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If x=p*n^k+p where n and k are positive integers, is x divisible by 2?

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If x=p*n^k+p where n and k are positive integers, is x divisible by 2?  [#permalink]

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If \(x=p*n^k+p\) where n and k are positive integers, is x divisible by 2?

1) n+kn=915
2)p^35+35^p is even




Source: Exercise given by gmat tutors

Originally posted by bettatantalo on 09 Sep 2018, 01:56.
Last edited by chetan2u on 10 Sep 2018, 02:27, edited 2 times in total.
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Re: If x=p*n^k+p where n and k are positive integers, is x divisible by 2?  [#permalink]

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New post 09 Sep 2018, 03:17
2
bettatantalo wrote:
If x=p*n^k+p where n and k are positive integers, is x divisible by 2?

1) n+kn=915
2)p^35+35^p is even




Source: Exercise given by gmat tutors


\(x=p*n^k+p=p(n^k+1)\)
So for X to be divisible by 2, any one of the two - p and n^k+1- should be even
n^k+1 is even means n is odd.

Let us see the statements

1) n+kn=915
n(1+k)=915
Therefore n and k+1 are odd. So n is odd and k is even
Means n^k is odd^even=odd
Ans is YES
Sufficient

2) p^35+35^p is even
So p is odd..
But we don't know if n is odd or even
If n is odd, yes
If n is even, no
Insufficient

A
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1) Absolute modulus : http://gmatclub.com/forum/absolute-modulus-a-better-understanding-210849.html#p1622372
2)Combination of similar and dissimilar things : http://gmatclub.com/forum/topic215915.html
3) effects of arithmetic operations : https://gmatclub.com/forum/effects-of-arithmetic-operations-on-fractions-269413.html
4) Base while finding % increase and % decrease : https://gmatclub.com/forum/percentage-increase-decrease-what-should-be-the-denominator-287528.html


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Re: If x=p*n^k+p where n and k are positive integers, is x divisible by 2?  [#permalink]

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New post 10 Sep 2018, 02:22
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If x=p*n^k+p where n and k are positive integers, is x divisible by 2?  [#permalink]

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New post 11 Sep 2018, 08:20
bettatantalo wrote:
If \(x=p*n^k+p\) where n and k are positive integers, is x divisible by 2?

1) n+kn=915
2)p^35+35^p is even

Source: Exercise given by gmat tutors


OA: A

\(x=p*n^k+p=p*(n^k+1)\)

Given \(n\) and \(k\) are positive integers.

Term \(p*(n^k+1)\) will be divisible by \(2\) if either \(p\) or \((n^k+1)\) or both are divisible by \(2\).

if \(n\) is odd and \(k\) can be any positive integer,\((n^k+1)\) will be of form ODD+ODD= EVEN i.e Term \(p*(n^k+1)\) will be even.

if \(n\) is even and \(k\) can be any positive integer,\((n^k+1)\) will be of form EVEN+ODD= ODD i.e Term \(p*(n^k+1)\) will be odd.

Statement (1) : \(n+kn=915\)

\(n(1+k)=3*5*61\)

\(n\) can be \(3,5,61,15,183,305\)

this implies that \(n\) will be odd, leading to the term \(p*(n^k+1)\) being even.

So \(x\) will be divisible by \(2\)

Statement \(1\) alone is sufficient.

Statement (2) : \(p^{35}+35^p\) is even

\(p^{35}+35^p\) will be even if \(p^{35}\) is odd as \(35^p\) is odd.

So \(p\) is odd, but term \((n^k+1)\) can be even or odd.

\(x\) can be odd or even, depending upon value of \((n^k+1)\).

Statement \(2\) alone is not sufficient.
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Re: If x=p*n^k+p where n and k are positive integers, is x divisible by 2?  [#permalink]

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New post 12 Sep 2018, 01:55
Hi chetan2u
How do you know that p is an integer from statement 1? I think we need statement 2 which confirms that p is an integer.
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Re: If x=p*n^k+p where n and k are positive integers, is x divisible by 2?   [#permalink] 12 Sep 2018, 01:55
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