Solution: To save time and improve accuracy on DS question 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.
Follow the first step of the Variable Approach by modifying and rechecking the original condition and the question.
We have to find whether n (n − 1) (n + 1) is divisible by 4, which means that we have to find whether n is odd since (n-1), n, (n+1) are 3 consecutive integers,
Thus, let’s look at condition (1), it tells us that ‘n’ is an odd integer
=> Say n = 2k + 1; where k is an integer.
=> n(n-1)(n+1) = (2k + 1) (2k) (2k + 2
=> 4k (2k + 1) (k + 1)
Hence, n (n − 1) (n + 1) divisible by 4 -
Yes
The answer is a 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 n(n+1) is divisible by 6, from which we cannot determine whether n=odd. For example,
If n = 3
=> (3) ( 3 + 1) = 3 * 4 = 12 is divisible by 6 , and n (n − 1) (n + 1) = 3 * 2 * 4 = 24 is divisible by 4 -
YES
If n = 2
=> (2) ( 2 + 1) = 2 * 3 = 6 is divisible by 6, however n (n − 1) (n + 1) = 2 * 1 * 3 = 6 is not divisible by 4 -
NO
The answer is not unique, YES or No, and condition (2) alone is 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
