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Quantitative of GMAT level 3 part 4

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; Subject: ; Class: ; with 37 questions; test in 75 minutes; update 01/11/2018
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Question 1.

A researcher plans to identify each participant in a certain medical experiment with a code consisting of either a single letter or a pair of distinct letters written in alphabetical order. What is the least number of letters that can be used if there are 12 participants, and each participant is to receive a different code?

(A)

4

(B)

5

(C)

6

(D)

7

(E)

8

Question 2.

An object thrown directly upward is at a height of h feet after t seconds, where h = –16(t – 3)2 + 150. At what height, in feet, is the object 2 seconds after it reaches its maximum height?

(A)

6

(B)

86

(C)

134

(D)

150

(E)

166

Question 3.

Which of the following is equivalent to the pair of inequalities x + 6 > 10 and x - 3 \(\leq\)  5?

(A)

\(\leq\) x \(\leq\) 16

(B)

\(\leq\) x < 4

(C)

2 < x \(\leq\) 8

(D)

4 < x \(\leq\) 8

(E)

\(\leq\) x \(\leq\) 16

Question 4.

David has d books, which is 3 times as many as Jeff and \(1\over 2\) as many as Paula. How many books do the three of them have altogether, in terms of d ?

(A)

\(5\over 6\)d

(B)

\(7\over 3\)d

(C)

\(10\over 3\)d

(D)

\(7\over 2\)d

(E)

\(9\over 2\)d

Question 5.

List I: 3, 6, 8, 19
List II: x, 3, 6, 8, 19

If the median of the numbers in list I above is equal to the median of the numbers in list II above, what is the value of x ?

(A)

6

(B)

7

(C)

8

(D)

9

(E)

10

Question 6.

There are 8 teams in a certain league and each team plays each of the other teams exactly once. If each game is played by 2 teams, what is the total number of games played?

(A)

15

(B)

16

(C)

28

(D)

56

(E)

64

Question 7.

An operation \(\theta\) is defined by the equation a \(\theta\) b = \({a - b}\over {a + b}\) , for all numbers a and b such that a \(\neq\) -b. If  a \(\neq\)  -c and a \(\theta\) c = 0, then c = 

(A)

-a

(B)

\(1\over a\)

(C)

0

(D)

\(1\over a\)

(E)

a

Question 8.

The price of lunch for 15 people was $207.00, including a 15 percent gratuity for service. What was the average price per person, EXCLUDING the gratuity?

(A)

$11.73

(B)

$12.00

(C)

$13.80

(D)

$14.00

(E)

$15.87

Question 9.

In Town X, 64 percent of the population are employed, and 48 percent of the population are employed males. What percent of the employed people in Town X are females?

(A)

16%

(B)

25%

(C)

32%

(D)

40%

(E)

52%

Question 10.

At his regular hourly rate, Don had estimated the labor cost of a repair job as $336 and he was paid that amount. However, the job took 4 hours longer than he had estimated and, consequently, he earned $2 per hour less than his regular hourly rate. What was the time Don had estimated for the job, in hours?

(A)

28

(B)

24

(C)

16

(D)

14

(E)

12

Question 11.

If \(p\over q\) < 1, and p and q are positive integers, which of the following must be greater than 1 ?

(A)

\(\sqrt{p\over q}\)

(B)

\(p\over q^2\)

(C)

\(p\over 2q\)

(D)

\(q\over p^2\)

(E)

\(q\over p\)

Question 12.

It would take one machine 4 hours to complete a large production order and another machine 3 hours to complete the same order. How many hours would it take both machines, working simultaneously at their respective constant rates, to complete the order?

(A)

\(7\over 12\)

(B)

1\(1\over 2\)

(C)

1\(5\over 7\)

(D)

3\(1\over 2\)

(E)

7

Question 13.

To mail a package, the rate is x cents for the first pound and y cents for each additional pound, where x > y. Two packages weighing 3 pounds and 5 pounds, respectively, can be mailed separately or combined as one package. Which method is cheaper, and how much money is saved?

(A)

Combined, with a savings of x - y cents

(B)

Combined, with a savings of y - x cents

(C)

Combined, with a savings of x cents

(D)

Separately, with a savings of x - y cents

(E)

Separately, with a savings of y cents

Question 14.

If money is invested at r percent interest, compounded annually, the amount of the investment will double in approximately \(70\over r\) years. If Pat’s parents invested $5,000 in a long-term bond that pays 8 percent interest, compounded annually, what will be the approximate total amount of the investment 18 years later, when Pat is ready for college?

(A)

$20,000

(B)

$15,000

(C)

$12,000

(D)

$10,000

(E)

$ 9,000

Question 15.

On a recent trip, Cindy drove her car 290 miles, rounded to the nearest 10 miles, and used 12 gallons of gasoline, rounded to the nearest gallon. The actual number of miles per gallon that Cindy’s car got on this trip must have been between

(A)

\(290\over 12.5\) and \(290\over 11.5\)

(B)

\(295\over 12\) and \(285\over 11.5\)

(C)

\(285\over 12\) and \(295\over 12\)

(D)

\(285\over 12.5\) and \(295\over 11.5\)

(E)

\(295\over 12.5\) and \(285\over 11.5\)

Question 16.

A factory has 500 workers, 15 percent of whom are women. If 50 additional workers are to be hired and all of the present workers remain, how many of the additional workers must be women in order to raise the percent of women employees to 20 percent?

(A)

3

(B)

10

(C)

25

(D)

30

(E)

35

Question 17.

