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Average Problem

by gmat009 » Sat Nov 22, 2008 8:22 pm
If x is the average (arithmetic mean) of 5 consecutive even integers, which of the following must be true?

I. x is an even integer.
II. x is a nonzero integer.
III. x is a multiple of 5.

(A) I only
(B) III only
(C) I and II only
(D) I and III only
(E) I, II, and III
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Re: Average Problem

by Stuart@KaplanGMAT » Sat Nov 22, 2008 10:38 pm
gmat009 wrote:If x is the average (arithmetic mean) of 5 consecutive even integers, which of the following must be true?

I. x is an even integer.
II. x is a nonzero integer.
III. x is a multiple of 5.

(A) I only
(B) III only
(C) I and II only
(D) I and III only
(E) I, II, and III
The average of a set of consecutive numbers with an odd number of terms will simply be the middle term of the set.

So, all we know at the moment is that x is an even number, since the middle term in our set will always be even.

I must be true.

II could be true (if our set were {2, 4, 6, 8, 10}) but also could be false (if our set were {-4, -2, 0, 2, 4}). Therefore, II is not a MUST be true.

III could be true (if our set were {-4, -2, 0, 2, 4}) but also could be false (if our set were {2, 4, 6, 8, 10}). Therefore, III is not a MUST be true.

Choose (A), I only.
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Re: Average Problem

by Mozartain » Sun Nov 23, 2008 4:02 am
Hi Stuart,

Is 0 considered an even integer? If not, then I is not necessarily true.

Asif
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by mals24 » Sun Nov 23, 2008 4:12 am
0 is an even integer.
But 0 is neither positive or negative. Nor is 0 prime or composite.
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by Stuart@KaplanGMAT » Sun Nov 23, 2008 10:17 am
mals24 wrote:0 is an even integer.
But 0 is neither positive or negative. Nor is 0 prime or composite.
Bingo!
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by lunarpower » Mon Nov 24, 2008 5:07 am
mals24 wrote:0 is an even integer.
But 0 is neither positive or negative. Nor is 0 prime or composite.
as stuart has point out, the above is true.

i have yet to see an official problem that turns on the classification of 0, -2, -4, ... as even numbers (or that of -1, -3, -5, ... as odd numbers), but you should still know that they are classified as such.
if anything, you may have to use this fact when you plug in your own numbers on a problem.
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