Problem Solving

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

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.