Que: If m and n are integers and p = 13m + 25n, is p odd? (1) One of m and n is odd. (2) n is even

[Max@Math Revolution]

Que: If m and n are integers and p = 13m + 25n, is p odd?

(1) One of m and n is odd.
(2) n is even

[Max@Math Revolution]

Solution: To save time and improve accuracy on DS questions in GMAT, learn, and apply Variable Approach.

Forget conventional ways of solving math questions. For DS problems, the VA (Variable Approach) method is the quickest and easiest way to find the answer without actually solving the problem.

Remember that equal numbers of variables and independent equations ensure a solution.

Visit https://www.mathrevolution.com/gmat/lesson for details.

Now we will solve this DS question using the Variable Approach.

Let’s apply the 3 steps suggested previously. [Watch lessons on our website to master these 3 steps]

Step 1 of the Variable Approach: Modifying and rechecking the original condition and the question.

We have to find ‘Is p odd’ ? - where 'm' and 'n' are integers and p = 13m + 25n.

Since 13m + 25n=12m + 24n + m + n and 12m + 24n is always even, we should know whether m+n is odd.

Thus, let’s look at condition (1), it tells us that one of ‘m’ and ‘n’ is odd, from which we can get m + n=odd since (m,n)=(odd, even) or (even, odd) and gives yes as an answer. The answer is unique, YES, and condition (1) alone is sufficient according to Common Mistake Type 1 which states that the answer should be a unique YES or a NO.

Condition (2) tells us that (2) n is even, from which we cannot determine whether 13m + 25n is odd.

For example, if (m,n)=(1,2), then 13m + 25n = 13(1) + 25(2)=63= ODD and we get YES as an answer.

However, if (m,n) = (2,2), then 13m + 25n = 13(2) + 25(2)=76=even and we get no as an answer.

The answer is not a unique YES or a NO therefore condition (2) alone is not sufficient according to Common Mistake Type 1 which states that the answer should be a unique YES or a NO.


Condition (1) alone is sufficient.

Therefore, A is the correct answer.

Answer: A