MGMAT: Good Qn

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MGMAT: Good Qn

by anantbhatia » Thu Oct 21, 2010 12:44 pm
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.

[spoiler]OA: A[/spoiler]

PS: Earlier, I thought that the OA was incorrect, but while posting my solution (I thought it shd have been D), I realized the mistake I had made and hence the correction.
Last edited by anantbhatia on Thu Oct 21, 2010 12:55 pm, edited 1 time in total.
Source: — Data Sufficiency |

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by anantbhatia » Thu Oct 21, 2010 12:54 pm
Posting my solution:-

exp can be written as:-
(k+1)(k+2)(k+3)

(1) Given that k=8a where a is any integer. Replacing in the above:-

(8a+1)(8a+2)(8a+3) = 2(8a+1)(4a+1)(8a+3)
ie. the expression will not be divisible by 4 in any case. Hence either (A) or (D)


(2) (k+1)/3 = 2a+1 (as it is an odd integer)
ie. k=6a+2
replacing,
(6a+3)(6a+4)(6a+5) = 6(2a+1)(3a+2)(6a+5)
ie. the expression may be divisible by 4 if a is even but may not be if it is odd. Hence Insufficient.

Ans: (A)