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GRE : Problem Solving
If a, b and c are consecutive positive integers and a < b < c, which of the following must be an odd integer?
(A) abc
(B) a + b + c
(C) a + bc
(D) a(b + c)
(E) (a + b)(b + c)
Each answer choice must be answered by assuming two different sets of values for (a, b, c), starting with an odd integer and even integer respectively.
Let us first consider the set (2, 3, 4).
The five choices for this set are 24, 9, 14, 14 and 35.
In this case, (B) and (E) are odd integers.
Now, let us consider the set (3, 4, 5).
The five choices for this set are 60, 12, 23, 27 and 63.
In this case, (C), (D) and (E) are odd integers.
It is only (E) which is an odd integer in both cases, and is the answer.