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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 < [#permalink] New post 29 Dec 2012, 05:44
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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
[Reveal] Spoiler: OA
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Re: If a, b, and c are consecutive positive integers and a < b < [#permalink] New post 29 Dec 2012, 05:49
Expert's post
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] New post 22 Jun 2013, 10:32
Hey Bunuel, I know I'm a few years late to this but I have a general question about consecutive integers.
According to your explanation, consecutive integers are always 1 apart. However in Sackmann's Total GMAT Math, he defines 'consecutive integers' as any set of integers that are EVENLY SPACED. I'm a little confused here. What's the correct way to think about them?
Thanks!
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Re: If a, b, and c are consecutive positive integers and a < b < [#permalink] New post 22 Jun 2013, 10:37
Expert's post
tricialin wrote:
Hey Bunuel, I know I'm a few years late to this but I have a general question about consecutive integers.
According to your explanation, consecutive integers are always 1 apart. However in Sackmann's Total GMAT Math, he defines 'consecutive integers' as any set of integers that are EVENLY SPACED. I'm a little confused here. What's the correct way to think about them?
Thanks!


When we see "consecutive integers" it ALWAYS means integers that follow each other in order with common difference of 1: ... x-3, x-2, x-1, x, x+1, x+2, ....

For example:

-7, -6, -5 are consecutive integers.

2, 4, 6 ARE NOT consecutive integers, they are consecutive even integers.

3, 5, 7 ARE NOT consecutive integers, they are consecutive odd integers.

So, not all evenly spaced sets represent consecutive integers.
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DS: 1. DS tough questions; 2. DS tough questions part 2; 3. DS tough questions part 3; 4. DS Standard deviation; 5. Inequalities; 6. 700+ GMAT Data Sufficiency Questions With Explanations; 7 Tough and tricky exponents and roots questions; 8 The Discreet Charm of the DS ; 9 Devil's Dozen!!!; 10 Number Properties set., 11 New DS set.


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Re: If a, b, and c are consecutive positive integers and a < b < [#permalink] New post 22 Jun 2013, 10:44
awesome. Thanks a lot.
Re: If a, b, and c are consecutive positive integers and a < b <   [#permalink] 22 Jun 2013, 10:44
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