as per the statement k is a set of following integers[-25,-24,-23......,0,......22,23]
now sum of all the integers in the following set will be equal to -25+(-24)= -49 ans

Shadow wrote:The sum of all the integers k such that –26 < k < 24 is

A. 0
B. -2
C. -25
D. -49
E. -51


Could anyone please let me know the answer for the above question?

Add -25 + -24 + -23 + .... + 0 + 1 + 2 +3 + ... -23

We are left out with -25 + -24 = -49
Hence D

Another way to look at this problem:

For CONSECUTIVE numbers in a set only...

SUM = (# of terms) x (middle number)

Determine # of terms:
23 - (-25) + 1 = 49
Thus, 49 terms in the set

Determine middle number:
[-25 + 23]/2 = -1
Thus, the middle number of the set is -1
NOTE: You can use upper and lower limit to determine the median when you have a consecutive set only

Finally, SUM = (49) x (-1) = -49

The previous methods are a lot faster and easier here. But in other questions where consecutive sets are apparent, these skills are crucial.

Later beh-beh

Thanks a lot for the detailed explanation which will help me solve problems of this nature