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# The average of five consecutive integers is an odd number.

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Manager
Joined: 10 Jan 2006
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The average of five consecutive integers is an odd number. [#permalink]

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03 Apr 2006, 13:18
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Question Stats:

100% (02:41) correct 0% (00:00) wrong based on 2 sessions

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The average of five consecutive integers is an odd number. Which of the following must be true?

I. The largest of the integers is even
II. The sum of the integers is odd
III. The difference between the largest and the smalles integers is an even number

A. I only
B. II only
C. III only
D. I and II only
E. II and III only
Manager
Joined: 25 Mar 2006
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Location: Stonybrook Univ
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03 Apr 2006, 13:49
II and III

If the avg is an odd number the sum is the avg * 5 = odd thus the sum is also odd.

III is also true because if the avg is an odd number the sum must be odd ... in order for the sum to be odd you need to start with an odd integer and end with an odd integer and odd - odd is even

1 doesnt hold

example
-1 0 1 2 3
Manager
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03 Apr 2006, 14:49
OA is 'E'
03 Apr 2006, 14:49
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