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.
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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 find the value of p.
Follow the second and the third step: From the original condition, we have 2 variables (p and q). To match the number of variables with the number of equations, we need 2 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 together.
Condition (1) tells us that \(\frac{q}{p}=\frac{1}{3}\) , and Condition (2) tells us that p < 0 and q < 0.
Number of possible cases for \(\frac{q}{p}\) such that ratio is 1:3 are
=> q = -1 and p = -3 (q < 0, p < 0)
=> q = -2 and p = -6 (q < 0, p < 0)
=> q = -6 and p = -18 (q < 0, p < 0)
And so on…
The answer is not a unique value; both conditions combined are not sufficient according to Common Mistake Type 2 which states that the answer should be a unique value.
Both conditions together are not sufficient.
Therefore, E is the correct answer.
Answer: E
