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

Ian Stewart: GMAT Instructor; Posts: 2623; Joined: Mon Jun 02, 2008 3:17 am; Location: Montreal; Thanked: 1090 times; Followed by:355 members; GMAT Score:780

by Ian Stewart » Wed Mar 06, 2019 1:42 am

In each column, if we list the numbers in increasing order, we get an equally spaced list with a multiple of 100 in the middle. So, for example, the second column contains the numbers:

-204, -202, -200, -198, -196

The sum of an equally spaced list is just equal to the average (which, in an equally spaced list, is the median) of the list times the number of things in the list, so the five numbers above add to (5)(-200). Doing that for each column, we get the overall sum:

(5)(100) + (5)(-200) + (5)(300) + (5)(-400) + (5)(500) = (5) (100-200+300-400+500) = (5)(300) = 1500

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Brent@GMATPrepNow: GMAT Instructor; Posts: 16207; Joined: Mon Dec 08, 2008 6:26 pm; Location: Vancouver, BC; Thanked: 5254 times; Followed by:1268 members; GMAT Score:770

by Brent@GMATPrepNow » Wed Mar 06, 2019 8:48 am

BTGmoderatorLU wrote:Source: Manhattan GMAT

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

A. 0
B. 300
C. 500
D. 1500
E. 6500
The OA is D

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 â‰ˆ500
COLUMN 2: Sum â‰ˆ-1000
COLUMN 3: Sum â‰ˆ1500
COLUMN 4: Sum â‰ˆ-2000
COLUMN 5: Sum â‰ˆ2500

TOTAL SUM â‰ˆ500 + (-1000) + 1500 + (-2000) + 2500
â‰ˆ1500

Answer: D

Cheers,
Brent

Brent Hanneson - Creator of GMATPrepNow.com

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Scott@TargetTestPrep: GMAT Instructor; Posts: 8083; Joined: Sat Apr 25, 2015 10:56 am; Location: Los Angeles, CA; Thanked: 43 times; Followed by:29 members

by Scott@TargetTestPrep » Fri Mar 08, 2019 6:46 am

BTGmoderatorLU wrote:Source: Manhattan GMAT

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

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

The OA is D

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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