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# If c and d are positive integers, is c even? (1) c2 - 1 is

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Manager
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If c and d are positive integers, is c even? (1) c2 - 1 is [#permalink]  29 Mar 2007, 05:14
2. If c and d are positive integers, is c even?

(1) c2 - 1 is odd.
(2) (c - 3) (d + 2) is odd.
SVP
Joined: 01 May 2006
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(D) for me

c EVEN?

From 1
c^2 - 1 = ODD
<=> (c+1) * (c-1) = ODD

At this point, we should notice that c+1 and c-1 are similar if one is odd, the other must be odd too.

Thus, c+1 and c-1 is ODD and c is EVEN

SUFF.

From 2
(c - 3) * (d + 2) = ODD
=> c - 3 is ODD and d+2 is ODD

Thus, c is EVEN (EVEN - ODD = ODD).

SUFF.
Director
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Re: odd/even [#permalink]  29 Mar 2007, 08:02
andrehaui wrote:
2. If c and d are positive integers, is c even?

(1) c2 - 1 is odd.
(2) (c - 3) (d + 2) is odd.

D.

1. c^2 - 1 = odd means c^2 is even. so c is even....... sufficient
2. (c - 3) (d + 2) = odd integer also means (c - 3) and (d + 2) both are odd. then c = even and d is odd........ suffficient.
Re: odd/even   [#permalink] 29 Mar 2007, 08:02
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