If a equals the sum of the even integers from 2 to 20, inclusive, and b equals the sum of the odd integers from 1 to 19,

BTGmoderatorLU wrote: ↑

Thu Jan 14, 2021 9:56 am

Source: GMAT Prep

If a equals the sum of the even integers from 2 to 20, inclusive, and b equals the sum of the odd integers from 1 to 19, inclusive, what is the value of a-b?

A. 1
B. 10
C. 19
D. 20
E. 21

The OA is B

Solution:

We are given that a equals the sum of the even integers from 2 to 20, inclusive, and b equals the sum of the odd integers from 1 to 19, inclusive, and we need to determine the value of a - b.

When comparing the two sets of numbers, we can see that each number from 2 to 20 (which we can call list a) is ONE GREATER than each number from 1 to 19 (which we can call list b). That is, we can pair a number from list a such that it is one more than a corresponding number from list b. Let’s explore this idea further, starting with the least numbers in each list and working up.

1st number in list a = 2
1st number in list b = 1

2nd number in list a = 4
2nd number in list b = 3

Last number in list a = 20
Last number in list b = 19

Again, notice that each number in list a is ONE MORE than the corresponding number in list b.

Since there are 10 numbers in each list, the sum of the numbers in list a must be 10 greater than the sum of the numbers in list b.

Answer: B