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## Percent problem

This topic has 1 expert reply and 0 member replies
GmatKiss Legendary Member
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#### Percent problem

Sat May 05, 2012 4:10 am
Elapsed Time: 00:00
• Lap #[LAPCOUNT] ([LAPTIME])
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

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### GMAT/MBA Expert

GMATGuruNY GMAT Instructor
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Sat May 05, 2012 4:31 am
GmatKiss wrote:
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
We can plug in the answers.

y = 50% of 50% of x = (1/2)(1/2)200 = 50.
y% of x = 50% of 200 = 100.
Success!

Algebraically:
y = 50% of 50% of x = (1/2)(1/2)x = x/4.

Since y% of x = 100:
(x/4)/100 * x = 100
x² = 100*100*4
x = 10*10*2 = 200.

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