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If x and y are integers, does x^y . y^(-x) = 1? (1) x^x

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Senior Manager
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If x and y are integers, does x^y . y^(-x) = 1? (1) x^x [#permalink] New post 20 Dec 2006, 13:55
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A
B
C
D
E

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If x and y are integers, does x^y . y^(-x) = 1?

(1) x^x > y

(2) x > y^y
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 [#permalink] New post 20 Dec 2006, 17:22
Tried with few numbers ..nothing is matching ..
Going for E..
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 [#permalink] New post 21 Dec 2006, 05:56
waiting for a detailed explanation - My bet is e
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 [#permalink] New post 21 Dec 2006, 06:14
Thought of adding a question

x ^ y = y ^ x is true for (2,4) and (-2,-4).

What are the other possible combinations???
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 [#permalink] New post 21 Dec 2006, 06:35
actually, answer is B

(x^y)*(y^(-x))=1 is very rare for integers...
it can happen only if x^y=y^x

there are only few integer solutions to that:
(2,4),(4,2),(-2,-4),(-4,-2) and (a,a) for every integer a not equals to 0.

just check to see that none of the options satisfy st2. which means that if st2 is true - x and y are not one of these, and the answer to stem question is no. hence sufficient.
st1, however, can accomodate some of the solutions (and of course accomodate more different combinations). hence insufficient.

answer is B
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 [#permalink] New post 21 Dec 2006, 06:40
i stand corrected.... answer is C

st2 rules out most solutions, except solutions of the form (a,a) where a<-1
(for example x=-3 y=-3).

however, together with st1 these solutions are also ruled out.

hence we need both st1 and st2 to rule out all solutions (and answer stem question).

if we new x,y are positive (which we don't), then B would be the correct answer.
  [#permalink] 21 Dec 2006, 06:40
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If x and y are integers, does x^y . y^(-x) = 1? (1) x^x

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