When trying to determine the sum of a set of evenly spaced integers, the key formula to keep in mind is: Average of items in the set * Number of items in the set = Sum of all the items in the set.
To figure out the average of a set of evenly-spaced integers, add up the first and last integer and divide by 2. In this case, we can disregard the first and last integers of the set (99 and 301) since the question is asking us about the sum of the EVEN integers. So, we do (300 + 100)/2 = 200.
To get the number of items in a set of evenly-spaced integers, use the formula: [(Greatest Integer - Smallest Integer)/Increment] + 1. In this case, the greatest integer is 300 and the smallest integer is 100 (since we're dealing with only even integers). The increment here is 2 since even integers are separated by 2. Thus, there are [(300 - 100)/2] + 1 integers in this set: 101.
To get the sum of these integers, we multiply the average (200) x number of integers (101) to arrive at 20,200.
The correct answer is B.
It's worth noting that this is the rare GMAT question in which the information provided in the question is not necessary to answer the problem.
Kevdog2834 wrote:Official Guide: 12th Edition
Problem Solving
#157
Can someone please help explain this problem to me. Some of the background information on the topic would be great. The explanation in the book uses Calculus and there is definitely an easier way.
How does it work with:
[Num Terms * Avg(High + Low term)] / 2
After that the number is suppose to be doubled?
Erfun Geula
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