• Varsity Tutors
    Award-winning private GMAT tutoring
    Register now and save up to $200

    Available with Beat the GMAT members only code

    MORE DETAILS
    Varsity Tutors
  • Kaplan Test Prep
    Free Practice Test & Review
    How would you score if you took the GMAT

    Available with Beat the GMAT members only code

    MORE DETAILS
    Kaplan Test Prep
  • examPAL
    Most awarded test prep in the world
    Now free for 30 days

    Available with Beat the GMAT members only code

    MORE DETAILS
    examPAL
  • Economist Test Prep
    Free Trial & Practice Exam
    BEAT THE GMAT EXCLUSIVE

    Available with Beat the GMAT members only code

    MORE DETAILS
    Economist Test Prep
  • EMPOWERgmat Slider
    1 Hour Free
    BEAT THE GMAT EXCLUSIVE

    Available with Beat the GMAT members only code

    MORE DETAILS
    EMPOWERgmat Slider
  • Magoosh
    Magoosh
    Study with Magoosh GMAT prep

    Available with Beat the GMAT members only code

    MORE DETAILS
    Magoosh
  • e-gmat Exclusive Offer
    Get 300+ Practice Questions
    25 Video lessons and 6 Webinars for FREE

    Available with Beat the GMAT members only code

    MORE DETAILS
    e-gmat Exclusive Offer
  • Target Test Prep
    5-Day Free Trial
    5-day free, full-access trial TTP Quant

    Available with Beat the GMAT members only code

    MORE DETAILS
    Target Test Prep
  • Veritas Prep
    Free Veritas GMAT Class
    Experience Lesson 1 Live Free

    Available with Beat the GMAT members only code

    MORE DETAILS
    Veritas Prep
  • PrepScholar GMAT
    5 Day FREE Trial
    Study Smarter, Not Harder

    Available with Beat the GMAT members only code

    MORE DETAILS
    PrepScholar GMAT

Integers - Sum

This topic has 6 expert replies and 2 member replies
singhmaharaj Senior | Next Rank: 100 Posts
Joined
10 Feb 2009
Posted:
38 messages
Followed by:
2 members
Target GMAT Score:
700

Integers - Sum

Post Tue May 06, 2014 2:43 am
The sum of the first 50 positive even integers is 2,550. What is the sum of the even integers from 102 to 200, inclusive?

A) 5,100

B) 7,550

C) 10,100

D) 15,500

E) 20,100

  • +1 Upvote Post
  • Quote
  • Flag

GMAT/MBA Expert

Post Tue Feb 17, 2015 6:04 pm
Hi j_shreyans,

The required level of 'detail' in these types of questions varies depending on the description of the terms, what you're asked to solve for and how "spread out" the answer choices are.

In this prompt, the answer choices are so "spaced out" that even if you mis-calculated the number of terms in the sequence, then assuming that the rest of your math was done correctly, you'd end up with an answer that was 'close enough' to the correct one for you to pick it without much concern.

Also, the first part of the prompt clues you in to how many terms there are:

The first 50 positive even integers are 2 through 100, inclusive (2x1, 2x2, 2x3 .....2x50). The NEXT 50 terms would have to be from 102 to 200, inclusive, because they're in the same 'format' as the first set of 50 terms (2x51, 2x52.....2x100).

You could even do a limited set of terms to define the pattern:

eg.
The first 5 terms: 2, 4, 6, 8, 10
The next 5 terms: 12, 14, 16, 18, 20
Etc.
Each set of 5 terms takes you "up" another 'multiple of 10'

So 50 terms = 10 sets of 5 = would take us up to 100
and 100 terms = 20 sets of 5 = would take us up to 200

Remember that almost everything that you'll face on Test Day is based on a pattern of some kind. If the 'big pattern' seems difficult, then try dealing with a smaller version of the same pattern and you'll likely learn what you need to deduce the big pattern.

GMAT assassins aren't born, they're made,
Rich

_________________
Contact Rich at Rich.C@empowergmat.com

  • +1 Upvote Post
  • Quote
  • Flag
deojason Newbie | Next Rank: 10 Posts Default Avatar
Joined
19 Jan 2017
Posted:
3 messages
Upvotes:
1
Post Thu Mar 30, 2017 11:29 am
Hey Brent,

""So, sum = [(102 + 300)/2][50]""

You have a typo here. The last term is 200, not 300.

  • +1 Upvote Post
  • Quote
  • Flag

GMAT/MBA Expert

Post Tue May 06, 2014 2:47 am
singhmaharaj wrote:
The sum of the first 50 positive even integers is 2,550. What is the sum of the even integers from 102 to 200, inclusive?

A) 5,100

B) 7,550

C) 10,100

D) 15,500

E) 20,100
The sum of the first 50 positive even integers is 2550.
In other words, 2 + 4 + 6 + 8 + ...+ 98 + 100 = 2550

We want the sum: 102 + 104 + 106 + . . . 198 + 200
IMPORTANT: Notice that each term in this sum is 100 GREATER than each term in the first sum.
In other words, 102 + 104 + 106 + . . . 198 + 200 is the SAME AS...
(100 + 2) + (100 + 4) + (100 + 6) + ... + (100 + 98) + (100 + 100)
We can rearrange these terms to get: (100 + 100 + ... + 100 + 100) + (2 + 4 + 6 + 8 + ...+ 98 + 100)

IMPORTANT: There are 50 100's in the red sum, and we're told that the blue sum = 2550

So, our sum = 50(100) + 2550
= 5000 + 2550
= 7550
= B

Cheers,
Brent

_________________
Brent Hanneson – Founder of GMATPrepNow.com
Use our video course along with Beat The GMAT's free 60-Day Study Guide

Check out the online reviews of our course
Come see all of our free resources

  • +1 Upvote Post
  • Quote
  • Flag
GMAT Prep Now's comprehensive video course can be used in conjunction with Beat The GMAT’s FREE 60-Day Study Guide and reach your target score in 2 months!

