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If x and y are positive integers, x^(y-2)=?

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Source: — Data Sufficiency |

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by Jay@ManhattanReview » Sun Oct 08, 2017 10:29 pm
Vincen wrote:If x and y are positive integers, x^(y-2)=?

1) x^2=1.
2) y^2=4.

The OA is D.

How can I prove that each statement alone is sufficient?
1) x^2 = 1

=> x = ±1. We take x = 1 as it is given that x is a positive integer.

So, @ x = 1, x^(y-2) = 1^(y-2). Whatever be the value of (y-2), positive, 0, or negative, the value of 1^(y-2) = 1. Sufficient.

2) y^2 = 4

=> y = ±2. We take y = 2 as it is given that y is a positive integer.

So, @ y = 2, x^(y-2) = x^(2-2) = x^0 = 1. Sufficient.

The correct answer: D

Hope this helps!

-Jay

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by [email protected] » Tue Oct 10, 2017 4:55 pm
Hi Vincen,

Certain DS questions are really just a 'test' of your 'thoroughness' - you don't have to do any advanced math to answer the question, but you do have to do enough work to PROVE what the correct answer is. Many Test Takers would get this question wrong simply because they weren't willing to do enough work.

We're told that X and Y are POSITIVE INTEGERS. We're asked for the value of X^(Y-2).

1) X^2 = 1

While this equation has 2 solutions, we're told that X is a POSITIVE integer, so only one of them applies here: X = 1. With that piece of information, the question now asks for the value of 1^(Y-2). Since 1 raised to ANY exponent = 1, the value of Y is irrelevant to the question. The answer is ALWAYS 1.
Fact 1 is SUFFICIENT

2) Y^2 = 4

While this equation has 2 solutions, we're told that Y is a POSITIVE integer, so only one of them applies here: Y = 2. With that piece of information, the question now asks for the value of X^(0). Since any value raised to a 0 exponent = 1, the value of X is irrelevant to the question. The answer is ALWAYS 1.
Fact 2 is SUFFICIENT

Final Answer: D

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Rich
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