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Percent problem

This topic has 3 expert replies and 0 member replies
GmatKiss Legendary Member Default Avatar
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Percent problem

Post Sat May 05, 2012 4:10 am
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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Post Tue Feb 20, 2018 4:26 pm
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 create the following equation:

y = (0.5)(0.5)x

y = 0.25x

Expressing y percent as y/100, we obtain the second equation:

(y/100)x = 100

Substituting y = 0.25x into the above equation:

(0.25x/100)x = 100

0.25x^2 = 10,000

x^2 = 40,000

x = 200

Answer: C

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Scott Woodbury-Stewart Founder and CEO

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GMAT/MBA Expert

Post Thu Feb 15, 2018 4:09 pm
Hi All,

This question can be solved by TESTing THE ANSWERS. We're told that:
1) Positive integer Y is 50 percent of 50 percent of positive integer X
2) Y percent of X equals 100

We're asked for the value of X.

Let's TEST Answer B: 100

IF....
X = 100
Y = (.5)(.5)(100) = 25
25% of 100 = 25 (but it's supposed to be 100). This answer is TOO SMALL.

Let's TEST Answer D: 1000

IF....
X = 1000
Y = (.5)(.5)(1000) = 250
250% of 1000 = 2500 (but it's supposed to be 100). This answer is TOO BIG.

The likely correct answer is C, but we can TEST it rather easily...

IF....
X = 200
Y = (.5)(.5)(200) = 50
50% of 200 = 100. This is an exact MATCH for what we were told, so this MUST be the answer.

Final Answer: C

GMAT assassins aren't born, they're made,
Rich

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Contact Rich at Rich.C@empowergmat.com

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GMAT/MBA Expert

Post 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.

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

The correct answer is C.

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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