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# The sum of seven consecutive integers is equal to 7. What is

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The sum of seven consecutive integers is equal to 7. What is [#permalink]  05 Nov 2017, 02:02
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The sum of seven consecutive integers is equal to 7. What is the average of the greatest and least terms in the series?

(A) 7

(B) 4

(C) 2

(D) 1

(E) -2

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Re: The sum of seven consecutive integers is equal to 7. What is [#permalink]  05 Nov 2017, 06:44
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In order to sum to 7, the seven consecutive integers must be positive and negative. Thus, if we consider the fact that numbers specular around the zero sum to zero, it is easy to notice that the seven integers are -2 -1 0 1 2 3 4, so that -2+2 = 0, -1+1 = 0, 0 = 0 and 3+4 = 7.

The mean of the highest and lowest numbers is $$\frac{-2+4}{2} = 1$$.

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Re: The sum of seven consecutive integers is equal to 7. What is [#permalink]  09 Jan 2018, 10:39
Expert's post
Bunuel wrote:
The sum of seven consecutive integers is equal to 7. What is the average of the greatest and least terms in the series?

(A) 7

(B) 4

(C) 2

(D) 1

(E) -2

Since 7 consecutive integers sum to 7, we can let x = the first integer and create the following equation:

x + x + 1 + x + 2 + x + 3 + x + 4 + x + 5 + x + 6 = 7

7x + 21 = 7

7x = -14

x = -2

Thus, the first integer is -2 and the seventh integer is 4. The average of those integers is (-2 + 4)/2 = 1.

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Re: The sum of seven consecutive integers is equal to 7. What is   [#permalink] 09 Jan 2018, 10:39
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