Positive Integer y is 50 Percent of 50 Percent of Positive GMAT Problem Solving

Question: 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) 1,000
(E) 2,000

Correct Answer: C

Solution and Explanation:
Approach Solution 1:

y= 50x/100∗50/100
y= 25x/100 .......... (1)
xy/100= 100
y= 100∗100/x ..... (2)

Equating (1) & (2)

25x/100= 100∗100/x
25x^2= 100∗100∗100
x^2= 4∗100∗100
x= 2*10*10= 200

Approach Solution 2:

Given: x > 0 and y > 0.

"Positive integer y is 50 percent of 50 percent of positive integer x" --> y= 0.5∗(0.5x)= 0.25x;
"y percent of x equals 100" --> y/100∗x= 100 --> xy= 100∗100 --> substitute y --> x^2= 4∗100∗100 --> as
x > 0, only one solution
x= 200.

Approach Solution 3:

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

“Positive integer y is 50 percent of 50 percent of positive”- is a topic of the GMAT Quantitative reasoning section of GMAT. This question has been taken from the book "The Official Guide for GMAT Review". To solve GMAT Problem Solving questions a student must have knowledge about a good amount of qualitative skills. GMAT Quant practice papers improve the mathematical knowledge of the candidates as it represents multiple sorts of quantitative problems.

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