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# If x is a positive integer, is √ √ x an integer?

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Intern
Joined: 28 Mar 2017
Posts: 21
If x is a positive integer, is √ √ x an integer?  [#permalink]

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30 Mar 2019, 04:15
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Difficulty:

15% (low)

Question Stats:

80% (00:42) correct 20% (00:55) wrong based on 49 sessions

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If x is a positive integer, is √ √ x an integer?

(1) x is the square of an integer.

(2) √ x is the square of an integer.
GMAT Tutor
Joined: 24 Jun 2008
Posts: 1802
Re: If x is a positive integer, is √ √ x an integer?  [#permalink]

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30 Mar 2019, 11:23
Using Statement 1, if x is the square of some integer n, then x = n^2. So we want to know if √√(n^2) = √n is an integer. We don't know, since we don't know if n itself is the square of an integer.

Using Statement 2, if √x is the square of some integer m, then √x = m^2. So we want to know if √√x = √(m^2) = m is an integer, and it is. So Statement 2 is sufficient.
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Re: If x is a positive integer, is √ √ x an integer?  [#permalink]

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30 Mar 2019, 12:07
Statement 1: INSUFFICIENT
Replacing x by square of an integer, the question becomes: ✓✓(square of a positive integer)
Or, ✓(a positive integer) = an integer?

Answer may be yes or NO.

IN CASE OF NUMBER PICKING:
if x=16, ✓✓16=2= integer (yes to main question)

if x=4, ✓✓4=✓2= NOT integer (NO to main question)

STATEMENT 2: SUFFICIENT

Replacing ✓x by square of an integer, the question becomes: ✓(square of a positive integer)
= (a positive integer) = an integer (YES TO MAIN QUESTION)

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Re: If x is a positive integer, is √ √ x an integer?   [#permalink] 30 Mar 2019, 12:07
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