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# If x and y are nonzero integers, is x^y < y^x?

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Math Expert
Joined: 02 Sep 2009
Posts: 47961
If x and y are nonzero integers, is x^y < y^x?  [#permalink]

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24 Dec 2017, 01:42
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Difficulty:

55% (hard)

Question Stats:

59% (01:34) correct 41% (02:07) wrong based on 65 sessions

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If x and y are nonzero integers, is x^y < y^x?

(1) x and y are consecutive integers.
(2) x^y = 64

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If x and y are nonzero integers, is x^y < y^x?  [#permalink]

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24 Dec 2017, 05:15
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Bunuel wrote:
If x and y are nonzero integers, is x^y < y^x?

(1) x and y are consecutive integers.
(2) x^y = 64

Statement 1: if x=1 & y=2, then we have a NO but if x=2 & y=1, then we have a Yes. Insufficient

Statement 2: if x=2 & y=6, then we have a NO but if x=4 & y=3, then we have a YES.Insufficient

Combining 1 & 2 we have x=4 & y=3, Hence a Yes. Sufficient

Option C
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Re: If x and y are nonzero integers, is x^y < y^x?  [#permalink]

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24 Dec 2017, 16:07
Bunuel wrote:
If x and y are nonzero integers, is x^y < y^x?

(1) x and y are consecutive integers.
(2) x^y = 64

x and y are integers, different from 0.

(1) x and y are consecutive integers. Then x = 4, y = 3 and $$4^3<3^4=64<81$$, answer yes. But, x = 3, y = 4, and $$3^4<4^3=81<64$$, answer no; insufficient.

(2) x^y = 64. Then, $$x^y=64=8^2=4^3=2^6$$. If x = 4, y = 3 and $$4^3<3^4=64<81$$, answer yes. x = 2, y = 6 and $$2^6<6^2=64<36$$, answer no; insufficient.

(1) & (2). The only case that fits is when x = 4, y = 3 and $$4^3<3^4=64<81$$, answer yes; sufficient.

Re: If x and y are nonzero integers, is x^y < y^x? &nbs [#permalink] 24 Dec 2017, 16:07
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