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If x and y are integers, is xy = yx? (1) x – y = 2 (2) xy = 8  [#permalink]

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If x and y are integers, is x^y = y^x?

(1) x – y = 2
(2) xy = 8

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Re: If x and y are integers, is xy = yx? (1) x – y = 2 (2) xy = 8  [#permalink]

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If x and y are integers, is x^y = y^x?

(1) x – y = 2. If x=3 and y=2, then the answer is NO but if x=4 and y=2, then the answer is YES. Not sufficient.

(2) xy = 8. If x=8 and y=1, then the answer is NO but if x=4 and y=2, then the answer is YES. Not sufficient.

(1)+(2) Solving x – y = 2 and xy = 8 gives two sets of solutions: (x, y) = (4, 2) and (x, y) = (-2, -4). For both x^y = y^x. Sufficient.

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Re: If x and y are integers, is xy = yx? (1) x – y = 2 (2) xy = 8  [#permalink]

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If x and y are integers, is x^y = y^x?
(1) x – y = 2
(2) xy = 8
Statement 1: If x=4 and y=2 then answer is Yes. If x=3 and y=1 then answer is No ==> Not sufficient.
Statement 2: If x=4 and y=2 then answer is Yes. If x=1 and y=8 then answer is No ==> Not sufficient
Both statements together. Either x=2 and y=4 or x=-2 and y=-4. In both cases the answer is Yes. Hope it is clear
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GMAT 1: 800 Q51 V49 GRE 1: Q170 V170 Re: If x and y are integers, is xy = yx? (1) x – y = 2 (2) xy = 8  [#permalink]

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Hi JusTLucK04,

The explanations in this thread both nicely explain the solution to this problem, so I won't rehash any of that here.

Instead, I want to point out that GMAT writers tend to hide Number Property patterns into the DS questions that you'll see on Test Day. Sometimes the Number Property patterns are fairly simple and obvious (odd numbers vs. even numbers, positives vs. negatives, etc.), but sometimes the patterns are rarer.

Here, we're told that X and Y are both integers and we're asked if X^Y = Y^X?

Just thinking about THAT question, there cannot be that many situations in which the two terms are equal to one another. Thinking about that, I can only come up 2 immediate possibilities and one that's a little tougher to spot:

X and Y
1) are the same number
2) one is 2 and the other is 4

The rarer one
3) one is -2 and the other is -4

Since those 3 options generate a "YES" answer, you can now look for those possibilities in the two Facts (knowing that most of the values you'd TEST randomly will generate a "NO" answer). That slight "time investment" in thinking about what the question specifically asks for can save you some serious time later on while you're working through the rest of the question.

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Re: If x and y are integers, is xy = yx? (1) x – y = 2 (2) xy = 8  [#permalink]

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_________________ Re: If x and y are integers, is xy = yx? (1) x – y = 2 (2) xy = 8   [#permalink] 01 Oct 2018, 22:32
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