GMAT Official Guide Quantitative Review 2019_ Book

5.5 Answer Explanations

DS05172

186. If x > 0, what is the value of x^5?

(1) ✓X = 32

(2) x^2 =^220

Algebra

(1) Given that忑=32, it follows that x = 3 22

and x5 = (3 2 千；SUFFICIENT.

( 2 ) Given that x2 = 2^20 , since xis positive, it

follows that x =✓ 产=l1°and x5 = (2^10 )气

SUFFICIENT.

Th e correct answer 1s D·

each statement alone is sufficient.

DSl 7640
187.ln the qu仆ting pattern shown above, a small square has
its vertices on the sides of a larger square. What is the
side length, in centimeters, of the larger square?

( 1 ) The side length of the smaller square is 10 cm.

( 2 ) Each vertex of the small square cuts 1 side of

the larger square into 2 segments with lengths in

the ratio of 1:2.

Geometry

c E

F

4

H

G

Determine the side length of the larger square or,

in the figure above, determine

AG= AH+ HG. Note that LiBAH, WCB, LiFED,

and凶GFare the same size and shape and that

AB= CD=EF= GHandBC=DE=FG=HA.

(1) This indicates that HF= 10, but it

is possible that HG= 6 and GF= 8

(16言妒= 1 0), from which it follows

that the side length of the larger square is

6 + 8 = 14, and it is possible that HG= 1

andGF=忘｀言=^10 ),from

which it follows that the side length of the

larger square is 1 +忘；NOT sufficient.

(2) This indicates that if HG= x, then AH= 2x.

If x = 2, then the side length of the larger

square is 2 + 2( 2 ) = 6, but if x = 5, then the

side length of the larger square is 5 + 2( (^5) ) =
15; NOT sufficient.
麟ng(1) and (2) together, 10 = /; 言示)2,
which can be solved for x. Then taking 3 times
the value of x gives the side length of the larger
square.
Th e correct answer 1s C·
both statements together are sufficient.
0S02589

188. Did Insurance Company K have more than $300 m曲on
     in total net profits last year?

(1) Last year Company K paid out $0.95 in claims

for every dollar of premiums collected.

(2) Last year Company K earned a total of

$150 million in profits from the investment of

accumulated surplus premiums from previous

years.

Arithmetic

Letting R and E, respectively, represent the

company's total revenue and total expenses last

year, determine if R - E > $300 million.

(^1 )

(2)

This indicates that, for $x in premiums

collected, the company paid $0.95x in

claims, but gives no information about other

sources of revenue or other types of

expenses; NOT sufficient.

This indicates that the company's profits

from the investment of accumulated surplus

premiums was $ 1 50 million last year, but

gives no information about other sources of

revenue or other types of expenses; NOT

sufficient.