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
If T is a set of 35 consecutive integers, of which 17 are
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- fskilnik@GMATH
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\[? = \sum\nolimits_{35} {\,{\text{consecutive}}\,\,{\text{integers}}} \,\,\,\,\,\,\left( {17\,\,{\text{are}}\,\,{\text{negative}}} \right)\]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
\[35\,\,{\text{consecutive}}\,\,{\text{integers}}:\,\,\,\,\underbrace { - 17\,, - 16\,,\,\, \ldots \,\,, - 1}_{17\,\,\,{\text{numbers}}}\,,\,\,0\,\,,\,\,\underbrace {1\,,\,2\,,\,\, \ldots \,\,,\,\,17}_{35 - 17 - 1\,\, = \,\,17\,\,\,{\text{numbers}}}\]
\[?\,\,\, = \,\,\,0\]
This solution follows the notations and rationale taught in the GMATH method.
Regards,
Fabio.
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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.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
Answer: C
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