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GMAT Quantitative University of Cambridge 2017

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; Subject: ; Class: ; with 37 questions; test in 75 minutes; update 26/07/2017
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Subjects Update 26/07/2017
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Question 1.

A not-so-good clockmaker has four clocks on display in the window. Clock #1 loses 15 minutes every hour. Clock #2 gains 15 minutes every hour relative to Clock #1 (i.e., as Clock #1 moves from 12:00 to 1:00, Clock #2 moves from 12:00 to 1:15). Clock #3 loses 20 minutes every hour relative to Clock #2. Finally, Clock #4 gains 20 minutes every hour relative to Clock #3. If the clockmaker resets all four clocks to the correct time at 12 noon, what time will Clock #4 display after 6 actual hours (when it is actually 6:00 pm that same day)?

(A)

5:00

(B)

5:34

(C)

5:42

(D)

6:00

(E)

6:24

Question 2.

Jolene entered an 18-month investment contract that guarantees to pay 2 percent interest at the end of 6 months, another 3 percent interest at the end of 12 months, and 4 percent interest at the end of the 18 month contract. If each interest payment is reinvested in the contract, and Jolene invested $10,000 initially, what will be the total amount of interest paid during the 18-month contract?

(A)

$506.00

(B)

$726.24

(C)

$900.00

(D)

$920.24

(E)

$926.24

Question 3.

Wes works at a science lab that conducts experiments on bacteria. The population of the bacteria multiplies at a constant rate, and his job is to notate the population of a certain group of bacteria each hour. At 1 p.m. on a certain day, he noted that the population was 2,000 and then he left the lab. He returned in time to take a reading at 4 p.m., by which point the population had grown to 250,000. Now he has to fill in the missing data for 2 p.m. and 3 p.m. What was the population at 3 p.m.?

(A)

50,000

(B)

62,500

(C)

65,000

(D)

86,666

(E)

125,000

Question 4.

The population of locusts in a certain swarm doubles every two hours. If 4 hours ago there were 1,000 locusts in the swarm, in approximately how many hours will the swarm population exceed 250,000 locusts?

(A)

6

(B)

8

(C)

10

(D)

12

(E)

14

Question 5.

Jim Broke’s only source of income comes from his job as a question writer. In this capacity, Jim earns a flat salary of $200 per week plus a fee of $9 for every question that he writes. Every year, Jim takes exactly two weeks of unpaid vacation to visit his uncle, a monk in Tibet, and get inspired for the next year. If a regular year consists of 52 weeks and the number of questions that Jim wrote in each of the past 5 years was an odd number greater than 20, which of the following could be Jim’s median annual income over the past 5 years?

(A)

$22,474

(B)

$25,673

(C)

$27,318

(D)

$28,423

(E)

$31,227

Question 6.

During a behavioral experiment in a psychology class, each student is asked to compute his or her lucky number by raising 7 to the power of the student's favorite day of the week (numbered 1 through 7 for Monday through Sunday respectively), multiplying the result by 3, and adding this to the doubled age of the student in years, rounded to the nearest year. If a class consists of 28 students, what is the probability that the median lucky number in the class will be a non-integer?  

(A)

0%

(B)

10%

(C)

20%

(D)

30%

(E)

40%

Question 7.

For the set of terms [x, y, x + y, x – 4y, xy, 2y], if y > 6 and the mean of the set equals y + 3, then the median must be

(A)

(x + y) / 2 

(B)

y + 3

(C)

y

(D)

3y/2

(E)

(x/2) + y

Question 8.

Set A: 3, x, 8, 10            Set  B:  4,  y,  9,  11.      The terms of  each  set  above are given in ascending order. If the median of Set A is equal to the median of Set B, what is the value of y x?

(A)

-2

(B)

-1

(C)

0

(D)

1

(E)

2

Question 9.

Set S includes elements {8, 2, 11, x, 3, y} and has a mean of 7 and a median of 5.5. If x < y, then which of the following is the maximum possible value of x?

(A)

0

(B)

1

(C)

2

(D)

3

(E)

4

Question 10.

The temperatures in Celsius recorder at 6 in the morning in various parts of a certain country were 10,5,-2,-1,-5 and 15. What is the median of these temperatures?

