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

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New post Updated on: 30 Dec 2017, 22:50
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A
B
C
D
E

Difficulty:

  25% (medium)

Question Stats:

75% (01:57) correct 25% (01:49) wrong based on 272 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
111.JPG [ 15.19 KiB | Viewed 6150 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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New post 15 Jan 2012, 15:27
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enigma123 wrote:
Image

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:

Image

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:

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

Answer: D.

Hope it's clear.

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New post 25 Aug 2018, 06:26
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enigma123 wrote:
Image
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


Always check the answer choices BEFORE solving the question!!
Since the answer choices are nicely spread apart, we can be quite aggressive in our estimation

Let's add the 5 numbers in each COLUMN

COLUMN 1: Sum ≈500
COLUMN 2: Sum ≈-1000
COLUMN 3: Sum ≈1500
COLUMN 4: Sum ≈-2000
COLUMN 5: Sum ≈2500

TOTAL SUM ≈500 + (-1000) + 1500 + (-2000) + 2500
≈1500

Answer: D

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New post 15 Jan 2012, 15:42
Absolutely and many thanks. As always, thorough and a very helpful answer.
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New post 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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New post 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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New post 13 Apr 2019, 19:06
enigma123 wrote:
Image
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



We don’t have actually add up all the numbers; we can just approximate the sum. Let’s add the numbers column by column.

We see that the 5 numbers in the first column are each about 100, so the sum is approximately 500. The 5 numbers in the second column are each about -200, so the sum is approximately -1000. The 5 numbers in the third column are each about 300, so the sum is approximately 1500. The 5 numbers in the fourth column are each about -400, so the sum is approximately -2000. Lastly, the 5 numbers in the fifth column are each about 500, so the sum is approximately 2500.

Therefore, the sum of all 25 numbers is approximately 500 + (-1000) + 1500 + (-2000) + 2500 = 4500 - 3000 = 1500

Answer: D.
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Re: What is the sum of all of the integers in the chart above?   [#permalink] 13 Apr 2019, 19:06
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