Set \(M\) consists of \(50\) consecutive integers. If the range of the negative integers in Set \(M\) is \(36,\) what is

[Gmat_mission]

Set \(M\) consists of \(50\) consecutive integers. If the range of the negative integers in Set \(M\) is \(36,\) what is the sum of all positive integers in Set \(M?\)

A. 78
B. 91
C. 105
D. 112
E. 120

Answer: A

Source: Veritas Prep

[Scott@TargetTestPrep]

Set \(M\) consists of \(50\) consecutive integers. If the range of the negative integers in Set \(M\) is \(36,\) what is the sum of all positive integers in Set \(M?\)

A. 78
B. 91
C. 105
D. 112
E. 120

Answer: A

Solution:

Since the range of the negative integers in set M is 36, the negative integers are from -1 to -37 inclusive. Thus, there are 37 negative integers in set M, and after accounting for zero, there are 12 positive integers left, i.e., the integers from 1 to 12 inclusive.

Thus, the sum of the consecutive integers from 1 to 12 is:

Sum = average x quantity

Sum = [(1 + 12)/2] x 12

Sum = 13/2 x 12

Sum = 13 x 6 = 78

Answer: A