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 ‘Is \(x^3-x\) a multiple of 12’- where ‘x’ is an integer
Modify the question:
=> \(x^3-x\) = 12p? – where ‘p’ is an integer
=> x(\(x^2-1\)) = 12p?
=> x (x-1) (x+1) = 12p?
=> (x-1) x (x+1) = 12p?
=> (x-1) x (x+1) = 4q? (since x-1, x, x+1 are consecutive integers and their product must be a multiple of 3.
So, we have to find whether x-1 = even or x = odd?
Condition (1) tells us that x-1 is an even integer
=> Is x-1 = even - YES
The answer is unique, so the condition (1) alone is sufficient, according to CMT 1 - there must be a unique YES or a NO.
Condition (2) tells us that x is an odd integer
=> Is x = odd - YES
The answer is unique, so condition (2) alone is sufficient, according to CMT 1 - there must be a unique YES or a NO.
** Tip 1: When condition (1) = condition (2) then 95% likely that answer is D
Each condition alone is sufficient.
Therefore, D is the correct answer.
Answer: D
