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There are 30 consecutive integers. What is the sum of the integers?

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There are 30 consecutive integers. What is the sum of the integers? [#permalink]

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New post 10 Mar 2017, 03:15
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There are 30 consecutive integers. What is the sum of the integers?

1) The sum of the smallest integer and the greatest integer is -1
2) The greatest integer is 14.
[Reveal] Spoiler: OA

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Re: There are 30 consecutive integers. What is the sum of the integers? [#permalink]

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MathRevolution wrote:
There are 30 consecutive integers. What is the sum of the integers?

1) The sum of the smallest integer and the greatest integer is -1
2) The greatest integer is 14.


St I
The sum of the smallest integer and the greatest integer is -1
x -- first integer and x + 29 --- last integer
x + x + 29 = -1
2x = -30
x = -15 and x + 29 = 14
since all the integers from 14 to -14 cancel out each other we are left with only -15
sum of the consecutive integers = -15 ---------Sufficient

St II
The greatest integer is 14
Since 14 is greatest, the consecutive integers will be 14 13 12 11.....-14 -15
since all the integers from 14 to -14 cancel out each other we are left with only -15
sum of the consecutive integers = -15 ---------Sufficient

Hence option D is correct
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Re: There are 30 consecutive integers. What is the sum of the integers? [#permalink]

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New post 12 Mar 2017, 18:47
==> In the original condition, there is 1 variable (n, n+1, n+2,……n+29), and in order to match the number of variables to the number of equations, there must be 1 equation. Since there is 1 for con 1) and 1 for con 2), D is most likely to be the answer.
For con 1), you get -15~14, so the sum=-15, hence unique and sufficient.
For con 2), you also get -15~14, so the sum=-15, hence unique and sufficient.
Thus, con 1) = con 2).

The answer is D.
Answer: D
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Re: There are 30 consecutive integers. What is the sum of the integers? [#permalink]

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New post 25 Sep 2017, 22:10
MathRevolution wrote:
There are 30 consecutive integers. What is the sum of the integers?

1) The sum of the smallest integer and the greatest integer is -1
2) The greatest integer is 14.


Sum of consecutive series

n/2 (first + last) where n is the number of numbers in the series

D

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Re: There are 30 consecutive integers. What is the sum of the integers?   [#permalink] 25 Sep 2017, 22:10
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