Bunuel
If S is a set of n consecutive integers, what is the sum of the integers in S ?
(1) n = 11
(2) The sum of the least integer and the greatest integer in S is zero.
DS20481
Inference from the question stem:S is a set of n consecutive Integers => the increment between any two consecutive numbers is Fixed.
All such sets where the difference between any two consecutive numbers is the same are defined as Evenly Spaced Sets.
So, above set S is an Evenly spaced set
Few facts about the Evenly spaced sets:[1) Mean of the set is always equal to the median of the set
2) Average of the first and last terms in the set is equal to mean of the set
Sum = Mean * number of terms in the given setUsing the facts, along with the above formula we can very easily find the sum of all numbers in the given evenly spaced set!
Now Analyze Stat (1) alone:1) n = 11
we only know the number of terms in the set but we need mean of the set also to find the Sum of integers in the set
Thus, stat (1) alone is not sufficient to find the answer to the given question
Analyze Stat (2) alone:2)
The sum of the least integer and the greatest integer in S is zero. We know that mean of the evenly spaced set is same as the average of the first and last terms in the set
here, as the sum of the least integer( First Term) and the greatest integer(Last term) in S is zero, thus the Mean of the first and last terms in the set is also Zero
which implies the sum of the set is also Zero asSum = Mean * number of terms in the given set
Thus, stat (2) alone is sufficient to find the sum of integers in the set SHence, the answer is B