Is the sum of six consecutive integers even? : DS Archive
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# Is the sum of six consecutive integers even?

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Is the sum of six consecutive integers even? [#permalink]

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17 Sep 2003, 01:26
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Hey, guys, look here:

Is the sum of six consecutive integers even?
1. The first integer is odd
2. The average of six integers is odd

1. As far as I did some calculations, the sum of 6 consectituve integers is ALWAYS odd, no matter the first integer is even or odd.
2. According to the number properties theory the SUM must be even here (even number divided by another even (6) may give either even or odd (which is actually odd here as mentioned));
What I see is some inconsistency here. According to DS logic the answer is D, but according to common sense this question is irrelevant, since the stimulus and both pieces of information contradict each other.

Can anybody help?
Thank you
GMAT Instructor
Joined: 07 Jul 2003
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Location: New York NY 10024
Schools: Haas, MFE; Anderson, MBA; USC, MSEE
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17 Sep 2003, 02:17
vaka wrote:
Hey, guys, look here:

Is the sum of six consecutive integers even?
1. The first integer is odd
2. The average of six integers is odd

1. As far as I did some calculations, the sum of 6 consectituve integers is ALWAYS odd, no matter the first integer is even or odd.
2. According to the number properties theory the SUM must be even here (even number divided by another even (6) may give either even or odd (which is actually odd here as mentioned));
What I see is some inconsistency here. According to DS logic the answer is D, but according to common sense this question is irrelevant, since the stimulus and both pieces of information contradict each other.

Can anybody help?
Thank you

This question only makes sense with an odd number of integers, say 5, not six, hence there must be a typo in your source. As you noticed, the sum of six consecutive integers is ALWAYS odd. Hence, there is no need for conditions. Were the number of integers odd, it would matter whether the starting number was odd or even (or equivalently, whether the middle number (which is the average) is odd or even.)
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AkamaiBrah
Former Senior Instructor, Manhattan GMAT and VeritasPrep
Vice President, Midtown NYC Investment Bank, Structured Finance IT
MFE, Haas School of Business, UC Berkeley, Class of 2005
MBA, Anderson School of Management, UCLA, Class of 1993

Manager
Joined: 08 Jan 2003
Posts: 128
Location: Ukraine
Followers: 1

Kudos [?]: 0 [0], given: 0

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17 Sep 2003, 03:46
Thank you, AkamaiBrah,
I took this question from this site (Qantitive Section Lessons) so I thought there could be no mistake. Wrong. A person, who uploaded the lesson must have made a typo.
17 Sep 2003, 03:46
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# Is the sum of six consecutive integers even?

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