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# If x and y are nonzero integers, is x^y < y^x? (1) x =

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GMAT Club Legend
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Re: If x and y are nonzero integers, is x^y < y^x? (1) x = [#permalink]

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30 Aug 2015, 22:10
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Re: If x and y are nonzero integers, is x^y < y^x? (1) x = [#permalink]

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19 Dec 2015, 00:09
Bunuel Would this approach be correct?

statement 1

x = y^2

y^2 is positive. So x is positive. But we aren't sure about the magnitude of y. So Statement 1 is insufficient.

Statement 2:
Insufficient since no relation between x and y

Combining the two, statement two assures that y is positive. Hence, C
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Senior Manager
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Re: If x and y are nonzero integers, is x^y < y^x? (1) x = [#permalink]

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23 Sep 2016, 11:01
I agree with C being correct

(1) x = y^2 --> from this we know x>0, but y can be either positive or negative, thus INSUFFICIENT

(2) y > 2 --> we don't know anything about x, thus INSUFFICIENT

(1) + (2) --> SUFFICIENT; we know that y must be positive from (2), therefore we can figure out the main equation without hesitation

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Senior Manager
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Location: India
Re: If x and y are nonzero integers, is x^y < y^x? (1) x = [#permalink]

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23 Feb 2017, 05:54
Prompt analysis
Let the number of tapes with carmen and rafael be x and y respectively.

x+12 = 2y

Superset
Value of x and y will be a whole number.

Translation
St 1: y =x +5. Solving 2 equations we get x = 2, y =7. ANSWER
St 2: x<12. Cannot determine the exact value of x. INSUFFICIENT

Option A

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Manager
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Re: If x and y are nonzero integers, is x^y < y^x? (1) x = [#permalink]

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03 Jun 2017, 21:16
conocieur wrote:
I would pick A

x = y^2

so y^2^y = y^y^2 which i think is

y^2y = y^2y

so they are equal and you can answer the question

The goal of this problem is to determine if x^y < y^x.

Statement 1) x = y^2

x | y
0 | 0
1 | 1
9 | 3

1^1 = 1^1 BUT 9^3 < 3^9. Not sufficient.

Statement 2) y > 2.

No information provided for x. Insufficient.

Statements 1+2) Now we can do some algebra.

x^y = y^2y

y^x = y^(y^2)

For all y, y^2 > 2y. Sufficient.

Kudos [?]: 12 [0], given: 21

Re: If x and y are nonzero integers, is x^y < y^x? (1) x =   [#permalink] 03 Jun 2017, 21:16

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# If x and y are nonzero integers, is x^y < y^x? (1) x =

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