are randomly selected from the box, what is the probability that a matched set (i.e., a left- and right-hand glove of the same color) will be among the three gloves selected?

 (A) 3/10 (B) 23/60 (C) 7/12 (D) 41/60 (E) 5/6

Question 30.

A football team has 99 players. Each player has a uniform number from 1 to 99 and no two players share the same number. When football practice ends, all the players run off the field one-by-one in a completely random manner. What is the probability that the first four players off the field will leave in order of increasing uniform numbers (e.g., #2, then #6, then #67, then #72, etc)?

 (A) 1/64 (B) 1/48 (C) 1/36 (D) 1/24 (E) 1/16

Question 31.

Bill and Jane play a simple game involving two fair dice, each of which has six sides numbered from 1 to 6 (with an equal chance of landing on any side). Bill rolls the dice and his score is the total of the two dice. Jane then rolls the dice and her score is the total of her two dice. If Jane’s score is higher than Bill’s, she wins the game. What is the probability the Jane will win the game?

 (A) 15/36 (B) 175/432 (C) 575/1296 (D) 583/1296 (E) 1/2

Question 32.

Kate and Danny each have $10. Together, they flip a fair coin 5 times. Every time the coin lands on heads, Kate gives Danny$1. Every time the coin lands on tails, Danny gives Kate $1. After the five coin flips, what is the probability that Kate has more than$10 but less than \$15?

 (A) 5/16 (B) 1/2 (C) 12/30 (D) 15/32 (E) 3/8

Question 33.

There is a 10% chance that it won’t snow all winter long. There is a 20% chance that schools will not be closed all winter long. What is the greatest possible probability that it will snow and schools will be closed during the winter?

 (A) 55% (B) 60% (C) 70% (D) 72% (E) 80%

Question 34.

There are y different travelers who each have a choice of vacationing at one of n different destinations. What is the probability that all y travelers will end up vacationing at the same destination?

 (A) 1/n! (B) n/n! (C) 1/ny (D) 1/ny -1 (E) n/yn

Question 35.

A small, experimental plane has three engines, one of which is redundant. That is, as long as two of the engines are working, the plane will stay in the air. Over the course of a typical flight, there is a 1/3 chance that engine one will fail. There is a 75% probability that engine two will work. The third engine works only half the time. What is the probability that the plane will crash in any given flight?

 (A) 7/12 (B) 1/4 (C) 1/2 (D) 7/24 (E) 17/24

Question 36.

Ms. Barton has four children. You are told correctly that she has at least two girls but you are not told which two of her four children are those girls. What is the probability that she also has two boys? (Assume that the probability of having a boy is the same as the probability of having a girl.)

 (A) 1/4 (B) 3/8 (C) 5/11 (D) 1/2 (E) 6/11

Question 37.

Laura has a deck of standard playing cards with 13 of the 52 cards designated as a "heart." If Laura shuffles the deck thoroughly and then deals 10 cards off the top of the deck, what is the probability that the 10th card dealt is a heart?

 (A) 1/4 (B) 1/5 (C) 5/26 (D) 12/42 (E) 13/42