GMAT Official Guide Quantitative Review 2019_ Book

4.5 ,ble>r1 < !-,, Answer Explanations

Algebra; Arithmetic ,bst巾 r r.

A If x is an intege:, y is an integer since y= x

Thus, the line given by y = x contains

points with integers as both coordinates.

B If xis an integer, then if y were an integer,

theny—x would be an integer. But,

y—x = -^1 and- is NOT^1 an integer. Since

2 2

assuming that y is an integer leads to a

contradiction, then y cannot be an integer and

1

the line given by y = x + -does NOT contain

2

any points with integers as both coordinates.

Since there can be only one correct answer, the

lines in C, D, and E need not be checked, but for

completeness,

C If x is an integer, x + 5 is an integer and

soy is an integer since y = x + 5. Thus, the

line given by y = x + 5 contains points with

integers as both coordinates.

D

E

1

If x is an even integer, - x is an integer and

(^2 1)
soy is an integer since y =—x. Thus, the
1 2
line given by y = -x contains points with
2
integers as both coordinates.
1
If x is an even integer, - x is an integer and
1 2
2

• x+5 is also an integer soy is an integer
  1
  since y =—x + 5. Thus, the line given by
  2
  y= -x + 5 contains points with integers as
  2
  both coordinates.

Th e correct answer 1s B.

PS04160

105. A certain financial institution reported that its a ssets
     totaled $2,377,366.30 on a certain day. Of this
     amount, $31,724.54 was held in cash. Approximately
     what percent of the reported assets was held in cash
     on that day?

(Al 0.00013%

(Bl 0.0013%

(Cl 0.013%

(D) 0.13%

(E) 1.3%

Arithmetic

The requested percent can be estimated by

converting the values into scientific notation.

31,724.54

2,377,366.30

value as fraction

3.172454 x 104 convert to scienti压

2.3 77366 30 x^106 notation

＝ 3.172454^10

(^4) anthmet1c proper
X
tyof
2 .3 7736630 106 fractions
= 3.172454 x 10-2 subtract exponents
2.37736630
"'-^3 X 10 - 2
= 1.5 X 10-^2
= 0.^015
= 1.5%
approximate
convert to decimal fraction
multiply
convert to percent
A more detailed computation would show that
1.3% is a better approximation. However, in order
to select the best value from the values given as
answer choices, the above computation is sufficient.
Th e correct answer 1s E.
AB

• BA
  PS09820

106. In the correctly worked addition problem shown, where

MC

，＇AlBlClDJEl 96320

，＇

�

．．

．．

．

the sum of the two-digit positive integers AB and BA is

the three-digit integer MC, and A, B, and C are different

digits, what is the units digit of the integer AAC?

Arithmetic

Determine the value of C.

It is given that (10A + B) + ( 10 B + A) =

100A + 10A + C or 11A + 11B = 110A + C. Thus,

11B -99A = C, or ll(B -9A) = C. Therefore, C is

divisible by 11, and O is the only digit that is

divisible by 11.

The correct answer is E.