b a multiple of 24?

[grandh01]

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 3,
(2) c is odd.

[eagleeye]

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 3,
(2) c is odd.

For both statements, separately and combined, try the following same 2 cases:

b = 3*4*5. (not multiple of 24)
b = 15*16*17 ( multiple of 24)

You will get the correct answer as E

[alex.gellatly]

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 3,
(2) c is odd.

For b to be a product of 24 b must have 2*2*2*3 within in its prime factorization. Lets look at the statements

Statement 1: b is a multiple of 3.
For b to be a multiple of 3, 3 must be in its prime factorization.
All this means is that b can equal
3*4*5= 60 which is not a multiple of 24.
or 24*25*26= 15600 which is a multiple of 24.
A yes and a no, Statement 1 is insufficient.

Statement 2: c is odd
Pick numbers to see what this means;
3 is odd so 3*4*5=60, not a multiple of 24
23 is odd so 23*24*25= a multiple of 24
A yes and a no, Statement 2 is insufficient.

Statement 1 and 2 combined tell us no new information so this is also insufficent.
The correct answer is E.
Let me know if this helps
(Side Note from statement 1: The product of three consecutive integers will be a multiple of 3. Actually the product of any k consecutive integers will be a multiple of k, for some integer k).