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 – where ‘p’ and ‘q’ are integers and p * q = 60.
Follow the second and the third step: From the original condition, we have 2 variables (p, and q) and 1 equation (p * q = 60). To match the number of variables with the number of equations, we need 1 more equation. Since conditions (1) and (2) will provide 1 equation each, D would most likely be the answer.
Recall 3- Principles and Choose D as the most likely answer. Let’s look at each condition.
Condition (1) tells us that p is an odd integer.
For p * q = 60, where ‘p’ is odd - we can have the following possible combinations
=> p = 5 and q = 12 – p is odd.
=> p = -5 and q = -12 – p is odd.
=> p = 3 and q = 20 – p is odd.
=> p = -3 and q = -20 – p is odd.
The answer is not unique, so Condition (1) alone is not sufficient according to Common Mistake Type 2 which states that the answer should be a unique value.
Condition (2) tells us that p > q.
For p * q = 60, where ‘p > q’ - we can have following possible combinations
=> p = 10 and q = 6 – p > q [Also p = -6 and q = -10].
=> p = 15 and q = 4 – p > q [Also p = -4 and q = -15].
=> p = 20 and q = 3 – p > q [Also p = -3 and q = -20].
The answer is not unique, so Condition (2) alone is not sufficient according to Common Mistake Type 2 which states that the answer should be a unique value.
Let’s look at both conditions combined:
For p * q = 60, where ‘p > q’ and ‘p’ is odd - we can have the following possible combinations
=> p = 15 and q = 4 – p > q and ‘p’ is odd.
=> p = -3 and q = -20 – p > q and ‘p’ is odd.
The answer is not unique, so 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
