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# x is a positive integer ,is x divisible by 2? 1) x^3+x is

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VP
Joined: 17 Jun 2008
Posts: 1373
x is a positive integer ,is x divisible by 2? 1) x^3+x is [#permalink]

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31 Aug 2008, 18:39
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x is a positive integer ,is x divisible by 2?
1)$$x^3+x$$ is divisible by 4
2)$$5x+4$$is divisible by 6

KINDLY SHARE THE METHOD OF SOLVING
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Its Now Or Never

Current Student
Joined: 11 May 2008
Posts: 553

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31 Aug 2008, 19:10
D

1) all given values of x whihc satisfy the given condition are even, so suff.

2) since only even nos. are divisible by 6, 5x+ 6 is even.
also, since even = even+ even, 5x= even or x=even, so divisible by 2. suff

Last edited by arjtryarjtry on 31 Aug 2008, 19:28, edited 1 time in total.
SVP
Joined: 29 Aug 2007
Posts: 2467

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31 Aug 2008, 19:18
spriya wrote:
x is a positive integer ,is x divisible by 2?
1)$$x^3+x$$ is divisible by 4
2)$$5x+4$$is divisible by 6

KINDLY SHARE THE METHOD OF SOLVING

1: (x^3+x) = 4k
x (x^2+1) = 4k, where k is an integer

either x or x^2+1 is divisible by 4. if x^2+1 were to divided by 4, x^2 must be odd. in that case, x is also odd. but square of any odd plus 1 cannot be a multiple of 4. for ex:
3^2+1 = 10, which is not divisible by 4.
5^2+1 = 26, which is not divisible by 4.
7^2+1 = 50, which is not divisible by 4.
9^2+1 = 81, which is not divisible by 4.

so x must be an even and also a multiple of 4. so suff...

2: 5x + 4 = 6m, where m is an integer
if 6 were to divide 5x+4 evenly, 5x+4 must be an even integer. in that case, 5x also be an even integer and eventually x is to an even integer.

so Suff.

D...
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VP
Joined: 17 Jun 2008
Posts: 1373

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01 Sep 2008, 18:12
GMAT TIGER wrote:
spriya wrote:
x is a positive integer ,is x divisible by 2?
1)$$x^3+x$$ is divisible by 4
2)$$5x+4$$is divisible by 6

KINDLY SHARE THE METHOD OF SOLVING

1: (x^3+x) = 4k
x (x^2+1) = 4k, where k is an integer

either x or x^2+1 is divisible by 4. if x^2+1 were to divided by 4, x^2 must be odd. in that case, x is also odd. but square of any odd plus 1 cannot be a multiple of 4. for ex:
3^2+1 = 10, which is not divisible by 4.
5^2+1 = 26, which is not divisible by 4.
7^2+1 = 50, which is not divisible by 4.
9^2+1 = 81, which is not divisible by 4.

so x must be an even and also a multiple of 4. so suff...

2: 5x + 4 = 6m, where m is an integer
if 6 were to divide 5x+4 evenly, 5x+4 must be an even integer. in that case, 5x also be an even integer and eventually x is to an even integer.

so Suff.

D...

Thanks for explanation guys!!
OA is D

second part of explanation is good
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cheers
Its Now Or Never

Re: DS-odds   [#permalink] 01 Sep 2008, 18:12
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