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

The OA is 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

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

The OA is C

Source: Magoosh

The number of integers in set M is (100 - 2)/2 + 1 = 50

The number of integers in Set N is (99 - (-1))/2 + 1 = 51

We can pair the 50 numbers from set M with the first 50 numbers from set N as follows:

2, -1

4, 1

6, 3, etc.

We see that each number in set M is 3 more than each number in set N. Thus, comparing the first 50 numbers in each set, the sum of those numbers in Set M is 3 x 50 = 150 greater.

However, set N has an extra number, which is 99.

So the overall sum of the integers in set M is actually 150 - 99 = 51 greater than the sum of the integers in set N.

Answer: C