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Quantitative of GMAT level 3 part 5

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; Subject: ; Class: ; with 37 questions; test in 75 minutes; update 20/11/2018
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Question 1.

A committee is composed of w women and m men. If 3 women and 2 men are added to the committee, and if one person is selected at random from the enlarged committee, then the probability that a woman is selected can be represented by

(A)

\(w\over m\)

(B)

\(w\over {w + m}\)

(C)

\({w + 3}\over {m + 2}\)

(D)

\({w + 3}\over {w + m + 3}\)

(E)

\({w + 3}\over {w + m + 5}\)

Question 2.

How many prime numbers between 1 and 100 are factors of 7,150 ?

(A)

1

(B)

2

(C)

3

(D)

4

(E)

5

Question 3.

The positive integer n is divisible by 25. If \(\sqrt n\) is greater than 25, which of the following could be the value of \(n\over 25\)?

(A)

22

(B)

23

(C)

24

(D)

25

(E)

26

Question 4.

Of the 300 subjects who participated in an experiment using virtual-reality therapy to reduce their fear of heights, 40 percent experienced sweaty palms, 30 percent experienced vomiting, and 75 percent experienced dizziness. If all of the subjects experienced at least one of these effects and 35 percent of the subjects experienced exactly two of
these effects, how many of the subjects experienced only one of these effects?

(A)

105

(B)

125

(C)

130

(D)

180

(E)

195

Question 5.

A fruit-salad mixture consists of apples, peaches, and grapes in the ratio 6:5:2, respectively, by weight. If 39 pounds of the mixture is prepared, the mixture includes how many more pounds of apples than grapes?

(A)

15

(B)

12

(C)

9

(D)

6

(E)

4

Question 6.

If m-1 = -\(1\over 3\) then m-2 is equal to

(A)

-9

(B)

-3

(C)

-\(1\over 9\)

(D)

\(1\over 9\)

(E)

9

Question 7.

If m > 0 and x is m percent of y, then, in terms of m, y is what percent of x ?

(A)

100m

(B)

\(1\over 100m\)

(C)

\(1\over m\)

(D)

\(10\over m\)

(E)

\(10,000\over m\)

Question 8.

A photography dealer ordered 60 Model X cameras to be sold for $250 each, which represents a 20 percent markup over the dealer’s initial cost for each camera.Of the cameras ordered, 6 were never sold and were returned to the manufacturer for a refund of 50 percent of the dealer’s initial cost. What was the dealer’s approximate profit or loss as a percent of the dealer’s initial cost for the 60 cameras?

(A)

7% loss

(B)

13% loss

(C)

7% profit

(D)

13% profit

(E)

15% profit

 

Question 9.

Seven pieces of rope have an average (arithmetic mean) length of 68 centimeters and a median length of 84 centimeters. If the length of the longest piece of rope is 14 centimeters more than 4 times the length of the shortest piece of rope, what is the maximum possible length, in centimeters, of the longest piece of rope?

(A)

82

(B)

118

(C)

120

(D)

134

(E)

152

Question 10.

Lois has x dollars more than Jim has, and together they have a total of y dollars. Which of the following represents the number of dollars that Jim has?

(A)

\({y - x}\over 2\)

(B)

y - \(x\over 2\)

(C)

\(y\over 2\) - x

(D)

2y - x

(E)

y - 2x

Question 11.

During a certain season, a team won 80 percent of its first 100 games and 50 percent of its remaining games. If the team won 70 percent of its games for the entire season, what was the total number of games that the team played?

(A)

180

(B)

170

(C)

156

(D)

150

(E)

105

Question 12.

Of 30 applicants for a job, 14 had at least 4 years’ experience, 18 had degrees, and 3 had less than 4 years’ experience and did not have a degree. How many of the applicants had at least 4 years’ experience and a degree?

(A)

14

(B)

13

(C)

9

(D)

7

(E)

5

Question 13.