(A)

-2

(B)

-1

(C)

2

(D)

3

(E)

5

Question 11.

Score

Number and Interval of Scores

50-59

2

60-69

10

70-79

16

80-89

27

90-99

18

The table above shows the distribution of test scores for a group of management trainees, which score interval contains the median of the 73 scores?

(A)

60-69

(B)

70-79

(C)

80-89

(D)

90-99 

(E)

Can’t get

Question 12.

Five pieces of wood have an average (arithmetic mean) length of 124 centimeters and a median length of 140 centimeters. What is the maximum possible length in centimeters of the shortest piece of wood?

(A)

90

(B)

100

(C)

110

(D)

130

(E)

140

Question 13.

Amy's grade was the 90th percentile of the 80 grades for her class. Of the 100 grades from another class, 19 was higher than Amy's and the rest was lower. If no other grade is the same as Amy' grade, then Army's grade was what percentile of grades of two class combined.

(A)

72nd 

(B)

80th

(C)

81st

(D)

85th

(E)

92nd

Question 14.

Set X consists of prime numbers {3, 11, 7, K, 17, 19}. If integer Y represents the product of all elements in set X and if 11Y is an even number, what is the range of set X?

(A)

14

(B)

16

(C)

17

(D)

20

(E)

26

Question 15.

What could be the range of a set consisting of odd multiples of 7?

(A)

21

(B)

24

(C)

35

(D)

62

(E)

70

Question 16.

What is the range of a set consisting of the first 100 multiples of 7 that are greater than 70? 

(A)

693

(B)

700

(C)

707

(D)

777

(E)

847

Question 17.

Set X consists of all two-digit primes and set Y consists of all positive odd multiples of 5 less than 100. If the two sets are combined into one, what will be the range of the new set?

(A)

84

(B)

89

(C)

90

(D)

92

(E)

95

Question 18.

Set A consists of integers {3, -8, Y, 19, -6} and Set B consists of integers {K, -3, 0, 16, -5, 9}. Number L represents the median of Set A, number M represents the mode of set B, and number Z = LM. If Y is an integer greater than 21, for what value of K will Z be a divisor of 26?

(A)

-2

(B)

-1

(C)

0

(D)

1

(E)

2

Question 19.

If a randomly selected non-negative single digit integer is added to set X {2, 3, 7, 8}, what is the probability that the median of the set will increase while its range will remain the same?

(A)

20%

(B)

30%

(C)

40%

(D)

50%

(E)

60%

Question 20.

Stock

number of shares

v

68

w

112

x

56

y

94

z

45

The table shows the number of shares of each of the 5 stocks owned by Mr. Sami. If Mr Sami was to sell 20 shares of Stock X and buy 24 shares of stock y, what would be the increase in range of the number of shares of the 5 stocks owned by Mr Sami?

(A)

4

(B)

6

(C)

9

(D)

15

(E)

20

Question 21.

A set of 15 different integers have a range of 25 and a median of 25. What is greatest possible integer that could be in this set?

(A)

32

(B)

37

(C)

40

(D)

43

(E)

50

Question 22.

Set A consists of all prime numbers between 10 and 25; Set B consists of consecutive even integers, and set C consists of consecutive multiples of 7. If all the three sets have an equal number of terms, which of the following represents the ranking of these sets in an ascending order of the standard deviation?

(A)

C, A, B

(B)

A, B, C

(C)

C, B, A 

(D)

B, C, A 

(E)

B, A, C

Question 23.

Set A consists of all even integers between 2 and 100, inclusive. Set X is derived by reducing each term in set A by 50, set Y is derived by multiplying each term in set A by 1.5, and set Z is derived by dividing each term in set A by -4. Which of the following represents the ranking of the three sets in descending order of standard deviation?

(A)

X, Y, Z

(B)

X, Z, Y

(C)

Y, Z, X

(D)

Y, X, Z

(E)

Z, Y, X

Question 24.

If M is a negative integer and K is a positive integer, which of the following could be the standard deviation of a set {-7, -5, -3, M, 0, 1, 3, K, 7}?
I. -1.5          II. -2       III. 0
 

(A)

I only

(B)

II only

(C)

III only

(D)

I and III only

(E)

None

Question 25.

