Sum of integers in table

Expert replies

Previous Topic Next Topic

cmr209: Senior | Next Rank: 100 Posts; Posts: 42; Joined: Thu Sep 11, 2008 11:07 pm; Location: California; Thanked: 3 times

by cmr209 » Sun Aug 16, 2009 1:03 am

I've never encountered a question like this before.

What is the sum of the integers in the table above?

A 28

B 112

C 336

D 448

E 784

Please help.

Like this post

Source: Beat The GMAT — Problem Solving | Sun Aug 16, 2009 1:03 am

Morgoth: Master | Next Rank: 500 Posts; Posts: 316; Joined: Mon Sep 22, 2008 12:04 amFollowed by: 1 member; Thanked: 36 times

Re: Sum of integers in table

by Morgoth » Sun Aug 16, 2009 3:27 am

There are many ways of solving this question, I'll show you 1

if you look at the rows closely, every row is a table of a number starting from 1 to 7

1+2+3+4+5+6+7 = 28

28 + -2(28) + 3(28) -4(28) + 5 (28) -6(28) + 7(28)

= 28 ( 1-2+3-4+5-6+7) = 4*28 = 112

Hope this helps.

Like this post

cmr209: Senior | Next Rank: 100 Posts; Posts: 42; Joined: Thu Sep 11, 2008 11:07 pm; Location: California; Thanked: 3 times

by cmr209 » Sun Aug 16, 2009 10:39 am

Yes! This does help, thank you!
I had never seen a problem like this.

Like this post

nafiul9090: Master | Next Rank: 500 Posts; Posts: 226; Joined: Thu Nov 25, 2010 12:19 amFollowed by: 2 members; Thanked: 3 times

by nafiul9090 » Wed May 18, 2011 2:28 am

what if last two rows are omitted?? is there any uniform method or formula....

Like this post

GMAT/MBA Expert

Anurag@Gurome: GMAT Instructor; Posts: 3835; Joined: Fri Apr 02, 2010 10:00 pmFollowed by: 523 members; Location: Milpitas, CA; Thanked: 1854 times; GMAT Score:770

by Anurag@Gurome » Wed May 18, 2011 7:17 pm

nafiul9090 wrote:what if last two rows are omitted?? is there any uniform method or formula....

Solution:
Let us say that the first row is 1,2,3,4,5,6...n.
So the sum of all the above numbers is {n*(n+1)/2}.
Now, the sum of numbers in second row is -2*n(n+1)/2, in the third row is +3*n(n+1)/2...and so on.
If this extends till k where k is even, then the sum of last row is -k*n(n+1)/2.
If k is odd, then the sum of last row is +k*n(n+1)/2.
Hence the sum of all integers where k is even is {n*(n+1)/2}*{1-2+3-4...-k) = {n*(n+1)/2}*{-k/2}
= -k*n*(n+1)/4.
Also, the sum of all the integers where k is odd is {n*(n+1)/2}*{-(k-1)/2+k} = {n*(n+1)/2}*{(k+1)/2}.
If the last 2 rows are removed, then n= 7, k = 5 and is odd. So, the sum is {7*(7+1)/2}*{(5+1)/2} = 28*3 = 84

Anurag Mairal, Ph.D., MBA
GMAT Expert, Admissions and Career Guidance
Gurome, Inc.
1-800-566-4043 (USA)

Join Our Facebook Groups
GMAT with Gurome
https://www.facebook.com/groups/272466352793633/
Admissions with Gurome
https://www.facebook.com/groups/461459690536574/
Career Advising with Gurome
https://www.facebook.com/groups/360435787349781/

Like this post

GMATGuruNY: GMAT Instructor; Posts: 15539; Joined: Tue May 25, 2010 12:04 pmFollowed by: 1906 members; Location: New York, NY; Thanked: 13060 times; GMAT Score:790

by GMATGuruNY » Thu May 19, 2011 3:21 am

cmr209 wrote:I've never encountered a question like this before.

What is the sum of the integers in the table above?

A 28

B 112

C 336

D 448

E 784

Please help.

Look for a pattern.
The table shows the results of multiplying every integer in the top row by every integer in the leftmost column.

Thus, we need to determine the sum of all these products:
(Top row)*(Leftmost column) = (1+2+3+4+5+6+7)(1-2+3-4+5-6+7) = 28*4 = 112.

The correct answer is B.

nafiul9090 wrote:what if last two rows are omitted?? is there any uniform method or formula....

Use the same reasoning as above, omitting the bottom 2 rows:
(Top row)*(Leftmost column) = (1+2+3+4+5+6+7)(1-2+3-4+5) = 28*3 = 84.

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

Like this post

Post new topic Post Reply

• Page 1 of 1

GMAT Course Reviews

559 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