mba878 wrote:

PrepTap wrote:

What is the GCD of a and b?

1. The only common prime factor of a and b is even.

2. b/p (where p is a prime number) and a don’t have a common prime factor.

This question is a part of the series of original questions posted every weekday by PrepTap. Follow us to receive more questions like this.The answer to the above question should be E And not C.

From statement 1 one can infer that 2 is a common factor to both a & b but what power o 2 goes into both a & b cannot be

determined from the given inormation.

From Statement 2 again one doesnt have enough information to evaluate the the GCD.

same follows when we combine A & B, hence E must be the answer.

Hi mba878

From the first statement, we learn that the common prime factor is 2. But we don't know whether 2 or 2^2 or 2^3.... is common between a and b.

The second statement says b/p and a don't have a common prime factor, so p (=2^1) must've been the common factor of a and b.

Essentially when we combine the two statements, we learn that 2 is the only common prime factor and only the first power of 2 is a factor of b.

If that weren't the case, b/2 would still contain at least one power of 2 and there would be a common factor between b/2 and a, which goes against statement 2.

As an example, take a = 6 and b = 10.

Their only common prime factor is 2, which is even.

And 6 and 10/2 (=5) don't have a common prime factor.

So we can easily say that 2 is the GCD here.