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

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by swerve » Tue Oct 30, 2018 9:23 am

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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

The OA is C.

Source: GMAT Prep
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If T is a set of 35 consecutive integers, of which 17 are

by fskilnik@GMATH » Tue Oct 30, 2018 10:02 am
swerve wrote:If T is a set of 35 consecutive integers, of which EXACTLY 17 are negative, what is the sum of all the integers in T?

A. -2
B. -1
C. 0
D. 1
E. 2
Source: GMAT Prep
\[? = \sum\nolimits_{35} {\,{\text{consecutive}}\,\,{\text{integers}}} \,\,\,\,\,\,\left( {17\,\,{\text{are}}\,\,{\text{negative}}} \right)\]
\[35\,\,{\text{consecutive}}\,\,{\text{integers}}:\,\,\,\,\underbrace { - 17\,, - 16\,,\,\, \ldots \,\,, - 1}_{17\,\,\,{\text{numbers}}}\,,\,\,0\,\,,\,\,\underbrace {1\,,\,2\,,\,\, \ldots \,\,,\,\,17}_{35 - 17 - 1\,\, = \,\,17\,\,\,{\text{numbers}}}\]
\[?\,\,\, = \,\,\,0\]

This solution follows the notations and rationale taught in the GMATH method.

Regards,
Fabio.
Fabio Skilnik :: GMATH method creator ( Math for the GMAT)
English-speakers :: https://www.gmath.net
Portuguese-speakers :: https://www.gmath.com.br
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by Scott@TargetTestPrep » Wed Oct 31, 2018 5:26 pm
swerve 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.

Answer: C

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