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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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Since we have 1 variable (x) and 0 equations, D is most likely to be the answer. So, we should consider each condition on its own first.
Condition 1)
Now, 170 = x*a + 2, so 168 = 2^3*3*7 = x*a. Note that x > 2 since the dividend must be greater than the remainder.
So, x is a factor of 168 greater than 2. The possible values of x are 3, 4, 6, ..., 168.
Since condition 1) doesn't yield a unique solution, it is not sufficient.
Condition 2)
Now, 140 = x*b + 4, so 136 = x*b. Note that x > 4 since the dividend must be greater than the remainder.
So, x is a factor of 136 = 2^3*17 greater than 4. The possible values of x are 8, 17 and 140.
Since condition 2) doesn't yield a unique solution, it is not sufficient.
Conditions 1) & 2).
When we consider both conditions together, x is a common factor greater than 4 of 168 = 2^3*3*7 and 136 = 2^3*17. The only possible value of x is 8.
Since both conditions together yield a unique solution, they are sufficient.
Therefore, C is the answer.
Answer: C
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.
