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

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Manager
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If x is a positive integer, is sqrt(x) an integer? (1) [#permalink] New post 26 Aug 2004, 09:21
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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

Please explain. :roll:
Joined: 31 Dec 1969
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Concentration: General Management, Entrepreneurship
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 [#permalink] New post 26 Aug 2004, 09:29
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
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 [#permalink] New post 26 Aug 2004, 09:39
Thanks.
I was confused with the sqrt function.:)
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 [#permalink] New post 26 Aug 2004, 10:01
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??
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 [#permalink] New post 26 Aug 2004, 10:13
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.
  [#permalink] 26 Aug 2004, 10:13
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If x is a positive integer, is sqrt(x) an integer? (1)

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