Problem Solving

AAPL wrote: ↑

Tue Nov 10, 2020 6:28 pm

Official Guide

Positive integer y is 50 percent of 50 percent of positive integer x, and y percent of x equals 100. What is the value of x?

A. 50
B. 100
C. 200
D. 1000
E. 2000

OA C

Solution:

We can create the following equations:

y = (0.5)(0.5)x

y = 0.25x

and

(y/100)x = 100

Substituting y = 0.25x into the above equation yields:

(0.25x/100)x = 100

0.25x^2 = 10,000

x^2 = 40,000

x = 200

Answer: C

AAPL wrote: ↑

Tue Nov 10, 2020 6:28 pm

Official Guide

Positive integer y is 50 percent of 50 percent of positive integer x, and y percent of x equals 100. What is the value of x?

A. 50
B. 100
C. 200
D. 1000
E. 2000

OA C

Positive integer y is 50 percent of 50 percent of positive integer x
We can write: y = (50/100)(50/100)(x)
Simplify: y = (1/2)(1/2)(x)
Simplify: y = x/4

y percent of x equals 100.
We can write: (y/100)(x) = 100
Simplify: xy/100 = 100
Multiply both sides of the equation by 100 to get: xy = 10,000

What is the value of x?
Take: xy = 10,000
Replace y with x/4 to get: x(x/4) = 10,000
Simplify: x²/4 = 10,000
Multiply both sides by 4 to get: x² = 40,000
Solve: x = 200 or x = -200
Since we're told x is positive, we can be certain that x = 200 \

Answer: C