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# If T is a set of 35 consecutive integers, of which 17 are negative

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Joined: 17 Oct 2016
Posts: 2
If T is a set of 35 consecutive integers, of which 17 are negative  [#permalink]

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Updated on: 05 Dec 2017, 16:02
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Difficulty:

5% (low)

Question Stats:

90% (00:32) correct 10% (00:37) wrong based on 92 sessions

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If T is a set of 35 consecutive integers, of which 17 are negative, what is the sum of all the integers in T ?

A. -2
B. -1
C. 0
D. 1
E. 2

Originally posted by Dav5599 on 05 Dec 2017, 12:33.
Last edited by Dav5599 on 05 Dec 2017, 16:02, edited 2 times in total.
Senior SC Moderator
Joined: 22 May 2016
Posts: 2117
Re: If T is a set of 35 consecutive integers, of which 17 are negative  [#permalink]

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05 Dec 2017, 13:43
Dav5599 wrote:
If T is a set of 35 consecutive integers, of which 37 are negative, what is the sum of all the integers in T?

A. -2
B. -1
C. 0
D. 1
E. 2

Dav5599 - are these numbers correct?
The set = 35, but 37 of the 35 are negative?
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Joined: 17 Oct 2016
Posts: 2
Re: If T is a set of 35 consecutive integers, of which 17 are negative  [#permalink]

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05 Dec 2017, 14:30
There was a typo in the question. Corrected now. Thanks.
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Re: If T is a set of 35 consecutive integers, of which 17 are negative  [#permalink]

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05 Dec 2017, 16:04
Dav5599 wrote:
If T is a set of 35 consecutive integers, of which 17 are negative, what is the sum of all the integers in T?

A. -2
B. -1
C. 0
D. 1
E. 2

17 of 35 consecutive integers are negative.
(35 - 17) = 18 terms left.
The first number after -1 is 0.
(18 - 1) = 17 terms left: all positive.

$$-17, -16, ... -2, -1, 0, 1, 2 ... 16, 17$$
The 17 negative integers cancel the 17 positive integers; the sum of 34 of the numbers is 0. Add to the remaining number, 0. (0 + 0) = 0

**If not sure, take fewer numbers, with an odd number of terms:
-3 + (-2) + (-1) + 0 + 1 + 2 + 3 = 0

Sum of negative: -6
Sum of positive: 6
Add 0: (-6 + 6 + 0) = 0
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Re: If T is a set of 35 consecutive integers, of which 17 are negative  [#permalink]

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31 Oct 2018, 17:32
Dav5599 wrote:
If T is a set of 35 consecutive integers, of which 17 are negative, what is the sum of all the integers in T ?

A. -2
B. -1
C. 0
D. 1
E. 2

If 17 of the numbers are negative, then 35 - 17 = 18 numbers are zero or greater. Thus, we have the consecutive integers from -17 to 17 (including 0), and thus, the sum is 0.

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Re: If T is a set of 35 consecutive integers, of which 17 are negative  [#permalink]

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31 Oct 2018, 22:10
1
Total 35 consecutive numbers

{-17,-16,-15..........-1} = 17 numbers and the sum is -153
{0} = 1 number
{17,16,15.................1} = 17 numbers and the sum is 153

-153 + 0 + 153 = 0

(In fact this question can be answered in under 30 seconds logically without any calculations)
Re: If T is a set of 35 consecutive integers, of which 17 are negative &nbs [#permalink] 31 Oct 2018, 22:10
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