If 1 + \(1\over x\)= 2 - \(2\over x\), then x = 

(A)

-1

(B)

\(1\over 3\)

(C)

\(2\over 3\)

(D)

2

(E)

3

Question 14.

Last year, for every 100 million vehicles that traveled on a certain highway, 96 vehicles were involved in accidents. If 3 billion vehicles traveled on the highway last year, how many of those vehicles were involved in accidents? (1 billion = 1,000,000,000)

(A)

288

(B)

320

(C)

2,880

(D)

3,200

(E)

28,880

Question 15.

Thirty percent of the members of a swim club have passed the lifesaving test. Among the members who have not passed the test, 12 have taken the preparatory course and 30 have not taken the course. How many members are there in the swim club?

(A)

60

(B)

80

(C)

100

(D)

120

(E)

140

Question 16.

What is the difference between the sixth and the fifth terms of the sequence 2, 4, 7, ... whose nth term is n + 2n - 1 ?

(A)

2

(B)

3

(C)

6

(D)

16

(E)

17

Question 17.

If (x - 1)2 = 400, which of the following could be the value of x - 5?

(A)

15

(B)

14

(C)

-24

(D)

-25

(E)

-26

Question 18.

Which of the following describes all values of x for which 1 -  x2 \(\ge\) 0?

(A)

\(\ge\) 1

(B)

\(\leq\) - 1

(C)

\(\leq\) x \(\leq\) 1

(D)

\(\leq\) - 1 or x  \(\ge\) 1

(E)

-1 \(\leq\) x \(\leq\) 1

Question 19.

The probability is \(1\over 2\) that a certain coin will turn up heads on any given toss. If the coin is to be tossed three times, what is the probability that on at least one of the tosses the coin will turn up tails?

(A)

\(1\over 8\)

(B)

\(1\over 2\)

(C)

\(3\over 4\)

(D)

\(7\over 8\)

(E)

\(15\over 16\)

Question 20.

Of the final grades received by the students in a certain math course, \(1\over 5\) are A’s, \(1\over 4\) are B’s, \(1\over 2\) are C’s, and the remaining 10 grades are D’s. What is the number of students in the course?

(A)

80

(B)

110

(C)

160

(D)

200

(E)

400

Question 21.

As x increases from 165 to 166, which of the following must increase?
I. 2x - 5

II. 1 - \(1\over x\)

III. \(1\over {x^2 - x}\)

(A)

I only

(B)

III only

(C)

I and II

(D)

I and III

(E)

II and III

Question 22.

From the consecutive integers –10 to 10, inclusive, 20 integers are randomly chosen with repetitions allowed. What is the least possible value of the product of the 20 integers?

(A)

(-10)20

(B)

(-10)10

(C)

0

(D)

-(10)19

(E)

-(10)20

Question 23.

A rectangular box is 10 inches wide, 10 inches long, and 5 inches high. What is the greatest possible (straight-line) distance, in inches, between any two points on the box?

(A)

15

(B)

20

(C)

25

(D)

10\(\sqrt2\)

(E)

10\(\sqrt3\)

Question 24.

Last Sunday a certain store sold copies of Newspaper A for $1.00 each and copies of Newspaper B for $1.25 each, and the store sold no other newspapers that day. If r percent of the store’s revenue from newspaper sales was from Newspaper A and if p percent of the newspapers that the store sold were copies of Newspaper A, which of the following expresses r in terms of p ?

(A)

\(100p\over {125 - p}\)

(B)

\(150p\over {250 - p}\)

(C)

\(300p\over {375 - p}\)

(D)

\(400p\over {500 - p}\)

(E)

\(500p\over {625 - p}\)

Question 25.

\(0.99999999\over 1.0001\) - \(0.99999991\over 1.0003\) = 

(A)

10-8

(B)

3(10-8)

(C)

3(10-4)

(D)

2(10-4)

(E)

10-4

Question 26.

