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GMAT Quantitative Melbourne 2018

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; Subject: ; Class: ; with 35 questions; test in 75 minutes; update 22/11/2017
Time 75 minutes
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Subjects Update 22/11/2017
Class Number of questions 35
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Question 1.

For a light that has an intensity of 60 candles at its source, the intensity in candles, S, of the light at a point d feet from the source is given by the formula S = \(60k\over d^2\)  where k is a constant. If the intensity of the light is 30 candles at a distance of 2 feet from the source, what is the intensity of the light at a distance of 20 feet from the source?

(A)

\(3 \over 10\) candle

(B)

\(1 \over 2\) candle

(C)

1 candle

(D)

2 candle

(E)

3 candle

Question 2.

If b< 2 and 2x- 3b = 0, which of the following must be true?

(A)

X> -3

(B)

X <2

(C)

X = 3 

(D)

X< 3

(E)

X >3

Question 3.

Rene earns $8.50 per hour on days other than Sundays and twice that rate on Sundays. Last week she worked a total of 40 hours, including 8 hours on Sunday. What were her earnings for the week?

(A)

$272

(B)

$340

(C)

$398

(D)

$408

(E)

$476

Question 4.

In a shipment of 120 machine parts, 5 percent were defective. In a shipment of 80 machine parts, 10 percent were defective. For the two shipments combined, what percent of the machine parts were defective?

(A)

6.5%

(B)

7.0%

(C)

7.5%

(D)

8.0%

(E)

8.5%

Question 5.

Of the following, the closest approximation to \( \sqrt{5.98(601.5) \over 15.79}\) is : 

(A)

5

(B)

15

(C)

20

(D)

25

(E)

225

Question 6.

Which of the following CANNOT be the greatest common divisor of two positive integers x and y?

(A)

1

(B)

x

(C)

y

(D)

x - y

(E)

x + y

Question 7.

If a, b, and c are nonzero numbers and a+ b = c, which of the following is equal to 1 ?

(A)

\(a-b \over c\)

(B)

\(a-c \over b\)

(C)

\(b - c \over a\)

(D)

\(b - a\over c\)

(E)

\(c - b \over a\)

Question 8.

Last year Carlos saved 10 percent of his annual earnings. This year he earned 5 percent more than last year and he saved 12 percent of his annual earnings. The amount saved this year was what percent of the amount saved last year?

(A)

122%

(B)

124%

(C)

126%

(D)

128%

(E)

130%

Question 9.

A corporation that had $115.19 billion in profits for the year paid out $230.10 million in employee benefits. Approximately what percent of the profits were the employee benefits? (Note: 1 billion= 109)

(A)

50%

(B)

20%

(C)

5%

(D)

2%

(E)

0,2%

Question 10.

In the coordinate plane, line k passes through the origin and has slope 2. If points (3,y) and (x,4) are on line k, then x+ y =

(A)

3.5

(B)

7

(C)

8

(D)

10

(E)

14

Question 11.

If a, b, and c are constants, a > b > c, and x3 - x = (x -a)(x- b)(x- c) for all numbers x, what is the value of b ?

(A)

-3

(B)

-1

(C)

0

(D)

1

(E)

3

Question 12.

If x + y = Bz, then which of the following represents the average (arithmetic mean) of x, y, and z, in terms of z?

(A)

2z+1

(B)

3z

(C)

5z

(D)

\(z \over 3\)

(E)

\(3z \over 2\)

Question 13.

On the number line, if r < s, if p is halfway between r and s, and if t is halfway between p and r, then \(s-t\over t-r\) = 

(A)

\(1 \over 4\)

(B)

\(1 \over 3\)

(C)

\(4 \over 3\)

(D)

3

(E)

4

Question 14.

If x andy are different integers and X2 = xy, which of the following must be true?  

I. X=O

II. Y=O

Ill. X= -y

(A)

I only

(B)

II only

(C)

Ill only

(D)

I and Ill only

(E)

I, II, and Ill

Question 15.

173 +  174

(A)

177

(B)

173(18)

(C)

176(18)

(D)

2(173) + 17 

(E)

2(173) - 17 

Question 16.

 Which of the following CANNOT yield an integer when divided by 10 ?

(A)

The sum of two odd integers

(B)

An integer less than 10

(C)

The product of two primes

(D)

The sum of three consecutive integers

(E)

An odd integer

Question 17.

A certain clock marks every hour by striking a number of times equal to the hour, and the time required for a stroke is exactly equal to the time interval between strokes. At 6:00 the time lapse between the beginning of the first stroke and the end of the last stroke is 22 seconds. At 12:00, how many seconds elapse between the beginning of the first stroke and the end of the last stroke?

(A)

72

(B)

50

(C)

48

(D)

46

(E)

44

Question 18.

What is the greatest number of identical bouquets that can be made out of 21 white and 91 red tulips if no flowers are to be left out? (Two bouquets are identical whenever the number of red tulips in the two bouquets is equal and the number of white tulips in the two bouquets is equal.)

(A)

3

(B)

4

(C)

5

(D)

6

(E)

7

Question 19.

For all numbers sand t, the operation* is defined by
s* t = (s -1)(t + 1).1f (-2)* x = -12, then x =

(A)

2

(B)

3

(C)

5

(D)

6

(E)

11

Question 20.

