Data Sufficiency

Que: If p, q, and r are positive integers and 2p + 3q = r, do r and 10 have a common factor other than 1?

(1) p is a multiple of 5.
(2) q is a multiple of 5.

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

Follow the first step of the Variable Approach by modifying and rechecking the original condition and the question.

We have to verify whether 'r' and '10' have a common factor other than 1 – where ‘p’, ‘q’, and ‘r’ are positive integers and 2p + 3q = r.

Follow the second and the third step: From the original condition, we have 2 variables (p, q, and r) and 1 equation (2p+3q=r). To match the number of variables with the number of equations, we need 2 more equations. Since conditions (1) and (2) will provide 1 equation each, C would most likely be the answer.

Recall 3- Principles and Choose C as the most likely answer. Let’s look at both conditions combined together.

Condition (1) tells us that p is a multiple of 5 and condition (2) tells us that q is a multiple of 5.

=> Let p = 5t and q=5s where t and s are any integers, we get 2p + 3q = 2(5t) + 3(5s) = 5(2t + 3s) = r, so r has a factor of 5.

Thus, r and 10 have a common factor other than 1, 5, so we get YES as an answer.

The answer is unique, YES, so both conditions (1) and (2) combined are sufficient according to Common Mistake Type 1 which states that the answer should be a unique YES or a NO.

Both conditions together are sufficient.

Therefore, C is the correct answer.

Answer: C