GMAT Official Guide Quantitative Review 2019_ Book

GMAT® Official Guide 2019 Quantitative Review

Arithmetic ~ I

Let n be the total number of people surveyed.

Then, the proportion of the people who had

type A who also had type B 1s. ---(3%)$ = -^3 = -,^1

(45%)$ 45 15

which as a percent is approximately 6.67%. Note

that by using j_ = 1 x 1, which equals 1 of 20%,

15 3 5 3

we can avoid dividing by a 2-digit integer.

The correct answer is B.

PS05146

142. On a certain transatlantic crossing, 20 percent of
     a ship's passengers held round-trip tickets and also
     took their cars aboard the ship. If 60 percent of the
     passengers with round-trip tickets did not take their
     cars aboard the ship, what percent of the ship's
     passengers held round-trip tickets?

(A) 33½%

(Bl 40%

(C) 50%

(D) 60%

(E) 66~%

Arithmetic

Since the number of passengers on the ship is

immaterial, let the number of passengers on the

ship be 100 for convenience. Let x be the number

of passengers that held round-trip tickets.

Then, since 20 percent of the passengers held a

round-trip ticket and took their cars aboard the

ship, 0.20(100) = 20 passengers held round-trip

tickets and took their cars aboard the ship. The

remaining passengers with round-trip tickets did

not take their cars aboard, and they represent 0.6x

(that is, 60 percent of the passengers with round-

trip tickets). Thus 0.6x + 20 = x, from which it

follows that 20 = 0.4x, and so x = 50. The percent

of passengers with round-trip tickets is, then,

50 = 50%.

100

The correct answer is C.

PS03696

143. If x and k are integers and (12X)(4^2 x+^1 ) = (2k)(3^2 ), what
     is the value of k?

(A) 5

(B) 7

(C) 10

(D) 12

(E) 14

Arithmetic

Rewrite the expression on the left so that it is a

product of powers of 2 and 3.

(12x )( 4 2x+l) = [(3 · 22 y ][(22 )2x+l]

= (3x)[(22Y][22(2x+l)]

= (3x)(22x)(24x+2)

= (3x )(26x+2)

Then, since (12x)(4^2 x+^1 ) = (2k)(3^2 ), it follows that

(3x)(2^6 x+^2 ) = (2k)(3^2 ) = (3^2 )(2k), so x = 2 and

k = 6x + 2. Substituting 2 for x gives

k = 6(2) + 2 = 14.

The correct answer is E.

PS 11024

144. If Sis the sum of the reciprocals of the 10 consecutive
     integers from 21 to 30, then S is between which of the
     following two fractions?

(A) -^1 and -^1

3 2

(B) -^1 and-^1

4 3

(C) -^1 and-^1

5 4

(D) -^1 and -^1

6 5

(E) -^1 and-^1

7 6

Arithmetiic [. .ir ation

The value of-+^1 -^1 + -^1 + ... + -^1. 1s LESS

21 22 23 30

than -^1 + -^1 + -^1 +. .. + -^1 (10 numbers

20 20 20 20

added), which equals 10 (_!_J = 1, and

20 2

GREATER , than -^1 + -^1 + -^1 + ... + -^1

30 30 30 30