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What is y in terms of x?

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by theCodeToGMAT » Thu Sep 26, 2013 10:04 am
Is the answer {C}
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by fourteenstix » Thu Sep 26, 2013 11:12 am
How did you get from:

5^x - 5^(x-3) = 5^(3+y) - 5^y

to:

x-3=y

by "comparing both sides"?
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by GMATGuruNY » Thu Sep 26, 2013 11:21 am
fourteenstix wrote:Image
Plug in a value for x and solve for y.
Let x=3, so that 5^(x-3) = 5� =1.
Plugging x=3 into the equation, we get:
5³ - 5� = 124 * 5^y
124 = 124 * 5^y
1 = 5^y
y=0.

Since the question stem asks for the value of y, our target is y=0.
Now plug x=3 into the answers to see which yields our target of 0.
A quick scan of the answer choices shows that only C works:
x-3 = 3-3 = 0.

The correct answer is C.
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by theCodeToGMAT » Thu Sep 26, 2013 11:30 am
fourteenstix wrote:How did you get from:

5^x - 5^(x-3) = 5^(3+y) - 5^y

to:

x-3=y

by "comparing both sides"?
The same rule by which we say:

5^x = 5^2 so x=2

the difference is just that we have similar structure on LHS & RHS but with "-" sign.. so compare the powers.
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