GMAT Test Tip - Consecutive Numbers

Just about once every GMAT, test takers will get a question using consecutive integers. Most often, the question is about the sum of consecutive numbers. Here’s a quick and easy way to always find the sum of consecutive numbers.

Example:
What is the sum of the consecutive integers from 51 – 101, inclusive?

Step 1: Find the middle number
The middle number in a set of consecutive numbers is also the average of that set of numbers. Interestingly, it is also the average of the first and last number.

In our example, the first number is 51 and the last is 101. The average is:

(51 + 101)/2 = 152/2 = 76

Step 2: Find the number of numbers
The number of integers is found by the following formula: Last Number – First Number + 1. That "plus 1" is the part most people forget. When you just subtract two numbers, by definition, you are finding one less than the number of total numbers between them. Adding 1 back in solves that problem.

In our example:

101 – 51 + 1 = 50 + 1 = 51

Step 3: Multiply
Because the middle number is actually the average and step two finds the number of numbers, you just multiply them together to get the sum:

76*51 = 3,876

Thus, the sum of 51 + 52 + 53 + … + 99 + 100 + 101 = 3,876

Click here to road test this tip on an IL700 GMAT question.

NOTE: This works with all consecutive sets, such as consecutive even sets, consecutive odd sets, consecutive multiples of five, etc. The only difference is in Step 2. In these cases, after you subtract Last – First, you must divide by the common difference between the numbers, and then add 1. Here are some examples:

Consecutive even integers from 14 – 24:
(24 – 14)/2 + 1 = 6 (the difference between each number in the set is 2)

Consecutive odd integers from 23 – 67:
(67 – 23)/2 + 1 = 23 (the difference between each number in the set is 2)

Consecutive multiples of five from 25 – 75:
(75 – 25)/5 + 1 = 11(the difference between each number in the set is 5)