GMAT Official Guide Quantitative Review 2019_ Book

(1) First of all, note that the choice of units

used to measure the amounts of data doesn't

matter. In particular, we can define one unit

of data to be D. Thus, 2R + 2S = 1. With

this in mind, consider the condition that

Rafael, when working alone, can tabulate

the data in 3 hours less time than Salvador

can when working alone. Given that Rafael

tabulates R units of data per unit time,

he takes—^1 units of time to tabulate one

unit of data. Similarly, Salvador takes -^1

s

units of time to tabulate one unit of data.

This unit, as defined, is simply the entire

set of data. Our given condition thus

becomes—^1 =—^1 - 3, and we have the set

R S

of simultaneous equations made up of this

equation and the equation 2R + 2S = 1.

One way to determine the number of hours

it would take Rafael to tabulate the data is

to solve one of these equations for S and

then substitute this solution into the other

equation. Considering the first of these

equations, we multiply both sides by RS and

then manipulate the result as follows.

S= R-3RS

S+3RS=R

S(l + 3R) = R

S= R

1+3R

Substituting into the equation 2R + 2S = 1,

2R+ 2R =1

1+3R

Multiplying both sides by 1 + 3R to eliminate the

fraction

2R(l + 3R) + 2R = 1 + 3R

2R+6R^2 = 1 +R

成+R-1=0

(3R - 1)(2R + 1) = 0

This equation has two solutions, ——^1 and-.^1

2 3

However, because the rate R cannot be negative, we

find that Rafael tabulates -^1 of a unit of data every

3

hour. Since one unit is the entire set, it takes Rafael

3 hours to tabulate the entire set; SUFFICIENT.

5. 5 1·, rf,< 1 Answer Explanations

(2) We are given that Rafael, working alone, can

tabulate the data in—^1 the amount of time

it takes Salvador, working alone, to tabulate

the data. As in the discussion of statement

1, we have that Rafael tabulates R units

of data every hour, and takes—^1 hours to

R

tabulate one unit of data. Similarly, it takes

Salvador - hours^1 to tabulate one unit of

data. One unit of data has been defined to

be the size of the entire set to be tabulated,

so statement 2 becomes the expression

—=^1 —1 1 X—=—^1

R 2 S 2S

We thus have 2S = R. Substituting this

value for 2S in the equation 2R + 2S = 1, we

have R + 2R = 1, and 3R = 1. Solving for R

we get -^1 ·SUFFICIENT.

Note that, for both statements 1 and 2, it would

have been possible to stop calculating once we

had determined whether it was possible to find

a unique value for R. The ability to make such

judgments accurately is part of what the test has

been designed to measure.

1h e correct answer 1s D·，

each statement alone is sufficient.

DS04039

216. If x and y are integers, what is the value of x?

(1) xy=l

(2) X ic-l

Arithmetic

Given that x and y are integers, determine the

value of x.

(1) If x = y = -1, then xy = 1, and if x = y = 1,

then xy = 1; NOT sufficient.

(2) Given that x-:/:- —1, the value of x could be

any other integer; NOT sufficient.

Taking (1) and (2) together, since the two

possibilities for the value of x are x =— 1 or x = 1

by (1), and x-:/:- -1 by (2), then x = 1.

Th e correct answer 1s C·

both statements together are sufficient.