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

Question

https://gmatclub.com/forum/download/file.php?id=16341 What is the sum of all of the integers in the chart above? A. 0 B. 300 C. 500 D. 1500 E. 6500 111.JPG

Bunuel · Accepted Answer

Reorder the numbers in columns in ascending absolute value: https://gmatclub.com/forum/download/file.php?id=16340 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. untitled.JPG

enigma123 · Answer

Absolutely and many thanks. As always, thorough and a very helpful answer.

mau5 · Answer

Sum of the first column = 5*100 = 500.
Sum of the last column = 500+5*400 = 2500 
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.

SaraLotfy · Answer

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.

BrentGMATPrepNow · Answer

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

RELATED VIDEO FROM OUR COURSE
 https://www.youtube.com/watch?v=8GqcJGUVIk4

ScottTargetTestPrep · Answer

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.

Farina · Answer

Hi,
your replies are really helpful in learning tricks and shortcuts. Can you please tell why did you take the middle line only

MHIKER · Answer

The complete property is:
 In any evenly spaced set the arithmetic mean (average) is equal to the median and the sum of the terms in any evenly spaced set is the mean (average) multiplied by the number of terms.

So, while you are arranging the columns you are getting the middle as average and multiplying it to get the sum.

Now, (100x5) + (-200x5) + (300x 5)+(-400x5)+(500x5)
you don't need to multy you take 5 Common
5 
5  = 1500

Birds just don't fly, they fall down and get up.

DrHuber · Answer

Average of first column = 100
Average of first column = -200
Average of first column = 300
Average of first column = -400
Average of first column = 500

(100+500)+(-400)+(-200) cancel out. Only left is 5x300=1,500

bumpbot · Answer

Automated notice from GMAT Club BumpBot: 

A member just gave Kudos to this thread, showing it’s still useful. I’ve bumped it to the top so more people can benefit. Feel free to add your own questions or solutions.

 This post was generated automatically.

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

Prep Toolkit

Top 5 GMAT Debrief Videos

615 to 715 in 15 Days (Ria's Strategies)

More than Quant/Verbal Abilities: Speed vs. Accuracy

745 with Only Self-Prep and GMAT Club

From 555 to 765: 210-point Improvement

Perfect 805 Score Debrief by Julia

My Rewards

GMAT Problem Solving (PS) Questions

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

Prep Toolkit

615 to 715 in 15 Days (Ria's Strategies)

More than Quant/Verbal Abilities: Speed vs. Accuracy

745 with Only Self-Prep and GMAT Club

From 555 to 765: 210-point Improvement

Perfect 805 Score Debrief by Julia

My Rewards