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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, 05:48
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  55% (hard)

Question Stats:

61% (02:01) correct 39% (02:33) wrong based on 171 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, 05:57
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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, 19:54
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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.
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x, y and z are positive. If x percent of y is z  [#permalink]

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New post 04 Jul 2018, 10:56
the question is to compute

\(\frac{x^2}{100}*\frac{1}{10}\)

according to the question:

(i) \(\frac{x}{100}y=z\)

(ii)\(\frac{z}{100}x=y\)

from (i) and (ii):


\(\frac{\left(\frac{x}{100}y\right)}{100}x=y \implies \frac{x^2}{100} = 100\)

\(\therefore \frac{x^2}{100}*\frac{1}{10} = 100 * \frac{1}{10} = 10\)

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 Jul 2018, 11:44
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

*Kudos for all correct solutions


\(x\) percent of \(y\) is \(z\) translates to \(\frac{x}{100} * y = z\) -> \(xy = 100z\)

Similarly, \(z\) percent of \(x\) is \(y\). This translates to \(\frac{z}{100} * x = y\) -> \(xz = 100y\)

This is only possible when x=100 and y=z.

Therefore, \(x^2\) percent is 10000th percent of \(\frac{1}{10}\), which is \(\frac{10000}{100} * \frac{1}{10}\) = 10(Option D)
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Re: x, y and z are positive. If x percent of y is z &nbs [#permalink] 04 Jul 2018, 11:44
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