Yesterday, Manhattan GMAT posted a 700 level GMAT question on our blog. Today, they have followed up with the answer:
We should first combine the expressions for m, n, and p to get the following:
p = 2m/n = 2(2a 3b) / 2c = 2a + 1 – c 3b
The question can be rephrased as “Does p have no 2’s in its prime factorization?” Since p is an integer, we know that the power of 2 in the expression for p above cannot be less than zero (otherwise, p would be a fraction). So we can focus on the exponent of 2 in the expression for p: “Is a + 1 – c = 0?” In other words, “Is a + 1 = c?”
Statement (1): INSUFFICIENT. The given inequality does not contain any information about c.
Statement (2): SUFFICIENT. We are told that a is less than c. We also know that a and c are both integers (given) and that a + 1 – c cannot be less than zero.
In other words, a + 1 cannot be less than c, so a + 1 is greater than or equal to c. The only way for a to be less than c AND for a + 1 to be greater than or equal to c, given that both variables are integers, is for a + 1 to equal c. No other possibility works. Therefore, we have answered our rephrased question “Yes.”
The correct answer is B: Statement (2) is sufficient, but Statement (1) is not.