(2 to the power x) to the power y

[binaras]

In the attached question the answer is D.

Not sure how the first statement is sufficient

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Hi binaras,

The prompt tells us that X and Y are INTEGERS, which is a specific 'restriction' to work with.

Fact 1 tells us that 2^X + 2^Y = 9

This might seem strange at first - how can two EVEN numbers, when raised to integer exponents, add up to an ODD number?

The ONLY way for that to occur in this situation is if one of the numbers is 0 and the other is 3.

2^0 = 1
2^3 = 8
1 + 8 = 9

So we know that the two variables MUST be 0 and 3. Knowing that, the answer to the question will be the same regardless of which variable is 0 and which is 3. Thus, Fact 1 is SUFFICIENT.

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