GMAT Official Guide Quantitative Review 2019_ Book

PS10493

72. Of the goose eggs laid at a certain pond, -^2 hatched,
    3 3
    and -of the geese that hatched from those eggs
    4
    survived the first month. Of the geese that survived
    the first month, -^3 did not survive the first year. If
    5 —
    120 geese survived the first year and if no more than
    one goose hatched from each egg, how many goose
    eggs were laid at the pond?

(A ) 280

(B ) 400

(Cl 540

(D ) 600

(E ) 840

Arithmetic

Let N represent the number of eggs laid at the

pond. Then 1 N eggs hatched and¾(伈）

goslings (baby geese) survived the first month.

Since -^3 of these goslings did not survive the first

5

year, then^2 - did survive the first year. This means

5

that识（伈）)goslings survived the first year.

�

ut this number is 120 and so,¾(¾(¾N))�120,

-N = 120 and N = 5(120) = 600.

5

The correct answer is D.

PS09305

73. If x^2 - 2x - 15 = 0 and x > 0, which of the following
    must be equal to O?

I. x^2 - 6x+ 9

II. x^2 - 7x + 10

Ill. x^2 - 1 Ox+ 25

(A ) I only

(8 ) II only

(C l Ill only

(D) II and Ill only

(E l I, II, and Ill

Algebra

Since x2-2x — 15 = 0, then (x - 5)(x + 3) = 0, so

x = 5 or x = -3. Since x > 0, then x = 5.

74.

4.5 Answer Explanations

I. 52 - 6(5) + 9 = 25 - 30 + 9 = 4 -::t- O

II. 52 - 7(5) + 10 = 25 - 35 + 10 = O

III. 52 —10(5) + 25 = 25 - 50 + 25 = O

The correct answer is D.

PSI0921

(39,897)(0.0096)

198.76

(A) 0.02

(B) 0.2

(C)^2

(D)^20

(E) 200

Arithmetic

1s approximately

(39, 897)(0.0096) (40, 000)(0.01) =

(^200 )(0.01) =^2

198.76

""

200

Th e correct answer 1s C.

PS13205

75. If a square region has area n, what is the length of the
    diagonal of the square in terms of n?

(A )高

(B l折

(C l 2.../n

(D ) 2n

(El 2n^2

Geometry

Ifs represents the side length of the square,

then n =?.By the Pythagorean theorem,

the length of the diagonal of the square is

护产了

1h e correct answer 1s A.

PS00817

76. The "prime sum" of an integer n greater than 1 is the
    sum of all the prime factors of n, including repetitions.
    For example, the prime sum of 12 is 7, since
    12 = 2 x 2 x 3 and 2 + 2 + 3 = 7. For which of the
    following integers is the prime sum greater than 35?

(A ) 440

(B l 512

(C l 620

(D ) 700

(El 750