Problem Solving

BTGmoderatorDC wrote: ↑

Thu Feb 16, 2023 10:28 pm

If X is the sum of first 50 positive even integers and Y is the sum of first 50 positive odd integers, what is the value of x - y ?

A. 0
B. 25
C. 50
D. 75
E. 100



OA C

Source: GMAT Prep

Solution:

The sum of the first 50 positive even integers is:

sum = average x quantity

sum = (100 + 2)/2 x 50 = 51 x 50

The sum of the first 50 positive odd integers is:

sum = (99 + 1)/2 x 50 = 50 x 50

Thus, x - y is 51 x 50 - 50 x 50 = 50(51 - 50) = 50.

Alternate solution:

The first 50 positive even integers are: 2, 4, 6, 8, …, 98, 100.

The first 50 positive odd integers are: 1, 3, 5, 7, …, 97, 99.

We see that each even integer is 1 more than its odd counterpart (2 is 1 more than 1, 4 is 1 more than 3, etc). Since there are 50 numbers in each set, the sum of the even integers will be 50 x 1 = 50 more than the sum of the odd integers.

Answer: C