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X as an integer

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X as an integer

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
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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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