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What is the sum of all of the integers in the chart above?

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What is the sum of all of the integers in the chart above? [#permalink]

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Updated on: 30 Dec 2017, 22:50
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25% (medium)

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76% (01:31) correct 24% (01:15) wrong based on 216 sessions

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What is the sum of all of the integers in the chart above?

A. 0
B. 300
C. 500
D. 1500
E. 6500

Attachment:

111.JPG [ 15.19 KiB | Viewed 4031 times ]

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Originally posted by enigma123 on 15 Jan 2012, 15:10.
Last edited by Bunuel on 30 Dec 2017, 22:50, edited 5 times in total.
Edited the question and added the chart
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Joined: 02 Sep 2009
Posts: 46991
What is the sum of all of the integers in the chart above? [#permalink]

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15 Jan 2012, 15:27
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5
enigma123 wrote:

What is the sum of all of the integers in the chart above?

A. 0
B. 300
C. 500
D. 1500
E. 6500

Reorder the numbers in columns in ascending absolute value:

Now, it's easy to spot that the numbers in each column represent an equally spaced set (AP) and the sum in each can be found by mean*# of terms:

$$Sum=5*100+5*(-200)+5*(300)+5*(-400)+5*(500)=500-1,000+1,500-2,000+2,500=1,500$$.

Hope it's clear.

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untitled.JPG [ 15.23 KiB | Viewed 4030 times ]

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Director
Status: Finally Done. Admitted in Kellogg for 2015 intake
Joined: 25 Jun 2011
Posts: 511
Location: United Kingdom
Concentration: International Business, Strategy
GMAT 1: 730 Q49 V45
GPA: 2.9
WE: Information Technology (Consulting)
Re: What is the sum of all of the integers in the chart above? [#permalink]

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15 Jan 2012, 15:42
Absolutely and many thanks. As always, thorough and a very helpful answer.
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E.

MGMAT 1 --> 530
MGMAT 2--> 640
MGMAT 3 ---> 610
GMAT ==> 730

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Re: What is the sum of all of the integers in the chart above? [#permalink]

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22 May 2013, 05:55
enigma123 wrote:
Attachment:
The attachment 111.JPG is no longer available
What is the sum of all of the integers in the chart above?

A. 0
B. 300
C. 500
D. 1500
E. 6500

Sum of the first column = 5*100 = 500.
Sum of the last column = 500+5*400 = 2500[As all the corresponding terms are increased by 400]
Sum of the second column = 5*-200 = -1000
Sum of the fourth column = -1000-5*200 = -2000
The total sum = 500+2500-1000-2000 = 0
Thus everything when added gets cancelled. Except the inner column. That is an AP and the sum = 5*300 = 1500.
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Re: What is the sum of all of the integers in the chart above? [#permalink]

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22 May 2013, 09:47
It is easy once you spot that in the same row, the 1st outer most and the second outer most cancel one another. You are then left with adding the column in the middle.
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Re: What is the sum of all of the integers in the chart above? [#permalink]

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29 Nov 2017, 12:16
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Re: What is the sum of all of the integers in the chart above?   [#permalink] 29 Nov 2017, 12:16
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