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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

by Brent@GMATPrepNow » Tue Mar 28, 2017 5:50 am
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

Answer: D

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by regor60 » Tue Mar 28, 2017 6:17 am
x percent of y is z: (X/100)*Y = Z

z percent of x is y: (Z/100)*X = Y

Therefore, (X/100)*X*(Z/100) = Z or X^2 = 10,000

and X = 100

what is x² percent of 1/10? : X^2 percent = (100*100/100) = 100 and 100 * (1/10) = D
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by DavidG@VeritasPrep » Tue Mar 28, 2017 6:27 am
Brent@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

Answer: D

Source: www.gmatprepnow.com
Difficulty level: 600 - 650
Or we can do a little clever number-picking. Say x = 100, y = 100, and z = 100. (100% of 100 is surely 100, right?)

x² = 100² = 10,000
10,000% of 1/10 = 10,000*(1/100) *(1/10) = 100 *(1/10) = 10.
The answer is D
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by Brent@GMATPrepNow » Tue Mar 28, 2017 8:00 am
Brent@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

Answer: D

Source: www.gmatprepnow.com
Difficulty level: 600 - 650

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 x² with 10,000 to get: (10,000/100)(1/10) = 10,000/1,000 = 10

Answer: D

Cheers,
Brent
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