gmatmachoman wrote:Sqrt of(ABC) =504 . Is B divisible by 2?
(1) C = 168
(2) A is a perfect square
Step 1 of the Kaplan Method for DS: Analyze the stem
If 504 is the sqrt of ABC, then ABC = 504^2. Since we want to know whether B is a multiple of 2, we can break 504^2 down into primes to give us a head start.
(Do some scratchwork.)
504 = 2*2*2*3*3*7
so 504^2 = (2*2*2*3*3*7)^2 = 2*2*2*2*2*2*3*3*3*3*7*7
Our task: to determine whether one or more of those 2s belongs to B.
Step 2 of the Kaplan Method for DS: Evaluate the statements
(1) C = 168
well, 168 = 2*2*2*3*7. Subbing in, that means that:
AB = 2*2*2*3*3*3*7
Could B be a multiple of 2? YES
Does B have to be a multiple of 2? NO
So, (1) is insufficient: elminate choices A and D.
(2) A is a perfect square.
If A is a perfect square, it has pairs of prime factors. Does this tell us anything about the requirements of B? Nope - insufficient. Eliminate choice B.
Now let's look at our statements together:
From (1), AB = 2*2*2*3*3*3*7
From (2), A must have an even number of each prime. So, A could have 0 factors of 2 or 2 factors of 2.
In the first case, B will have 3 factors of 2, giving us a YES answer.
In the second case, B will have 1 factor of 2, giving us a YES answer.
Accordingly, when we take the statements together we get a definite YES: sufficient, choose choice C.
