gmatt1476 wrote:
If b is the product of three consecutive positive integers c, c + 1, and c + 2, is b a multiple of 24 ?
(1) b is a multiple of 8.
(2) c is odd.
DS85502.01
b = c(c+1)(c+2)
now if
c = even, then c and (c+2) are even and b = 8k as the smallest positive even integer is 2 so c+2 = 4. and c+1 = 3.
and if
c = odd, then c and (c+2) are odd and (c+1) = even.
So for c = even it will be a multiple of 24.
We need to check for the case c=odd. Statement 1 -
b is a multiple of 8.
now, for
c= even we already know that
b = 8k, and it will be a multiple of 24.
we can check as well by taking a few cases (2,3,4), (4,5,6),(6,7,8) and so on.
and if
c = odd and b is a multiple of 8 so it implies that
c+1 = 8k. The cases possible are (7,8,9), (15,16,17) and so on and we can see that all will be multiple of 24.
Sufficient.
Statement 2 -
As seen from above just knowing that c is odd doesn't make sure that it will be a multiple of 24.
For cases such as (7,8,9)
b will be a multiple of 24
BUT
for cases such as (1,2,3),
b will not be a multiple of 24.
Not sufficient.IMO, Answer is A.