In a small snack shop, the average (arithmetic mean) revenue was $400 per day over a 10-day period. During this period, if the average daily revenue was $360 for the first 6 days, what was the average daily revenue for the last 4 days?

(A)

$420

(B)

$440

(C)

$450

(D)

$460

(E)

$480

Question 18.

A certain country had a total annual expenditure of $1.2 x 1012 last year. If the population of the country was 240 million last year, what was the per capita expenditure?

(A)

$500

(B)

$1,000

(C)

$2,000

(D)

$3,000

(E)

$5,000

Question 19.

 At a loading dock, each worker on the night crew loaded \(3\over 4\) as many boxes as each worker on the day crew. If the night crew has \(4\over 5\) as many workers as the day crew, what fraction of all the boxes loaded by the two crews did the day crew load?

(A)

\(1\over 2\)

(B)

\(2\over 5\)

(C)

\(3\over 5\)

(D)

\(4\over 5\)

(E)

\(5\over 8\)

Question 20.

A restaurant meal cost $35.50 and there was no tax. If the tip was more than 10 percent but less than 15 percent of the cost of the meal, then the total amount paid must have been between

(A)

$40 and $42

(B)

$39 and $41

(C)

$38 and $40

(D)

$37 and $39

(E)

$36 and $37

Question 21.

In a weight-lifting competition, the total weight of Joe’s two lifts was 750 pounds. If twice the weight of his first lift was 300 pounds more than the weight of his second lift, what was the weight, in pounds, of his first lift?

(A)

225

(B)

275

(C)

325

(D)

350

(E)

400

Question 22.

A club collected exactly $599 from its members. If each member contributed at least $12, what is the greatest number of members the club could have?

(A)

43

(B)

44

(C)

49

(D)

50

(E)

51

Question 23.

If y is the smallest positive integer such that 3,150 multiplied by y is the square of an integer, then y must be

(A)

2

(B)

5

(C)

6

(D)

7

(E)

14

Question 24.

If [x] is the greatest integer less than or equal to x, what is the value of [-1.6] + [3.4] + [3.7] ?

(A)

3

(B)

4

(C)

5

(D)

6

(E)

7

Question 25.

If \({4 - x}\over {2 + x }\) = x, what is the value of x2 + 3x - 4 ?

(A)

-4

(B)

-1

(C)

0

(D)

1

(E)

2

Question 26.

In the first week of the year, Nancy saved $1. In each of the next 51 weeks, she saved $1 more than she had saved in the previous week. What was the total amount that Nancy saved during the 52 weeks?

(A)

$1,326

(B)

$1,352

(C)

$1,378

(D)

$2,652

(E)

$2,756

Question 27.

In a certain sequence, the term xn is given by the formula xn = 2xn - 1 - \(1\over 2\)(xn - 2) for all n\(\geq\) 2. If  x0 = 3 and x1 = 2 , what is the value of x3 ?

(A)

2.5

(B)

3.125

(C)

4

(D)

5

(E)

6.75

Question 28.

During a trip, Francine traveled x percent of the total distance at an average speed of 40 miles per hour and the rest of the distance at an average speed of 60 miles per hour. In terms of x, what was Francine’s average speed for the entire trip?

(A)

\({180 - x}\over 2\)

(B)

\({x + 60}\over 4\)

(C)

\({300 - x}\over 5\)

(D)

\(600\over 115 - x\)

(E)

\(12,000\over x + 200\)

Question 29.

If n = (33)43 + (43)33, what is the units digit of n ?

(A)

0

(B)

2

(C)

4

(D)

6

(E)

8

Question 30.

If x = -1, then \({x^4 - x^3 + x^2}\over x - 1\)

(A)

-\(3\over 2\)

(B)

-\(1\over 2\)

(C)

0

(D)

\(1\over 2\)

(E)

\(3\over 2\)

Question 31.

A border of uniform width is placed around a rectangular photograph that measures 8 inches by 10 inches. If the area of the border is 144 square inches, what is the width of the border, in inches?

(A)

3

(B)

4

(C)

6

(D)

8

(E)

9

Question 32.

Jack is now 14 years older than Bill. If in 10 years Jack will be twice as old as Bill, how old will Jack be in 5 years?

(A)

9

(B)

19

(C)

21

(D)

23

(E)

33

Question 33.

An empty pool being filled with water at a constant rate takes 8 hours to fill to of its capacity. How much more time will it take to finish filling the pool?

(A)

5 hr 30 min

(B)

5hr 20 min

(C)

4 hr 48 min

(D)

3 hr 12 min

(E)

2 hr 40 min

Question 34.

A positive number x is multiplied by 2, and this product is then divided by 3. If the positive square root of the result of these two operations equals x, what is the value of x ?

(A)

\(9\over 4\)

(B)

\(3\over 2\)

(C)

\(4\over 3\)

(D)

\(2\over 3\)

(E)

\(1\over 2\)

Question 35.

If d = \(1\over {2^3 x 5^7}\) is expressed as a terminating decimal, how many nonzero digits will d have?

(A)

1

(B)

2

(C)

3

(D)

7

(E)

10

Question 36.

A tank contains 10,000 gallons of a solution that is 5 percent sodium chloride by volume. If 2,500gallons of water evaporate from the tank, the remaining solution will be approximately what percent sodium chloride?

(A)

1.25%

(B)

3.75%

(C)

6.25%

(D)

6.67%

(E)

11.7%

Question 37.

For any positive integer n, the sum of the firstn positive integers equals \({n(n + 1)}\over 2\) . What is the sum of all the even integers between 99 and 301 ?

(A)

10,100

(B)

20.200

(C)

22,625

(D)

40,200

(E)

45,125

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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