X as an integer

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Baldini: Senior | Next Rank: 100 Posts; Posts: 90; Joined: Mon Mar 02, 2009 6:06 am; Thanked: 3 times

by Baldini » Mon Mar 09, 2009 2:31 am

If x is an integer, is (x^2+1)(x+5) an even number?

(1) x is an odd number
(2) Each prime factor of x^2 is greater than 7

OA is D. Can someone please explain?
Thanks

GMAX

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Source: Beat The GMAT — Data Sufficiency | Mon Mar 09, 2009 2:31 am

scoobydooby: Legendary Member; Posts: 1035; Joined: Wed Aug 27, 2008 10:56 pmFollowed by: 1 member; Thanked: 104 times

by scoobydooby » Mon Mar 09, 2009 2:39 am

(x^2+1)(x+5) an even number?

stmnt 1) x odd
=> x^2=odd
=>(x^2+1)=even (odd+1)=even. each odd followed by even
(x+5)=even (sum of 2 odd is an even)
(x^2+1)(x+5)=even*even=even
sufficient

stmnt 2) Each prime factor of x^2 is greater than 7
=> (every even number has to have 2 as a prime factor. 2 is the only even prime)
=> if X^2 was even, it must have had 2 as a prime factor, since all prime factors are greater than 7 and all are odd, we can conclude x is odd

sufficient, and hence D

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