Carcass wrote:
Let u represent the sum of the integers from 1 through 20, and let v represent the sum of the integers from 21 through 40. What is the value of v – u ?
(A) 21
(B) 39
(C) 200
(D) 320
(E) 400
Kudos for the right answer and explanation
Question part of the project GRE Quantitative Reasoning Daily Challenge - (2021) EDITIONGRE - Math Book u = 1 + 2 + 3 + 4 + . . . . + 19 + 20v = 21 + 22 + 23 + 24 + . . . . 39 + 40
Now let's
write v a special way by recognizing that each value in v is
20 greater than its corresponding value in u.
For example, 21 =
1 +
20And 22 =
2 +
2023 =
3 +
20.
.
.
40 =
20 +
20So, v = (
1 +
20) + (
2 +
20) + (
3 +
20) + . . . (
19 +
20) + (
20 +
20)
Notice that we have added
20 to twenty values.
(20)(20) =
400, so we can say: v =
1 + 2 + 3 + 4 + . . . . + 19 + 20 +
400So, v - u = [
1 + 2 + 3 + 4 + . . . . + 19 + 20 +
400] - [
1 + 2 + 3 + 4 + . . . . + 19 + 20]
=
400Answer: E
Cheers,
Brent