Sets A, B and C are shown below. If number 100 is included in each of these sets, which of the following represents the correct ordering of the sets in terms of the absolute increase in their standard deviation, from largest to smallest?
A {30, 50, 70, 90, 110}, B {-20, -10, 0, 10, 20}, C {30, 35, 40, 45, 50}
 

(A)

A, C, B

(B)

A, B, C

(C)

C, A, B

(D)

B, A, C

(E)

B, C, A

Question 26.

Let Set T = {2, 4, 5, 7}. Which of the following values, if added to Set T, would most increase the standard deviation of Set T?

(A)

1

(B)

3

(C)

6

(D)

8

(E)

14

Question 27.

9.4, 9.9, 9.9, 9.9, 10.0, 10.2, 10.2, 10.5
The mean and the standard deviation of the 8 numbers shown are 10 and 0.3, respectively. What percentage of the 8 number's are within 1 standard deviation?

(A)

90%

(B)

85%

(C)

80%

(D)

75%

(E)

70%

Question 28.

70, 75,80,85,90,105,105,130,130,130
The list shown consists of the times, in seconds, that i took each of 10 schoolchildren to run a distance of 400 on of meters. If the standard devastation of the 10 running times is 22.4 seconds, rounded to the nearest tenth of a second, how many of the 10 running times are more than 1 standard deviation below the mean of the 10 running times?

(A)

one

(B)

two

(C)

three

(D)

four

(E)

five

Question 29.

The residents of town x participated in a survey to determine the number of hours per week each resident spent watching television. The distribution of the result of the survey had a mean of 21 hours and a standard deviation of 6 hours. The number of hours of that participated, a resident of town x watching television last week was between 1 and 2 standard deviations below the mean. Which of the following could be the number of hours the participated watched television last week?

(A)

30

(B)

20

(C)

18

(D)

12

(E)

6

Question 30.

A certain list of 100 data has an average of 6 and a standard deviation of d, where d is positive. Which of the following pairs of data, when added to the list, must result in a list of 102 data with standard deviation less than d?

(A)

-6 and 0

(B)

0 and 0

(C)

0 and 6

(D)

0 and 12

(E)

6 and 6

Question 31.

If -1 < x < 0, which of the following must be true?

I. x3 < x2              II. x5 < 1 – x                III. x4 < x2

(A)

I only

(B)

I and II only

(C)

II and III only

(D)

I and III only

(E)

I, II and III

Question 32.

If a b > a + b, where a and b are integers, which of the following must be true?

I. a < 0     II.  b < 0           III. ab < 0

(A)

I only

(B)

II only 

(C)

I and II only

(D)

I and III only

(E)

II and III only

Question 33.

If |a| = 1/3 and |b| = 2/3, which of the following CANNOT be the result of a + b?

(A)

-1

(B)

-1/3

(C)

1/3

(D)

2/3

(E)

1

Question 34.

If |a| = |b|, which of the following must be true?

a = b     II. |a| = -b        III. -a = -b

(A)

I only

(B)

II only

(C)

III only

(D)

I and III only

(E)

None

Question 35.

Which of the following inequalities has a solution set that when graphed on the number line, is a single segment of finite length?

(A)

x4 ≥ 1

(B)

x3 ≤ 27

(C)

x2 ≥ 16

(D)

2≤ |x| ≤ 5

(E)

2 ≤ 3x+4 ≤ 6

Question 36.

If \(\sqrt{[(x + 4)^2]}\) = 3, which of the following could be the value of x – 4?

(A)

-11 

(B)

-7

(C)

-4

(D)

-3

(E)

5

Question 37.

​​​​​If (a b)c < 0, which of the following cannot be true?

(A)

a < b    

(B)

c < 0

(C)

|c| < 1

(D)

ac > bc

(E)

a2 – b2  > 0

Question 1    Question 2    Question 3    Question 4    Question 5    Question 6    Question 7    Question 8    Question 9    Question 10    Question 11    Question 12    Question 13    Question 14    Question 15    Question 16    Question 17    Question 18    Question 19    Question 20    Question 21    Question 22    Question 23    Question 24    Question 25    Question 26    Question 27    Question 28    Question 29    Question 30    Question 31    Question 32    Question 33    Question 34    Question 35    Question 36    Question 37   
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