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For positive integer k, is the expression (k + 2)(k^2 + 4k +

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Intern
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Joined: 18 May 2016
Posts: 20

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Re: For positive integer k, is the expression (k + 2)(k^2 + 4k + [#permalink]

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New post 20 Dec 2016, 08:58
Simplify to: (K+1)(K+2)(K+3). This expression will not be divisible by 4 if k is a multiple of 4: factors of 4 repeat once every 4 consecutive integers, thus in between no factors of 4.
Stat1 gives you k=8q. So k=4*2q, k has 4 as a factor. Suff.
Stat2 does not tell you anything about factors of 4 in the expression. Insuff.
A

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Joined: 28 Mar 2017
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Re: For positive integer k, is the expression (k + 2)(k^2 + 4k + [#permalink]

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New post 22 Aug 2017, 08:49
kishankolli wrote:
For positive integer k, is the expression (k + 2)(k^2 + 4k + 3) divisible by 4?

(1) k is divisible by 8.
(2) (k + 1)/3 is an odd integer


Factorise the expression and we get --> (k+1)(k+2)(k+3)
If k is a multiple of 4 then (k+1)(k+2)(k+3) won't be divisible by 4, else for every non-multiple of 4 value of k (k+1)(k+2)(k+3) will be divisible by 4.

Statement A --> k is divisible by 8; that means it is divisible by 4 also. Thus (k+1)(k+2)(k+3) will never be divisible by 4. SUFFICIENT

Statement B --> (k+1)/3 = 2n+1 => k+1=6n+3 =>k=6n+2
Now, for n=1; k=8 ----> (k+1)(k+2)(k+3) won't be divisible by 4.
Now, for n=2; k=14 ---> (k+1)(k+2)(k+3) will be divisible by 4. Thus INSUFFICIENT

Answer: A
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GMAT 1: 670 Q49 V33
Re: For positive integer k, is the expression (k + 2)(k^2 + 4k + [#permalink]

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New post 25 Aug 2017, 21:03
One way to look at statement 1 using divisibility rule:

k is divisible by 8
so k is divisible by 4
k+1 :4 gives remainder of 1
k+2 :4 gives remainder of 2
k+3 :4 gives remainder of 3

None of the factor in the product (k+1)(k+2)(k+3) is divisible by 4, therefore the product is not divisible by 4.

Kudos [?]: 9 [0], given: 17

Re: For positive integer k, is the expression (k + 2)(k^2 + 4k +   [#permalink] 25 Aug 2017, 21:03

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