tarn151 wrote:
Please provide your thoughts on this one. The question comes from one of the
GMAT Club Tests on Number Props.
Is a*b*c divisible by 24?
1) a,b, and c are consecutive even integers
2) a*b is divisible by 12
Here's the answer from the
GMAT Club Test:
Statement (1) by itself is sufficient. One of any three consecutive even integers is divisible by 3. Because this integer is even, it is also divisible by 6. When multiplied by two more even integers, it renders a product that is divisible by 24.
Statement (2) by itself is insufficient. We need to know something about c.
Correct me if I'm wrong, but I thought Zero is not divisible 24? If either a, b, or c is zero, then a*b*c= 0, which is not divisible
The answer is A. Why?
First, you need to factor out the number 24. 24 is composed of 4*6 or 2*2*2*3. So, in order for a*b*c to be divisible by 24, it must contain at least 3 2's and a 3 as its factors.
1) a, b and c are consecutive positive integers. This means two things: a, b and c have at least 3 2's, because they are all even, and one of them must be divisible by 3. Product of any 3 consecutive integers will be divisible by 3. Try it: 1,2,3 are divisible by 3. 4,5,6 are divisible by 3. 8,10,12 are divisible by 3. In addition, it is good to know that any set of 3 consecutive integers will be divisible by 3 or 3! Also, set of 8 consecutive integers will be divisible by 8! Any set of n consecutive integers will be divisible by n!
So, since a, b, and c contain at least 2*2*2*3, it must be divisible by 24.
2) If ab is divisible by 12, we know nothing about c. If c is 1, a*b*c is not divisible by 24. If c is 2, it is. So the answer is: maybe. Not sufficient.
Finals answer: A.
Hope this helps, friend.