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.