=>
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.
Since we have 1 variable (a) and 0 equations, D is most likely the answer. So, we should consider each condition on its own first.
Let’s look at the condition 1). It tells us that a could be any value other than 3.
x/3 + a = x/2 – x - 18/6
⇔ x/3 + a = x/3 + 3
⇔ a = 3.
It means if a = 3, the equation has an infinite number of solutions, and if a ≠ 3, the equation has no solution. Thus, a can be any value other than 3.
The answer is not unique, and the condition is not sufficient, according to Common Mistake Type 2, which states that the number of answers must be only one.
Let’s look at the condition 2). It tells us that a does not have a unique solution.
Any integer can be the value of a.
The answer is not unique, and the condition is not sufficient, according to Common Mistake Type 2, which states that the number of answers must be only one.
Conditions 1) & 2) together tell us that we don’t have a unique solution, as a can be any integer other than 3.
The answer is not unique, and the conditions 1) and 2) together are not sufficient according to Common Mistake Type 2, which states that the number of answers must be only one.
Both conditions 1) & 2) together are not sufficient.
Therefore, E is the correct answer.
Answer: E
If the original condition includes “1 variable”, or “2 variables and 1 equation”, or “3 variables and 2 equations,” etc., one more equation is required to answer the question. If each of conditions 1) and 2) provide an additional equation, there is a 59% chance that D is the answer, a 38% chance that A or B is the answer, and a 3% chance that the answer is C or E. Thus, answer D (conditions 1) and 2), when applied separately, are sufficient to answer the question) is most likely, but there may be cases where the answer is A, B, C, or E.
