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For positive integer k, is the expression (k +

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Senior Manager
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For positive integer k, is the expression (k + [#permalink]  21 Feb 2010, 13:40
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For positive integer k, is the expression (k + 2)(k^2 + 4k + 3) divisible by 4?

(1) k is divisible by 8.

(2) \frac{k + 1}{3} is an odd integer.

SOURCE: Manhattan Tests

[Reveal] Spoiler: OA
A

Please explain. A little doubtful with this OA
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Re: For positive integer k, is the expressio [#permalink]  21 Feb 2010, 13:55
Expert's post
1) if k is divisible by 8 (and by 4 too), then k+2 is even but isn't divisible by 4 or 8.
(k^2+4k+3) - an odd integer. ---> (even but not divisible by 4 or 8)*odd ---> the expression isn't divisible by 4.

2)k+1/3 is odd --> k+1 is odd --> k is even --> k+2 is even. if k+2:
- is divisible by 4, the expression is also divisible by 4
- isn't divisible by 4, the expression isn't divisible by 4
insufficient
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Re: For positive integer k, is the expressio [#permalink]  22 Feb 2010, 11:57
jeeteshsingh wrote:
For positive integer k, is the expression (k + 2)(k^2 + 4k + 3) divisible by 4?

(1) k is divisible by 8.

(2) \frac{k + 1}{3} is an odd integer.

SOURCE: Manhattan Tests

[Reveal] Spoiler: OA
A

Please explain. A little doubtful with this OA

Another way of looking at it ..
the expression (k + 2)(k^2 + 4k + 3) can be written as (K+2)(K+1)(K+3)

which means they are consecutive numbers.

St1. K is divisible by 8 lets say K = 8

then the expression becomes 9*10*11 which is not divisible by 4, ( which holds for any value of K which is a multiple of 8)

Hence Sufficient

St 2 \frac{k + 1}{3} is an odd integer.

Which K + 1 is an odd integer lets take K=2

If K =2 then the expression is divisible by 4

but not lets assume K = 8 then then again the expression is not divisible by 4

Hence Insufficient.
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Re: For positive integer k, is the expressio [#permalink]  25 Feb 2010, 09:37
IMO it is A. I solved this the same way as nitishmahajan did.
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Re: For positive integer k, is the expressio [#permalink]  12 Mar 2010, 07:30
IMO A

expression = (k+2)(k+1)(k+3)
(1): (k+1)(k+3) is odd integer, (k+2) is only divisible by 2 but not by 4 so (1) is sufficient!
(2): k=2 then expression=4*odd integer is divisible by 4
k=5 then expression=6*odd integer is not divisible by 4
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Re: For positive integer k, is the expressio [#permalink]  12 Mar 2010, 10:59
clearly A.

B) when k=8 8+1/3 = divisible; when k=14 14+1/3 not divisible. Insuff
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Re: For positive integer k, is the expressio [#permalink]  15 Mar 2010, 09:12
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A. Same logic as the above.
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Re: For positive integer k, is the expressio [#permalink]  15 Mar 2010, 21:51

Solved using a similar method as nitishmahajan's.
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Re: For positive integer k, is the expressio [#permalink]  25 Apr 2010, 00:12
nitishmahajan wrote:
jeeteshsingh wrote:
For positive integer k, is the expression (k + 2)(k^2 + 4k + 3) divisible by 4?

(1) k is divisible by 8.

(2) \frac{k + 1}{3} is an odd integer.

SOURCE: Manhattan Tests

[Reveal] Spoiler: OA
A

Please explain. A little doubtful with this OA

Another way of looking at it ..
the expression (k + 2)(k^2 + 4k + 3) can be written as (K+2)(K+1)(K+3)

which means they are consecutive numbers.

St1. K is divisible by 8 lets say K = 8

then the expression becomes 9*10*11 which is not divisible by 4, ( which holds for any value of K which is a multiple of 8)

Hence Sufficient

St 2 \frac{k + 1}{3} is an odd integer.

Which K + 1 is an odd integer lets take K=2

If K =2 then the expression is divisible by 4

but not lets assume K = 8 then then again the expression is not divisible by 4

Hence Insufficient.

good explanation...
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Re: For positive integer k, is the expressio [#permalink]  13 Jul 2010, 03:56
Another way to look at it:
i)k is divisible by 8, so k is also divisible by 4. From the property of consecutive multiple , we know that the next term that is divisible by 4 after k is (k+4) (that is every 4th number from k). That means (K+2)(K+1)(K+3) is not divisible by 4.

ii) k+2 is even, but we don't know if it is a multiple of 4 or not. Plug in 1 and 3 for k+1 yields different answer
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Re: For positive integer k, is the expressio [#permalink]  13 Jul 2010, 07:18
nitishmahajan wrote:
jeeteshsingh wrote:
For positive integer k, is the expression (k + 2)(k^2 + 4k + 3) divisible by 4?

(1) k is divisible by 8.

(2) \frac{k + 1}{3} is an odd integer.

SOURCE: Manhattan Tests

[Reveal] Spoiler: OA
A

Please explain. A little doubtful with this OA

Another way of looking at it ..
the expression (k + 2)(k^2 + 4k + 3) can be written as (K+2)(K+1)(K+3)

which means they are consecutive numbers.

St1. K is divisible by 8 lets say K = 8

then the expression becomes 9*10*11 which is not divisible by 4, ( which holds for any value of K which is a multiple of 8)

Hence Sufficient

St 2 \frac{k + 1}{3} is an odd integer.

Which K + 1 is an odd integer lets take K=2

If K =2 then the expression is divisible by 4

but not lets assume K = 8 then then again the expression is not divisible by 4

Hence Insufficient.

Nice work...

I liked the factorization part, to get the consecutive numbers.

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Re: For positive integer k, is the expressio   [#permalink] 13 Jul 2010, 07:18
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