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by theachiever » Fri Dec 07, 2012 2:40 am
If x percent of y is equal to y percent less than z,what is y in terms of x and z?

A.100(x+z)/x
B.100x/x+z
C.100(x+z)/x-z
D.100z/x-z
E.100z/x+z
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by GMATGuruNY » Fri Dec 07, 2012 3:37 am
theachiever wrote:If x percent of y is equal to y percent less than z,what is y in terms of x and z?

A.100(x+z)/x
B.100x/x+z
C.100(x+z)/x-z
D.100z/x-z
E.100z/x+z
et z=50.
Let y=20.
y% less than z = 20% less than 50 = 40.
Thus, x% of y = 40.
Thus, x=200.
The question asks for the value of y=20. This is our target.
Now we plug x=200 and z=50 into the answers to see which yields our target of 20.

Only answer choice E works:
100z/(x+z) = (100*50)/(200+5) = 20.

The correct answer is E.
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by Brent@GMATPrepNow » Fri Dec 07, 2012 10:37 am
theachiever wrote:If x percent of y is equal to y percent less than z,what is y in terms of x and z?

A.100(x+z)/x
B.100x/x+z
C.100(x+z)/x-z
D.100z/x-z
E.100z/x+z
Here's the algebraic solution...
x percent of y is the same as (x/100)y
y percent less than z is the same as z - (y/100)z

So, x percent of y is equal to y percent less than z tells us that:
(x/100)y = z - (y/100)z (now solve for y)
Multiply both sides by 100 to get: xy = 100z - yz
Add yz to both sides to get: xy + yz = 100z
Factor left side: y(x+z) = 100z
Divide both sides by y to get: y = 100z/(x+z) = E

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