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If x and y are positive integers and

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If x and y are positive integers and

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If x and y are positive integers and \(x^y =x^{2y-3} \) what is the value of \(x^y\)?

(1) \(x=2\)

(2) \(x^3=8\)

OA=D

Source: Veritas Prep

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Gmat_mission wrote:
If x and y are positive integers and \(x^y =x^{2y-3} \) what is the value of \(x^y\)?

(1) \(x=2\)

(2) \(x^3=8\)
Statement 1: x=2
\(2^y =2^{2y-3} \)
Since each side has the same base, the two exponents must be equal:
y = 2y-3
3 = y
Since the values of x and y are known, the value of \(x^y\) can be determined.
SUFFICIENT.

Statement 2:
Thus, x=2.
Same information as in Statement 1.
Since Statement 1 is sufficient, so is Statement 2.
SUFFICIENT.

The correct answer is D.

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