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# For positive integer k, is the expression (k + 2)(k2 + 4k +

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Senior Manager
Joined: 20 Feb 2008
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Schools: R1:Cornell, Yale, NYU. R2: Haas, MIT, Ross
For positive integer k, is the expression (k + 2)(k2 + 4k + [#permalink]

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30 Nov 2008, 10:41
For positive integer k, is the expression (k + 2)(k2 + 4k + 3) divisible by 4?

(1) k is divisible by 8.

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

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30 Nov 2008, 11:02
Good question

(k2 + 4k + 3)=(k+1)(k+3), so we are asked is (k+1)(k+2)(k+3) divisible by 4?

1) k can be 8,16,24 etc. so (k+1)(k+2)(k+3) is product of 3 consequtive integers such as 9x10x11. It is 'yes or no' question and we have the answer 'no'. Suff
2) - k is an even integer and can be 2,8,14 etc. (k+1)(k+2)(k+3) can be divisible by 4 if k=2, and can not if k=8. Insuff.

A
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30 Nov 2008, 11:05
key here is K is Positive and Integer..

so the stem becomes (k+1)(K+2)(k+3)

1) now if K is divisible by 8, then the stem is NOT divisible by 4..sufficient

2) means K is even say 2 or 4, if K=2 then it is divible by 4 if anything else yes no..insuff

A it is
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30 Nov 2008, 11:23
Great Thanks guys, the OA is A.

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Re: Mgmat Divisibility   [#permalink] 30 Nov 2008, 11:23
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# For positive integer k, is the expression (k + 2)(k2 + 4k +

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