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GMAT Question of the Day – DS – Exponents Puzzle 4

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GMAT Question of the Day – Data Sufficiency – Exponents

If \( 2^x = y^{24} \) what is the value of x – y?

(1) x = 48

(2) x and y are both multiples of 2

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Correct Answer: E.

GMAT Question of the Day Solution

Whenever you see even exponents consider that a negative value could be hidden. In this case you can see that because of the even exponent \( y^{24} \) will be positive even if y is negative. For Statement (1) if x is 48 y must be 4 or -4. Two values of y yield two values for x – y so this statement is insufficient. Statement 2 tells us that both x and y are integers but we can use the same values from statement (1) and get multiple outcomes for x – y. Insufficient. Putting both statements together there is no new information.

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