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

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

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02 Jan 2009, 21:41
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If x is an integer , is (x^2+1)(x^2+5) an even number?

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

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Re: An Even expression [#permalink]

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03 Jan 2009, 01:22
krishan wrote:
If x is an integer , is (x^2+1)(x^2+5) an even number?

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

D. make sure whether x is even or odd.
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Re: An Even expression [#permalink]

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03 Jan 2009, 06:33
how do we know that the 2nd stat is enough as well ? im having a little difficulty making sense of it.

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Re: An Even expression [#permalink]

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03 Jan 2009, 06:37
pmenon wrote:
how do we know that the 2nd stat is enough as well ? im having a little difficulty making sense of it.

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

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

the second means that x^2 has only prime factor that is greater than 7, and prime greater than 7 must be odd. So x^2 +5 must be even number. Suff
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Re: An Even expression [#permalink]

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03 Jan 2009, 06:55
sondenso wrote:
pmenon wrote:
how do we know that the 2nd stat is enough as well ? im having a little difficulty making sense of it.

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

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

the second means that x^2 has only prime factor that is greater than 7, and prime greater than 7 must be odd. So x^2 +5 must be even number. Suff

Thanks, sondenso. How do we know that if prime factor is greater than 7, number will be odd ? Is it a rule somewhere ?

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Re: An Even expression [#permalink]

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03 Jan 2009, 10:45
pmenon wrote:
Thanks, sondenso. How do we know that if prime factor is greater than 7, number will be odd ? Is it a rule somewhere ?

primes are: 2, 3, 5, 7, 11, 13, 17, 19, 23, 29, 31, 37, 41, 43, 47, 53, 59, 61, 67, 71, 73, 79, and so on..........................
Only prime that is even is 2; all, except 2, primes are odd and any prime greater than 7 is always an odd integer..
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Re: An Even expression [#permalink]

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03 Jan 2009, 15:32
pmenon wrote:
sondenso wrote:
pmenon wrote:
how do we know that the 2nd stat is enough as well ? im having a little difficulty making sense of it.

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

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

the second means that x^2 has only prime factor that is greater than 7, and prime greater than 7 must be odd. So x^2 +5 must be even number. Suff

Thanks, sondenso. How do we know that if prime factor is greater than 7, number will be odd ? Is it a rule somewhere ?

If a number has all its prime factors greater than 7, it means that such numbers are odd and prime. Try with some numbers from 11 through 20. You will see it yourself.

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Re: An Even expression   [#permalink] 03 Jan 2009, 15:32
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# If x is an integer , is (x^2+1)(x^2+5) an even number? (1) x

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