M7MBA wrote: ↑Fri Aug 06, 2021 11:14 am
Set \(M\) is composed of 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
Answer:
C
Source: Magoosh
Set M is composed of the positive even integers up to 100.
Set M = {
2, 4, 6, 8, . . . . 96, 98, 100}
Set N is composed of the odd integers from –1 to 99
Set N = {
-1, 1, 3, 5, . . . 95, 97, 99}
What is the value of (the sum of Set M) – (the sum of Set N)?
SUM of set M =
2 + 4 + 6 + 8 + . . . .+ 96 + 98 + 100
SUM of set N =
-1 + 1 + 3 + 5 + . . . 95 + 97 + 99
ASIDE: Notice that there are 100 POSITIVE integers from 1 to 100 inclusive
HALF of them are EVEN and HALF are ODD
So,
set M consists of 50 integers
and
set N consists of 51 integers (since set N also has one NEGATIVE odd number)
(the sum of Set M) – (the sum of Set N) = (
2 + 4 + 6 + 8 + . . . .+ 96 + 98 + 100) - (
-1 + 1 + 3 + 5 + . . . 95 + 97 + 99)
= (
2 + 4 + 6 + 8 + . . . .+ 96 + 98 + 100) - (
1 + 3 + 5 + . . . 95 + 97 + 99)
+ 1
= (2 - 1) + (4 - 3) + (6 - 5) + . . . + (98 - 97) + (100 - 99) + 1
= (1) + (1) + (1) + . . . + (1) + (1) + 1
= 50 + 1 [since we have 50 PAIRS of even and odd numbers]
= 51
Answer: C
Cheers,
Brent
