Exponents

[tapanmittal]

If x and y are positive integers and 5^x - 5^y = (2^(y - 1))(5^(x - 1)), what is the value of xy?

Ans-12

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Hi tapanmittal,

What is the source of this question? If it's a GMAT question then there should be 5 answer choices - seeing those answer might provide some insight into how you might best solve this problem. As it stands, there's a great 'brute force' solution to this question that does NOT require any advanced math, but it does require that you write down some 'powers of 5' and 'powers of 2'....

I'm going to give you a couple of hints so that you can try this question again:

Since this prompt includes 3 'powers of 5', I'm going to write down the first several for reference...

5^1 = 5
5^2 = 25
5^3 = 125
5^4 = 625

With the given equation....
5^X - 5^Y = (2^(Y - 1))(5^(X - 1))

We need both 'sides' to equal one another. Since the 'right side' involves multiplication, that product will be POSITIVE. That means that 5^X must be GREATER than 5^Y (so the 'left side' ends up positive), and X > Y.

Using the above list of 'powers of 5', how much work would it really take you to figure out the respective values of X and Y.....?

Final Answer: [spoiler]X=4, Y=3; (X)(Y) = 12[/spoiler]

GMAT assassins aren't born, they're made,
Rich