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19 Jul 2006, 07:30
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N is a positive integer. Is N an even integer?
(1) root(2n) is even.
(2) root(n^3) is even.
OA a few posts below.
(1) root(2n) is even.
(2) root(n^3) is even.
OA a few posts below.
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19 Jul 2006, 07:53
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(1) let Root(2n) = 2K , where k is a positive integer.
->2n = 4(k^2)
->n = 2(k^2)
So n is EVEN
(2) let root (n^3) = 2K
-> n^3 = 4k^2
since n is a integer, 4*k^2 should be a perfect cube. Since it already has 4 (2*2) as a factor there should be another 2 as a factor of this, making n even.
So Ans – (C) both alone are sufficient.
->2n = 4(k^2)
->n = 2(k^2)
So n is EVEN
(2) let root (n^3) = 2K
-> n^3 = 4k^2
since n is a integer, 4*k^2 should be a perfect cube. Since it already has 4 (2*2) as a factor there should be another 2 as a factor of this, making n even.
So Ans – (C) both alone are sufficient.
