GMAT Official Guide Quantitative Review 2019_ Book

GMAT® Official Guide 2019 Quantitative Review

4.5 Answer Explanations

1.

The following discus,;ion i,; intended to familiarize you with the most efficient and effective approaches

to the kinds of problems common to problem solving questions The p rticul r questions in this h pter

ar£' generally repre,;entative of the kinds of problem solving question,; you will encounter on the GMAT.

Remember that it Is the problem solving str tegy th t is import nt, not the specific dc-t its of p rticul r

question

' PS0 3439

Working at a constant rate, a copy machine makes

20 copies of a one-page document per minute. If the

machine works at this constant rate, how many hours

does it take to make 4,800 copies of a one-page

document?

(A) 4

(Bl 5

(C) 6

(D) 7

(El 8

Arithmetic

The copy machine produces 20 copies of the

one-page document each minute. Because there

are 60 minutes in an hour, the constant rate of

20 copies per minute is equal to 60 x 20 = 1,200

copies per hour. With the machine working

at this rate, the amount of time that it takes

to produce 4,800 copies of the document is

4800 copies _

4

--~-. - - h ours.

1200

copies

hour

The correct answer is A.

PSl 1042

Algebra r

x+y= 2

y=2-x

x2 + (2 - x)^2 = 2

2x2- 4x+4 = 2

2x2-4x+ 2 = 0

x2 - 2.x: + 1 = 0

(x - l)(x -1) = 0

x=l

y=l

xy = l

given

subtract x from both sides

substitute y = 2 -x into

x2+y2=2

expand and combine like

terms

subtract 2 from both sides

divide both sides by 2

factor

set each factor equal to 0

use x = l and y = 2 -x

multiply 1 and 1

Alternatively, the value of xy can be found by first

squaring both sides of the equation x + y = 2.

x + y = 2 given

(x + y)^2 = 4 square both sides

x2 + 2xy + y2 = 4 expand and combine like terms

2 + 2xy = 4 replace x2 + y2 with 2

2xy = 2 subtract 2 from both sides

xy = l divide both sides by 2

The correct answer is D.

2. If x+ y= 2 and x^2 + y2 = 2, what is the value of xy? PS0^2978

(A) -2

(B) -1

(C) 0

(D)

(E)

1

2

3. The sum S of the first n consecutive positive even
   integers is given by S = n(n + l). For what value of n is
   this sum equal to 110?

(A) 10

(B) 11

(C) 12

(D) 13

(El 14

• These numbers correlate with the online test bank question number. See the GMAT Quantitative Review Online Index in the back of this book.