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

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

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 ≈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

Cheers,
Brent

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.