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x, y and z are positive. If x percent of y is z

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x, y and z are positive. If x percent of y is z [#permalink]

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New post 28 Mar 2017, 06:48
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  55% (hard)

Question Stats:

65% (01:18) correct 35% (01:44) wrong based on 136 sessions

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x, y and z are positive. If x percent of y is z, and z percent of x is y, then what is x² percent of 1/10?

A) 1/100
B) 1/10
C) 1
D) 10
E) 100

*Kudos for all correct solutions

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Re: x, y and z are positive. If x percent of y is z [#permalink]

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New post 29 Mar 2017, 06:57
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GMATPrepNow wrote:
x, y and z are positive. If x percent of y is z, and z percent of x is y, then what is x² percent of 1/10?

A) 1/100
B) 1/10
C) 1
D) 10
E) 100



Here's one approach:

x percent of y is z
So (x/100)(y) = z
Simplify: xy/100 = z

z percent of x is y
So (z/100)(x) = y
Simplify: xz/100 = y

Multiply the two equations to get: (xy/100)(xz/100) = (z)(y)
Simplify: x²yz/10,000 = yz
Divide both sides by yz to get: x²/10,000 = 1
This means x² = 10,000

What is x² percent of 1/10?
In other words, (x²/100)(1/10) = ?
Replace with 10,000 to get: (10,000/100)(1/10) = 10,000/1,000 = 10

Answer: D

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Re: x, y and z are positive. If x percent of y is z [#permalink]

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New post 04 Apr 2017, 20:54
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Eqn.1: (yx/100)=z
Eqn.2: (xz/100)=y

Eqn. 2: (100y/x)=z

(yx/100)= (100y/x)
yx^2=10000y
x^2=10000

So 0.1*10000%=10

Kudos if you agree! If you have a better solution please comment.
Re: x, y and z are positive. If x percent of y is z   [#permalink] 04 Apr 2017, 20:54
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x, y and z are positive. If x percent of y is z

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