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# If x is a positive number is x^(1/2) an integer?

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Math Expert
Joined: 02 Sep 2009
Posts: 46128
If x is a positive number is x^(1/2) an integer? [#permalink]

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21 Sep 2017, 05:01
00:00

Difficulty:

55% (hard)

Question Stats:

66% (01:20) correct 34% (01:33) wrong based on 44 sessions

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If x is a positive number is $$\sqrt{x}$$ an integer?

(1) $$(x^{(-\frac{1}{4})})^2>1$$

(2) $$(x + 1)^2 = (x – 2)^2$$

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Joined: 09 Sep 2017
Posts: 8
Concentration: Strategy, General Management
GMAT 1: 710 Q50 V35
WE: Consulting (Computer Software)
If x is a positive number is x^(1/2) an integer? [#permalink]

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21 Sep 2017, 08:43
1
Bunuel wrote:
If x is a positive number is $$\sqrt{x}$$ an integer?

(1) $$(x^{(-\frac{1}{4})})^2>1$$

(2) $$(x + 1)^2 = (x – 2)^2$$

Statement 1:

(X^ (-1/4))^2 > 1 => X^(-1/2) > 1 => 1/(X^ 1/2) > 1

If 1/ (Something) > 1 => Something must be between 0-1 (something can't be 0, otherwise 1/something will be undefined)

Here Something is X^1/2. So 0<(X^1/2)<1. Hence X^1/2 is not an integer.

Sufficient

Statement 2:

(x + 1)^2 = (x – 2)^2 => X^2 + 2x + 1 = X^2 + 4 - 4X
=> 2x + 1 = 4 - 4X
=> 6X = 3
=> X = 1/2 (not an integer)

Sufficient.

Both statement 1 and 2 are sufficient. Ans D
If x is a positive number is x^(1/2) an integer?   [#permalink] 21 Sep 2017, 08:43
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