GMAT Official Guide Quantitative Review 2019_ Book

4.5 Answer Explanations

PS16977
172.A certain grocery purchased x pounds of produce for
p dollars per pound. If y pounds of the produce had to
be discarded due to spoilage and the grocery sold the
rest for s dollars per pound, which of the following
represents the gross profit on the sale of the produce?

(Al (x -y)s -xp

(B) (x -y)p -ys

(C) (s - p)y-xp

(D) xp -ys

(El {x -y){s -p)

Algebra

Since the grocery bought x pounds of produce for

p dollars per pound, the total cost of the produce

was xp dollars. Since y pounds of the produce

was discarded, the grocery sold x - y pounds

of produce at the price of s dollars per pound,

yielding a total revenue of (x -y)s dollars. Then,

the grocery's gross profit on the sale of the

produce is · ·its tota^1 revenue mmus its total cost or

(x -y)s -xp dollars.

Th e correct answer 1s A.
PS16990
173.If x, y, and z are positive integers such that x 1s a
factor of y, and x is a multiple of z, which of the
following is NOT necessarily an integer?

Substitute these expressions for x and/or y into

each answer choice to find the one expression

that is NOT necessarily an integer.

A

x+z = mz+z = (m+l)z =

m + l, which

z z z

MUST be an integer

y+z y z kx z 1

B =-+-=—+-=妇—, which

X X X X mz m

NEED NOT be an integer

Because only one of the five expressions need not

be an integer, the expressions given in C, D, and

E need not be tested. However, for completeness,

C

x+ Y mz+kx mz五(mz) mz(l+及）

之 = z = z =

名

(Al

x+z

z

(B) y

+z

X

(Cl 江z y

(D)

xy

z

{E) y

z

X

= m(l + k), which MUST be an integer

D

xy ＝ (mz) y =

my, which MUST be an

z z

integer

E

—yz = (kx)(z)

= kz, which MUST be an

X X

integer

The correct answer is B.

PS08416

174.Running at their respective constant rates, Machine X

takes 2 days longer to produce w widgets than

Machine Y. At these rates, if the two machines together

produce—^5 w widgets in 3 days, how many days would

4

it take Machine X alone to produce 2w widgets?

(Al^4

(Bl^6

(Cl^8

(D)^10

(El^12

Arithmetic

Since the positive integer x is a factor of y, then

y=女xfor some positive integer k. Since x is a

mult iple of the positive integer z, then x = mz for

some positive integer m.