The ratio, by volume, of soap to alcohol to water in a certain solution is 2:50:100. The solution will be altered so that the ratio of soap to alcohol is doubled while the ratio of soap to water is halved. If the altered solution will contain 100 cubic centimeters of alcohol, how many cubic centimeters of water will it contain?

(A)

50

(B)

200

(C)

400

(D)

625

(E)

800

Question 27.

If 75 percent of a class answered the first question on a certain test correctly, 55 percent answered the second question on the test correctly, and 20 percent answered neither of the questions correctly, what percent answered both correctly?

(A)

10%

(B)

20%

(C)

30%

(D)

50%

(E)

65%

Question 28.

A store currently charges the same price for each towel that it sells. If the current price of each towel were to be increased by $1, 10 fewer of the towels could be bought for $120, excluding sales tax. What is the current price of each towel?

(A)

1$

(B)

2$

(C)

3$

(D)

4$

(E)

12$

Question 29.

If n = 4p , where p is a prime number greater than 2, how many different positive even divisors does n have, including n ?

(A)

2

(B)

3

(C)

4

(D)

6

(E)

8

Question 30.

John and Mary were each paid x dollars in advance to do a certain job together. John worked on the job for 10 hours and Mary worked 2 hours less than John. If Mary gave John y dollars of her payment so that they would have received the same hourly wage, what was the dollar amount, in terms of y, that John was paid in advance?

(A)

4y

(B)

5y

(C)

6y

(D)

8y

(E)

9y

Question 31.

Car A is 20 miles behind Car B, which is traveling in the same direction along the same route as Car A. Car A is traveling at a constant speed of 58 miles per hour and Car B is traveling at a constant speed of 50 miles per hour. How many hours will it take for Car A to overtake and drive 8 miles ahead of Car B ?

(A)

1.5

(B)

2.0

(C)

2.5

(D)

3.0

(E)

3.5

Question 32.

For the past n days, the average (arithmetic mean) daily production at a company was 50 units. If today’s production of 90 units raises the average to 55 units per day, what is the value of n ?

(A)

30

(B)

18

(C)

10

(D)

9

(E)

7

Question 33.

If a two-digit positive integer has its digits reversed, the resulting integer differs from the original by 27. By how much do the two digits differ?

(A)

3

(B)

4

(C)

5

(D)

6

(E)

7

Question 34.

In an electric circuit, two resistors with resistances x and y are connected in parallel. In this case, if r is the combined resistance of these two resistors, then the reciprocal of r is equal to the sum of the reciprocals of x and y. What is r in terms of x and y ?

(A)

xy

(B)

x + y

(C)

\(1\over {x + y}\)

(D)

\(xy\over {x + y}\)

(E)

\({x + y}\over xy\)

Question 35.

Xavier, Yvonne, and Zelda each try independently to solve a problem. If their individual probabilities for success are \(1\over 4\),  \(1\over 2\) and \(5\over 8\), respectively, what is the probability that Xavier and Yvonne, but not Zelda, will solve the problem?

(A)

\(11\over 8\)

(B)

\(7\over 8\)

(C)

\(9\over 64\)

(D)

\(5\over 64\)

(E)

\(3\over 64\)

Question 36.

If \(1\over x\) - \(1\over {x + 1}\) = \(1\over {x + 4}\), then x could be

(A)

0

(B)

-1

(C)

-2

(D)

-3

(E)

-4

Question 37.

List T consists of 30 positive decimals, none of which is an integer, and the sum of the 30 decimals is S. The estimated sum of the 30 decimals, E, is defined as follows. Each decimal in T whose tenths digit is even is rounded up to the nearest integer, and each decimal in T whose tenths digit is odd is rounded down to the nearest integer; E is the sum of the resulting integers. If \(1\over 3\) of the decimals in T have a tenths digit that is even, which of the following is a possible value of E – S ?
I. –16
II. 6
III. 10

(A)

I only

(B)

I and II only

(C)

I and III only

(D)

II and III only 

(E)

I, II and III

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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