If a, b, and c are consecutive positive integers and a < b

If a, b, and c are consecutive positive integers and a < b <

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If a, b, and c are consecutive positive integers and a < b < [#permalink]

29 Dec 2012, 06:44

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Re: If a, b, and c are consecutive positive integers and a < b < [#permalink]

29 Dec 2012, 06:49

If a, b, and c are consecutive positive integers and a < b < c, which of the following must be true?

I. c - a = 2
II. abc is an even integer.
III. (a + b + c)/3 is an integer.

(A) I only
(B) II only
(C) I and II only
(D) II and III only
(E) I, II, and III

Since a, b, and c are consecutive positive integers and a < b < c, then c = a + 2, from which it follows that c - a = 2. So, I is true.

Next, out of 3 consecutive integers at least 1 must be even, thus abc=even. II is true.

Finally, since b = a + 1, and c = a + 2, then (a + b + c)/3 = (a + a + 1 + a + 2)/3 = a + 1 = integer. III is true as well.

Answer: E.
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Re: If a, b, and c are consecutive positive integers and a < b < [#permalink] 29 Dec 2012, 06:49

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If a, b, and c are consecutive positive integers and a < b <

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If a, b, and c are consecutive positive integers and a < b <

If a, b, and c are consecutive positive integers and a < b <

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