GMAT Official Guide Quantitative Review 2019_ Book

DS05989

202. What is the value of 2x + 2-x?

(1) X > 0

(2) 4 x + 4一X= 23

Algebra

Can we determine the value of 2气2勺

(1) The condition x > 0 by itself is not sufficient

for determining the value of 2x + 2飞For

example, if x = l, then 2气沪= 21 + 2-^1 =

2-.^1 And if x = 2, then 2气沪= 22 + 2-2 =

2

4 —^1 ; NOT sufficient.

4

(2) Given 4气尸= 23, it may be tempting to

Th

reason that this is an equation with only one

unknown, and that it is therefore possible to

determine the value of x and then the value

of 2x + 2-x. However, this reasoning can

often produce erroneous results. For example

the equation (y - l)(y - 3) = 0 has only one

unknown but is consistent with two values

for y (l and 3). To be sure that the statement

4 x + 4女 = 23 is sufficient for determining

the value of 2x + 2飞consider first the square

of 2x + 2飞

(^2 x +2平=(^2 平+(2-x)^2 + 2(^2 节(^2 芍

= 22x + r2x + 2( 2 炉X)

= (2年+(r^2 t +2

=4x+4-x+2.

So 4勹尸=( 2 x + 2

一

平-2. The condition

that 4x + 4-x = 23 thus becomes

( 2 x +2平-2 = 23, or ( 2 x + 2

一

乎=25.

And because we know that 2x + 2-x > 0

(because both 2x > 0 and Tx > O), we

see that statement 1 implies ( 2 x + 2可＝

忘=5; SUFFICIENT.

e correct answer 1s B· ，
statement 2 alone is sufficient.
DSl3457
203.What is the ratio of c to d?

(1) The ratio of 3c to 3d is 3 to 4.

(2) The ratio of c + 3 to d + 3 is 4 to 5.

5.5 Answer Explanations

Arithmetic

Determine the value of仁

d

(1) Given that—3c =—^3 , it follows that

3d 4

—= -2c C =-·^3 SUFFICIENT.

2d d 4

(2) Given that c+3 =—^4 , then it is not possible

d+3 5

to determine the value of!..... For example,

d

if c = 1 and d = 2, then c+3 = - and^4

d+3 5

三-^1 .However, if c = 5 and d= 7, then

d 2

c+3 =- (^8) = (^4) —and —=C 5—; NOT sufficient.
d +3 10 5 d 7
Th e correct answer 1s A· ，
statement (1) alone is sufficient.
DS15099
204.A candle company determines that, for a certain
specialty candle, the supply function is p = m1x + b1
and the demand function is p = m2x + b2, where p is
the price of each candle, x is the number of candles
supplied or demanded, and m1, m2, b1, and b2 are
constants. At what value of x do the graphs of the
supply function and demand function intersect?
(1) m1 = -吓= 0.005
(2) b2 - b 1 = 6
Algebra
The graphs will intersect at the value of x such
that m1x +仇=m 2 x+幻or(m 1 - m沁＝勿－妇
(1)加sindicates that m 1 = -m 2 = 0.005. It
follows that m 1 - m 2 = 0.01, and so O.Olx =
朽—妇orx = 100也－纠），whichcan vary as
the values of约and纠vary;NOT sufficient.
(2) This indicates that勿-b1 = 6. It follows
that (m 1 —m沁= 6. This implies that
m1 -:t: m2, and so x = b -么 6^2 = ,
m 1 - m 2 m 1 - m 2
咖chcan vary as the values of m1 and m2
vary; NOT sufficient.
Taking (1) and (2) together, m 1 - m 2 = 0.01 and
勿－纠=6 and so the value of x is^6 = 600.
0.01
Th e correct answer 1s C·
both statements together are sufficient.