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Bunuel
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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100 to 200 => 100 & 101 to 200 (100 numbers) ==> total 101 numbers

Sum of numbers from 101 to 200 can be obtained by taking an average of all the terms and then multiplying it by 100.
If you try to use the "mirror approach" to get the average, you will notice 150.5 divides the set of 100 numbers in the middle. So, the total sum is-

\((150.5 * 100) + 100 = 15150\)

25 to 125 => 25 & 26 to 125 (100 numbers) ==> total 101 numbers

Apply the same approach here. Get the average of numbers from 26 to 125 by mirror approach and multiple by 100. Don't forget to add 25 to this number.

\((75.5 * 100) + 25 = 7575\)

Finally, \(15150 - 7575 = 7575\)

Answer is B

Took me 1:48 minutes to get to the answer.
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Sum of numbers of A = (100+101+...+199+200)
Sum of numbers of B = (25+26+...+124+125)
Difference of sums of numbers of A and B=(100-25)+(101-26)+...(199-124)+(200-125) = 75+75+..+75+75= 75*101 = 7500+75 = 7575
Answer is B
Hope it helps
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