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

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CEO
Joined: 11 Sep 2015
Posts: 3238
x, y and z are positive. If x percent of y is z  [#permalink]

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28 Mar 2017, 05:48
1
Top Contributor
4
00:00

Difficulty:

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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CEO
Joined: 11 Sep 2015
Posts: 3238
Re: x, y and z are positive. If x percent of y is z  [#permalink]

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29 Mar 2017, 05:57
1
Top Contributor
1
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

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Manager
Joined: 13 Dec 2013
Posts: 155
Location: United States (NY)
GMAT 1: 710 Q46 V41
GMAT 2: 720 Q48 V40
GPA: 4
WE: Consulting (Consulting)
Re: x, y and z are positive. If x percent of y is z  [#permalink]

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04 Apr 2017, 19:54
2
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.
Intern
Joined: 09 May 2018
Posts: 6
Concentration: Finance, Technology
x, y and z are positive. If x percent of y is z  [#permalink]

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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):

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

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

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

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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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