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# Which one of the following could be an integer?

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Founder
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Which one of the following could be an integer? [#permalink]  16 Apr 2018, 11:09
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Question Stats:

86% (00:31) correct 13% (01:40) wrong based on 15 sessions
Which one of the following could be an integer?

(A) The average of two consecutive integers
(B) The average of three consecutive integers
(C) The average of four consecutive integers
(D) The average of six consecutive integers
(E) The average of 6 and 9
[Reveal] Spoiler: OA

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Re: Which one of the following could be an integer? [#permalink]  18 Apr 2018, 01:42
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let $$x$$be the first integer than 2nd integer is$$x+1$$
There average will be $$\frac{2x + 1}{2} = x + \frac{1}{2}$$ which is not a integer

For option B
1st integer = $$x$$
2nd integer = $$x+1$$
3rd integer = $$x+2$$

Hence there average $$= \frac{3x +3}{3}$$ or, $$\frac{3(x+1)}{3} = x + 1$$
since x is an integer $$x +1$$ is also a integer
option B
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Re: Which one of the following could be an integer? [#permalink]  11 Jun 2019, 19:17
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Expert's post
Carcass wrote:
Which one of the following could be an integer?

(A) The average of two consecutive integers
(B) The average of three consecutive integers
(C) The average of four consecutive integers
(D) The average of six consecutive integers
(E) The average of 6 and 9

Since the average of 3 consecutive integers is equal to the median, and since the median would be the middle integer of 3 consecutive integers, we see that the average of 3 consecutive integers must be an integer.

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Re: Which one of the following could be an integer?   [#permalink] 11 Jun 2019, 19:17
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