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