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# If x is a positive integer, is sqrt(x) an integer? (1)

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Manager
Joined: 21 Apr 2004
Posts: 88
Location: VA
If x is a positive integer, is sqrt(x) an integer? (1) [#permalink]

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26 Aug 2004, 10:21
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If x is a positive integer, is sqrt(x) an integer?

(1) sqrt(4x) is an integer
(2) sqrt(3x) is not an integer

Joined: 31 Dec 1969
Location: Russian Federation
Concentration: Entrepreneurship, International Business
GMAT 3: 740 Q40 V50
GMAT 4: 700 Q48 V38
GMAT 5: 710 Q45 V41
GMAT 6: 680 Q47 V36
GMAT 9: 740 Q49 V42
GMAT 11: 500 Q47 V33
GMAT 14: 760 Q49 V44
WE: Supply Chain Management (Energy and Utilities)

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26 Aug 2004, 10:29
1) sqrt4X=sqrt4xsqrtX since sqrt4 is always an integer, X is an integer then sqrt X must also be an integer, so 1) is sufficient
2) sqrt 3 is not an integer, same reasoning as above sqrt3 is not an integer then sqrtX can be or can not be an integer so 2) is insufficient
Manager
Joined: 21 Apr 2004
Posts: 88
Location: VA

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26 Aug 2004, 10:39
Thanks.
I was confused with the sqrt function.
Senior Manager
Joined: 05 Feb 2004
Posts: 290
Location: USA

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26 Aug 2004, 11:01
Shygo, Guest........In statement one it says sqrt 4x is an integer......or we can say:
sqrt4 * sqrt x = INTEGER
or 2*sqrt x= INT
dow we assume that the INT is always even??what if it was odd??
Manager
Joined: 21 Apr 2004
Posts: 88
Location: VA

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26 Aug 2004, 11:13
cbrf3,

Since we multiply sqrt (x) by 2 the result is always even (any integer multipled by 2 always results in an even integer)
Hope it is clear.
26 Aug 2004, 11:13
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# If x is a positive integer, is sqrt(x) an integer? (1)

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