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Positive integer y is 50 percent of 50 percent of positive integer x,

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Carcass
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Positive integer y is 50 percent of 50 percent of positive integer x, [#permalink] New post   11 May 2022, 01:57
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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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C
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Re: Positive integer y is 50 percent of 50 percent of positive integer x, [#permalink] New post   11 May 2022, 06:15
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Carcass 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


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
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gmatclubot
Re: Positive integer y is 50 percent of 50 percent of positive integer x, [#permalink]
11 May 2022, 06:15
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