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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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Intern
Joined: 26 Apr 2018
Posts: 39
If x=p*n^k+p where n and k are positive integers, is x divisible by 2?  [#permalink]

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Updated on: 10 Sep 2018, 02:27
1
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Difficulty:

95% (hard)

Question Stats:

44% (02:16) correct 56% (02:26) wrong based on 68 sessions

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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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Joined: 02 Aug 2009
Posts: 7334
Re: If x=p*n^k+p where n and k are positive integers, is x divisible by 2?  [#permalink]

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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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10 Sep 2018, 02:22
Senior Manager
Joined: 18 Jun 2018
Posts: 262
If x=p*n^k+p where n and k are positive integers, is x divisible by 2?  [#permalink]

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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.
Intern
Joined: 04 Apr 2017
Posts: 23
Re: If x=p*n^k+p where n and k are positive integers, is x divisible by 2?  [#permalink]

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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.
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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