PS Question

Question

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

a. 10,100
b. 20,200
c. 22,650
d. 40,200
e. 45,150

Why is it 2(150(150+1))/2 - 2(49(49+1))/2, instead of 150(150+2)/2 - 49(49+1)/2???

Why do I have to multiply by two instead of just plugging the numbers into the orginal equation?

22,200 is the correct answer and when you don't multiply by 2 you obviously come to 10,100 which is another answer choice...

Apologies if I confused anyone, I am just frustrated about this and I am sure there is an easy explanation

Thanks!

GMATGuruNY · Answer

jscpba wrote:For any positive integer n, the sum of the first n positive integers equals n(n+1)/2. What is the sum of all even integers between 99 and 301?

a. 10,100
b. 20,200
c. 22,650
d. 40,200
e. 45,150

Why is it 2(150(150+1))/2 - 2(49(49+1))/2, instead of 150(150+2)/2 - 49(49+1)/2???

Why do I have to multiply by two instead of just plugging the numbers into the orginal equation?

22,200 is the correct answer and when you don't multiply by 2 you obviously come to 10,100 which is another answer choice...

Apologies if I confused anyone, I am just frustrated about this and I am sure there is an easy explanation

Thanks!

We need to count the even integers from 100 to 300, inclusive.

Ignore the formula given. Instead, use the following:

Sum = (number of integers) * (average of biggest and smallest)

To count the number of evenly spaced integers in a set:

Number of integers = (Biggest - Smallest)/(distance between each successive pair) + 1

Since we're adding only the even integers, the distance between each successive pair is 2.
Thus, the number of even integers from 100 to 300 = (300-100)/2 + 1 = 101.
Average of biggest and smallest = (300+100)/2 = 200.
Sum = (number of integers) * (average of biggest and smallest) = 101*200 = 20,200.

The correct answer is B.

Private tutor exclusively for the GMAT and GRE, with over 20 years of experience.
Followed here and elsewhere by over 1900 test-takers.
I have worked with students based in the US, Australia, Taiwan, China, Tajikistan, Kuwait, Saudi Arabia -- a long list of countries.
My students have been admitted to HBS, CBS, Tuck, Yale, Stern, Fuqua -- a long list of top programs.

As a tutor, I don't simply teach you how I would approach problems.
I unlock the best way for YOU to solve problems.

For more information, please email me (Mitch Hunt) at [email protected].
Student Review #1
Student Review #2
Student Review #3

jscpba · Answer

Perfect!! You have been of such help for me in my studies. I want to thank you for that! I sit for the exam in 18ish days, I hope I can apply all this when it counts!

Choose how you want to prepare

Get Ready for GMAT Test Day Faster with Live Online Classes

Target Test Prep EA OnDemand

Target Test Prep GMAT OnDemand

PS Question

Chicago Booth

GMAT Course Reviews

Admissions Consulting Reviews

FREE GMAT PREP RESOURCES

GMAT PREP DEAL TRACKER