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 whether xy is a multiple of 12 – where ‘x’ and ‘y’ are positive integers.
=> xy = 12n – where ‘n’ must be an integer
Follow the second and the third step: From the original condition, we have 2 variables (x and y). 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 combined together.
Condition (1) tells us that x is a multiple of 3.
=> x = 3m - where m is an integer
Condition (2) tells us that y is a multiple of x.
=> y = xp - where p is an integer
From them, we cannot determine whether xy is a multiple of 12.
For example, if x = 6 and y = 12, then y = 12 = 2*6 = 2x (y is a multiple of x) and we get xy = 6*12, which is a multiple of 12, so we get yes as an answer.
However, if x = y = 9, then y = 9 = 1 * 9 = x (y is a multiple of x) and we get xy = 9 * 9 = 81, which is not a multiple of 12, so we get no as an answer.
The answer is not a unique YES or a NO; both conditions combined are not sufficient according to Common Mistake Type 1 which states that the answer should be a unique YES or a NO.
Both conditions together are not sufficient.
Therefore, E is the correct answer.
Answer: E
