Data Sufficiency

[GMAT math practice question]

Five consecutive integers satisfies a < b < c < d < e. what is the maximum of a + e?

1) the summation of five integers is negative
2) e is positive

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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 5, 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)
a + b + c + d + e = a + a + 1 + a + 2 + a + 3 + a + 4 = 5a + 10 < 0 or a < -2. Then the maximum of a is -3 and e = a + 4 = 1.
Thus the maximum value of a + e = (-3) + 1 = -2.
Since condition 1) yields a unique solution, it is sufficient.

Condition 2)
If e = 1, then a = -3 we have a + e = -2.
If e = 2, then a = -2 we have a + e = 0.
If e = 3, then a = -1 we have a + e = 2.
...
As e increases, a + e increases and approaches infinity.
Thus we don't have a maximum value of a + e.
Condition 2) is not sufficient.

Therefore, A is the answer.
Answer: A

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.