GMAT/MBA Expert

Post Tue May 06, 2014 2:48 am
singhmaharaj wrote:
The sum of the first 50 positive even integers is 2,550. What is the sum of the even integers from 102 to 200, inclusive?

A) 5,100

B) 7,550

C) 10,100

D) 15,500

E) 20,100
Another approach:

We want to evaluate: 102 + 104 + 106 + . . . 198 + 200
Since the terms in this series are EQUALLY SPACED, the sum = (average of first and last term)(# of terms)
So, sum = [(102 + 200)/2][50]
= [(302)/2][50]
= [151][50]
= 7550
= B

Cheers,
Brent

_________________
Brent Hanneson – Founder of GMATPrepNow.com
Use our video course along with Beat The GMAT's free 60-Day Study Guide

Check out the online reviews of our course
Come see all of our free resources



Last edited by Brent@GMATPrepNow on Thu Mar 30, 2017 12:03 pm; edited 1 time in total

  • +1 Upvote Post
  • Quote
  • Flag
GMAT Prep Now's comprehensive video course can be used in conjunction with Beat The GMAT’s FREE 60-Day Study Guide and reach your target score in 2 months!
j_shreyans Legendary Member Default Avatar
Joined
07 Aug 2014
Posted:
510 messages
Followed by:
5 members
Upvotes:
3
Post Tue Feb 17, 2015 9:44 am
Hi Brent ,

In this question how did you find the no. of term by which formula?


Please advise.

Thanks,

Shreyans

  • +1 Upvote Post
  • Quote
  • Flag

GMAT/MBA Expert

Post Tue Feb 17, 2015 10:08 am
j_shreyans wrote:
Hi Brent ,

In this question how did you find the no. of term by which formula?


Please advise.

Thanks,

Shreyans
Hi Shreyans,

The most popular rule says: the number of integers from x to y inclusive equals y - x + 1 BUT this applies only to consecutive integers.

There are other formulas that people like to remember when we're dealing with multiples, but it only takes a couple of seconds to apply the green rule above.

We have the sequence: 102 + 104 + 106 + . . . 198 + 200
If we factor out a 2, we get: 2(51 + 52 + 53 + . . . 99 + 100)
Notice that the number of terms in 102 + 104 + 106 + . . . 198 + 200 is THE SAME AS the number of terms in 51 + 52 + 53 + . . . 99 + 100
Since 51, 52, 53, ...99, 100 are consecutive integers, we can apply the green rule above.
The number of terms = 100 - 51 + 1 = 50

Cheers,
Brent

_________________
Brent Hanneson – Founder of GMATPrepNow.com
Use our video course along with Beat The GMAT's free 60-Day Study Guide

Check out the online reviews of our course
Come see all of our free resources

  • +1 Upvote Post
  • Quote
  • Flag
GMAT Prep Now's comprehensive video course can be used in conjunction with Beat The GMAT’s FREE 60-Day Study Guide and reach your target score in 2 months!

GMAT/MBA Expert

Post Tue Feb 17, 2015 10:10 am
Quote:
The sum of the first 50 positive even integers is 2,550. What is the sum of the even integers from 102 to 200 inclusive?

a. 5,100
b. 7,550
c. 10,100
d. 15,500
e. 20,100
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

The distance between each successive pair of even integers is 2.
Thus, the number of even integers from 102 to 200 = (200-102)/2 + 1 = 50.
Average of biggest and smallest = (200+102)/2 = 151.
Sum = (number of integers) * (average of biggest and smallest) = 50*151 = 7550.

The correct answer is B.

_________________
Mitch Hunt
GMAT Private Tutor
GMATGuruNY@gmail.com
If you find one of my posts helpful, please take a moment to click on the "UPVOTE" icon.
Available for tutoring in NYC and long-distance.
For more information, please email me at GMATGuruNY@gmail.com.

  • +1 Upvote Post
  • Quote
  • Flag
Free GMAT Practice Test How can you improve your test score if you don't know your baseline score? Take a free online practice exam. Get started on achieving your dream score today! Sign up now.

GMAT/MBA Expert

Post Thu Mar 30, 2017 12:04 pm
deojason wrote:
Hey Brent,

""So, sum = [(102 + 300)/2][50]""

You have a typo here. The last term is 200, not 300.
Thanks for catching that.
I've edited my post.

Cheers,
Brent

_________________
Brent Hanneson – Founder of GMATPrepNow.com
Use our video course along with Beat The GMAT's free 60-Day Study Guide

Check out the online reviews of our course
Come see all of our free resources

  • +1 Upvote Post
  • Quote
  • Flag
GMAT Prep Now's comprehensive video course can be used in conjunction with Beat The GMAT’s FREE 60-Day Study Guide and reach your target score in 2 months!

Best Conversation Starters

1 lheiannie07 112 topics
2 ardz24 71 topics
3 Roland2rule 69 topics
4 LUANDATO 53 topics
5 swerve 45 topics
See More Top Beat The GMAT Members...

Most Active Experts

1 image description GMATGuruNY

The Princeton Review Teacher

154 posts
2 image description Rich.C@EMPOWERgma...

EMPOWERgmat

107 posts
3 image description Jeff@TargetTestPrep

Target Test Prep

106 posts
4 image description Scott@TargetTestPrep

Target Test Prep

98 posts
5 image description EconomistGMATTutor

The Economist GMAT Tutor

91 posts
See More Top Beat The GMAT Experts