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

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12 00:00

Difficulty:   25% (medium)

Question Stats: 75% (01:57) correct 25% (01:49) wrong based on 272 sessions

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

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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.

Attachment: untitled.JPG [ 15.23 KiB | Viewed 6121 times ]

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

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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

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

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

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Absolutely and many thanks. As always, thorough and a very helpful answer.
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Re: What is the sum of all of the integers in the chart above?  [#permalink]

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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.
Attachments image.jpg [ 14.15 KiB | Viewed 5252 times ]

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

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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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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

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

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