Bunuel wrote:
Set A contains all of the integers from 100 to 200, inclusive. Set B contains all of the integers from 25 to 125, inclusive. What is the sum of set A minus the sum of set B?
A. 7500
B. 7575
C. 8050
D. 9875
E. 12925
Since we see there is overlap between sets, we can just determine the sum of the integers from 25 to 99 inclusive and 126 to 200 inclusive. Remember average = (first number + last number)/2.
For set B (excluding 100 to 125 inclusive):
sum = avg x quantity
sum = (25 + 99)/2 x (99 - 25 + 1)
sum = 62 x 75
For set A (excluding 100 to 125 inclusive):
sum = avg x quantity
sum = (126 + 200)/2 x (200 - 126 + 1)
sum = 163 x 75
Thus, A - B = 163 x 75 - 62 x 75 = 75(163 - 62) = 75(101) = 7,575.
Alternate solution:
Even though some of the numbers in B overlap with those in A, we can just find the sum of all the numbers in B and subtract that from the sum of all the numbers in A.
We use the formulas sum = average x quantity and average = (first number + last number)/2.
For set B:
sum = avg x quantity
sum = (25 + 125)/2 x (125 - 25 + 1)
sum = 75 x 101
For set A:
sum = avg x quantity
sum = (100 + 200)/2 x (200 - 100 + 1)
sum = 150 x 101
Thus, A - B = 150 x 101 - 75 x 101 = 101(150 - 75) = 101(75) = 7,575.
Answer: B
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