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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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The first step of the VA (Variable Approach) method is to modify the original condition and the question. We then recheck the question. We should simplify conditions if necessary.
Since the mid-point of x and y is 4, (x+y)/2 = 4, and x + y = 8.
Since we have 2 variables (x and y) and 1 equation, D is most likely to be the answer. So, we should consider each condition on its own first.
Condition 1)
Since |x|=6, we must have x=6 or x=-6.
Since 4 lies midway between x and y, we must have either x=6 and y=2, or x=-6 and y=14.
Since condition 1) does not yield a unique solution, it is not sufficient.
Condition 2)
There are many possible pairs of integers, x and y, satisfying condition 2) and the original condition.
Examples are x=1 and y=7, and x=2 and y=6.
Condition 2) is not sufficient since it does not yield a unique solution.
Conditions 1) & 2)
Condition 1) tells us that x=6 and y=2, or x=-6 and y=14.
Since condition 2) tells us that x<y, we must have x=-6 and y=14.
Both conditions together are sufficient, since they yield a unique solution.
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.
