For any positive integer $n,$ the sum of the first $n$ positive integers equals $\dfrac{n(n+1)}2.$ What is the sum

Expert replies

Previous Topic Next Topic

Vincen: Legendary Member; Posts: 2898; Joined: Thu Sep 07, 2017 2:49 pmFollowed by: 5 members; Thanked: 6 times

by Vincen » Tue Jan 19, 2021 9:47 am

Timer

00:00

Answers

Stats

Difficulty—

For any positive integer $n,$ the sum of the first $n$ positive integers equals $\dfrac{n(n+1)}2.$ What is the sum of all the even integers between $99$ and $301?$

A. 10,100
B. 20,200
C. 22,650
D. 40,200
E. 45,150

Answer: B

Source: Official Guide

Like this post

Source: Beat The GMAT — Problem Solving | Tue Jan 19, 2021 9:47 am

GMAT/MBA Expert

Scott@TargetTestPrep: GMAT Instructor; Posts: 8175; Joined: Sat Apr 25, 2015 10:56 amFollowed by: 29 members; Location: Los Angeles, CA; Thanked: 43 times

Re: For any positive integer $n,$ the sum of the first $n$ positive integers equals $\dfrac{n(n+1)}2.$ What is the

by Scott@TargetTestPrep » Wed Jan 27, 2021 5:26 am

Vincen wrote: ↑
Tue Jan 19, 2021 9:47 am
For any positive integer $n,$ the sum of the first $n$ positive integers equals $\dfrac{n(n+1)}2.$ What is the sum of all the even integers between $99$ and $301?$

A. 10,100
B. 20,200
C. 22,650
D. 40,200
E. 45,150

Answer: B

Source: Official Guide

Solution:

The phrase “between 99 and 301” does not include the endpoints. The sum of the even integers from 100 to 300 is:

[(100 + 300)/2] * [(300 - 100)/2 + 1]

= 200 * 101

= 20,200

[Note: The first factor is the average of the even integers and the second factor is the number of even integers from 100 to 300.]

Answer: B

Scott Woodbury-Stewart
Founder and CEO
[email protected]

See why Target Test Prep is rated 5 out of 5 stars on BEAT the GMAT. Read our reviews

Like this post

Post new topic Post Reply

• Page 1 of 1

GMAT Course Reviews

560 reviews

1168 reviews

431 reviews

359 reviews

147 reviews

5/5

5 Star (560 Reviews)

"Target Test Prep is the closest to the official version of the GMAT exam, about 99% accuracy in terms of the quality and quantity of information. The course has excellently created singular sets of focused lessons and tests for every possible topic that one could come across in the official GMAT exam."

"The TTP course maximizes the efficiency of the time you spend studying. It will take time and effort but I could almost guarantee that if you complete the course exactly as it is laid out you will get an amazing score. They also have a very responsive team willing to help with any questions you might have."

"TTP has two things that I think no other test prep company offers: A teaching approach that reinforces understanding and an attitude that will give you the mental preparedness needed to succeed on the test. TTP gives you a deep understanding of the concept you need to know while teaching you how to think."

Write a Review