GMAT Official Guide Quantitative Review 2019_ Book

Arithmetic

Consider the table below in which T represents

the total number of students in the dormitory.

1

Since -of the students are first-year students and

the rest are second-year students, it follows that

1

• of the students are second-year students, and so
  2
  the totals for the first-year and second-year columns
  4
  are both 0.5T. Since -of the first-year students
  5
  have not declared a major, it follows that the middle
  4
  entry in the first-year column is - (0.57) = 0.4T
  and the first entry in the first-year column is
  0.5T-OAT= O.lT. Since the fraction of
  second-year students who have declared a major
  is 3 times the fraction of first-year students who
  have declared a major, it follows that the first entry
  in the second-year column is 3(0.1 T) = 0.3 Tand
  the second entry in the second-year column is
  0.5T-0.3T= 0.2T. Thus, the fraction of students
  that are second-year students who have not
  d 1.

0.2T^1

ec ared a maJor is = 0.2 = -.

T 5

／．

First- Second-

year year

Declared major 0.1T 0.3T

Not declared major 0.4T 0.2T

\_Total 0.5T 0.5T

1h e correct answer 1s B.

PS09050

＼

Total

0.4T

0.6T

T

115. If the average (arithmetic mean) of x, y, and z is 7x and
     x :1= 0, what is the ratio of x to the sum of y and z?

(Al 1:21

(Bl 1:20

(Cl 1:6

(D) 6:1

(El 20:1

4.5 I:: 伈r• I、, Answer Explanations

Algebra

Given that the average of x, y, and z is 7 x, it

x+y+z

follows that = 7 x, or x + y + z = 21x,

3

or y + z = 20x. Dividing both sides of the last

..^1 X
equation by 20 y + z) gives（ — 20 = y+z , so the

ratio of x to the sum of y and z is 1:20.

Th e correct answer 1s B.

PS02352

116. In the coordinate plane, line k passes through the
     origin and has slope 2. If points (3,y) and (x,4) are on
     line k, then x + y =

(Al 3.5

(Bl 7

(C) 8

(D) 1

(El^0 14

Algebra

Since line k has slope 2 and passes through the

origin, the equation ofline k is y = 2x. If the

point (3,y) is on line k, then y = 2(3) = 6. If the

point (x,4) is on line k, then 4 = 2x and so x = 2.

Therefore, x + y = 6 + 2 = 8.

Th e correct answer 1s C.

PS08661

117. If a, b, and c are constants, a> b > c, and
     x^3 - x = (x - a)(x - b)(x - c) for all numbers x, what is
     the value of b?

(A) -3

(Bl - 1

(Cl O

(D)

(El

1

3

Algebra

Since (x - a)(x - b)(x - c) = x^3 - x = x(x (^2) - 1) =
x(x + l)(x - 1) = (x - O)(x - l)(x + 1) then a, b,
and care 0, 1, and -1 in some order. Since a>
b > c, it follows that a= 1, b = 0, and c = -1.
Th e correct answer 1s C.