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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.
Consecutive integers have two variables for the first number and the number of integers. Since the number of integers is 3, we need one more equation and D is most likely to be the answer. So, we should consider each condition on its own first.
Condition 1)
If x = 1, y = 2 and z = 3, then we have x = 1.
If x = 2, y = 3 and z = 4, then we have x = 2.
Since condition 1) doesn't yield a unique solution, it is not sufficient.
Condition 2)
Since 12 + 13 + 14 + 15 = x + y + z, we have x + y + z = 54.
If x = 17, y = 18, z = 19, then we have x = 17.
If x = 19, y = 18, z = 17, then we have x = 19.
Since condition 2) doesn't yield a unique solution, it is not sufficient.
Conditions 1) & 2)
Since y = x + 1 and z = x + 2 from condition 1), we have 12 + 13 + 14 + 15 = 54 = x + y + z = x + x + 1 + x + 2 = 3x + 3 or 3x = 51.
Thus we have x = 17.
Since both conditions together yield a unique solution, they are sufficient.
Since this question is an integer question (one of the key question areas), CMT (Common Mistake Type) 4(A) of the VA (Variable Approach) method tells us that we should also check answers A and B.
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.
