For positive integer k, is the expression (k + 2)(k^2 + 4k + 3) divisible by 4? => (k+1)*(k+2)*(k+3) divisible by 4?

(1) k is divisible by 8. => K is also a multiple of 4
=> k+1 is not a multiple of 4
=> k+2 is not a multiple of 4
=> k+3 is not a multiple of 4
=> k+4 is a multiple of 4

So definitely (k+1)*(k+2)*(k+3) is divisible by 4. - Sufficient

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

=> K+1 = 3*odd => k+1 = odd

k+1 = odd
k+2 = even
k+3 = odd

Insufficient as k+2 can be a multiple of 2 or a multiple of 4 or a multiple of 6. Hence Insufficient

gmatblood 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.

Simplify the statement -- (k + 2)(k^2 + 4k + 3) = (k+1)(k+2)(k+3)

stmt 1 - K is divisible by 8.

K = 8,16,24... etc

K = 8.. 9*10*11 -- Not divisible by 4

K = 16.. 17*18*19 -- Not divisible by 4

Likewise, you can prove this for other multiples of 8. Hence, STATEMENT A is Sufficient.


Stmt 2: --(k + 1)/3 -- that means (k+1) is odd, or K is EVEN

put K =2 .. 4*5*6 -- Divisible by 4

Put K =8 .. We have already seen that the expression will not be divisible by 4 in this case.

Hence, STATEMENT 2 is NOT sufficient.

Correct Answer - OPTION A

gmatblood 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.

IMO A.