swerve wrote:Set M is composed of the positive even integers up to 100. Set N is composed of the odd integers from -1 to 99. What is the value of (the sum of set M)-(the sum of set N)?
A. 49
B. 50
C. 51
D. 100
E. 101
For any EVENLY SPACED SET:
Count = (biggest - smallest)/(increment) + 1.
Average = (biggest + smallest)/2.
Sum = (count)(average).
The INCREMENT is the difference between successive values.
Even integers between 2 and 100, inclusive:
Here, the integers are EVEN, so the increment = 2.
Count = (100-2)/2 + 1 = 50.
Average = (100+2)/2= 51.
Sum = (50)(51).
Odd integers between -1 and 99, inclusive:
Here, the integers are ODD, so the increment = 2.
Count = (99-(-1))/2 + 1 = 51.
Average = (99+(-1))/2= 49.
Sum = (51)(49).
Subtracting the second sum from the first, we get:
(50*51) - (51*49) = 51(50-49) = 51*1 = 51.
The correct answer is
C.
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