Bunuel wrote:
If x is a positive integer, is (x)(x + 2)(x + 4) divisible by 12?
Notice that no matter whether x is even or odd, out of x, x+2 and x+4 one must be a multiple of 3. So, we are basically asked to find whether (x)(x + 2)(x + 4) is divisible by 4. Now, if x=odd, then all three multiples are odd, thus (x)(x + 2)(x + 4) will be odd and not divisible by 4. If x=even, then (x)(x + 2)(x + 4)=even*even*even, thus it'll be divisible by 4.
Therefore, the question boils down to find whether x is even.
(1) x^2 + 2x is a multiple of 3 --> if x=1=odd, then the answer is NO but if x=4, then the answer is YES. Not sufficient.
(2) 3x is a multiple of 2. This statement implies that x=even. Sufficient.
Answer: B.
Hope it's clear.
Hi Bunuel - you mentioned the following :
"Notice that no matter whether x is even or odd, out of x, x+2 and x+4 one must be a multiple of 3." -
-I AGREE So, we are basically asked to find whether (x)(x + 2)(x + 4) is divisible by 4. =
QUESTION ON THIS STATEMENT Should it not be 2 out of the 3 is divisible by 4, i.e. we need to find whether x and (x+2) or (x+2) and (x+4) or (X+2) and (x+4) are divisible by 4 ....Given either x or (x+2) or (x+4) is going to be a multiple of 3 .....ONLY THE OTHER TWO have to be multiples of 4 instead ...
Please let me know your thoughts