Salesperson A's compensation for any week is $360 plus 6 percent of the portion of A's total sales above $1,000 for that week. Salesperson B's compensation for any week is 8 percent of B's total sales for that week. For what amount of total weekly sales would both salespeople earn the same compensation?

(A)

$21,000

(B)

$18,000

(C)

$15,000

(D)

$4,500

(E)

$4,000

Question 21.

The sum of the ages of Doris and Fred is y years. If Doris is 12 years older than Fred, how many years old will Fred be y years from now, in terms of y?

(A)

y-6

(B)

2y-6

(C)

\(y \over 2\) -6

(D)

\(3y \over 2\) -6

(E)

\(5y \over 2\) -6

Question 22.

If a basketball team scores an average (arithmetic mean) of x points per game for ngames and then scores y points in its next game, what is the team's average score for the n+ 1games?

(A)

\(nx +y \over n +1\)

(B)

x + \(y \over n +1\)

(C)

 x + \(y \over n\)

(D)

\(n(x+y) \over n +1\)

(E)

\(x +ny\over n+1\)

Question 23.

If xy > 0 and yz < 0, which of the following must be negative?

(A)

xyz

(B)

xyz2

(C)

xy2z

(D)

xy2z2

(E)

x2y2z2

Question 24.

Two trains, X andY, started simultaneously from opposite ends of a 100-mile route and traveled toward each other on parallel tracks. Train X, traveling at a constant rate, completed the 100-mile trip in 5 hours; Train Y, traveling at a constant rate, completed the 100-mile trip in 3 hours. How many miles had Train X traveled when it met Train Y?

(A)

37.5

(B)

40.0

(C)

60.0

(D)

62.5

(E)

77.5

Question 25.

One week a certain truck rental lot had a total of 20 trucks, all of which were on the lot Monday morning. If 50 percent of the trucks that were rented out during the week were returned to the lot on or before Saturday morning of that week, and if there were at least 12 trucks on the lot that Saturday morning, what is the greatest number of different trucks that could have been rented out during the week?

(A)

18

(B)

16

(C)

12

(D)

8

(E)

4

Question 26.

What is the value of 2x 2 - 2.4x -1.7 for x = 0.7?

(A)

-0.72

(B)

-1.42

(C)

-1.98

(D)

-2.40

(E)

-2.89

Question 27.

If s, u, and v are positive integers and 2s = 2u + 2v, which of the following must be true?

I. S=U

II. u≠v

Ill. s > v

(A)

None

(B)

I only

(C)

II only

(D)

Ill only

(E)

II and Ill

Question 28.

In the rectangular coordinate system shown above, which quadrant, if any, contains no point (x,y) that satisfies the inequality 2x- 3y ≤  -6?

(A)

None 

(B)

I

(C)

II

(D)

III

(E)

IV

Question 29.

The cost to rent a small bus for a trip is x dollars, which is to be shared equally among the people taking the trip. If 10 people take the trip rather than 16, how many more dollars, in terms of x, will it cost per person?

(A)

\(x \over 6\)

(B)

\(x \over 10\)

(C)

\(x \over 16\)

(D)

\(3x \over 40\)

(E)

\(3x \over 80\)

Question 30.

If x is an integer andy= 3x + 2, which of the following CANNOT be a divisor of y?

(A)

4

(B)

5

(C)

6

(D)

7

(E)

8

Question 31.

Acertain electronic component is sold in boxes of 54 for $16.20 and in boxes of 27 for $13.20. A customer who needed only 54 components for a project had to buy 2 boxes of 27 because boxes of 54 were unavailable. Approximately how much more did the customer pay for each component due to the unavailability of the larger boxes?

(A)

$0.33

(B)

$0.19

(C)

$0.11

(D)

$0.06

(E)

$0.03

Question 32.

As a salesperson, Phyllis can choose one of two methods of annual payment: either an annual salary of $35,000 with no commission or an annual salary of $10,000 plus a 20 percent commission on her total annual sales. What must her total annual sales be to give her the same annual pay with either method?

(A)

$100,000

(B)

$120,000

(C)

$125,000

(D)

$130,000

(E)

$132,000

Question 33.

Last year Department Store Xhad a sales total for December that was 4 times the average (arithmetic mean) of the monthly sales totals for January through November. The sales total for December was what fraction of the sales total for the year?

(A)

\(1 \over 4\)

(B)

\(4 \over 15\)

(C)

\(1 \over 3\)

(D)

\(4 \over 11\)

(E)

\(4 \over 5\)

Question 34.

In the sequence x0, x1, x2, ... , xn, each term from x1 to xk is 3 greater than the previous term, and each term from xk + 1to xn is 3 less than the previous term, where n and k are positive integers and k < n. If x0 = Xn = 0 and if xk = 15, what is the value of n?

(A)

5

(B)

6

(C)

9

(D)

10

(E)

15

Question 35.

A company that ships boxes to a total of 12 distribution centers uses color coding to identify each center. If either a single color or a pair of two different colors is chosen to represent each center and if each center is uniquely represented by that choice of one or two colors, what is the minimum number of colors needed for the coding? (Assume that the order of the colors in a pair does not matter.)

(A)

4

(B)

5

(C)

6

(D)

12

(E)

24

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   
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