What is the sum of the integers in the table above?

Question

https://gmatclub.com/forum/download/file.php?id=14563 What is the sum of the integers in the table above? (A) 28 (B) 112 (C) 336 (D) 448 (E) 784 Table.jpg

fluke · Accepted Answer

All rows are evenly spaced.
The numbers in 4th column are the averages of respective rows.
Every row has 7 elements.

Thus,
Total = (4-8+12-16+20-24+28)*7 = (64-48)*7= 16*7= 112

Ans: "B"

Bunuel · Answer

https://gmatclub.com/forum/download/file.php?id=14563

Each row represents an evenly spaced set (aka arithmetic progression).  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 .

The median of each row is the middle number and each row has 7 numbers in it so the sum of the table is:

7*4+7*(-8)+7*12+7*(-16)+7*20+7*(-24)+7*28=7(4-8+12-16+20-24+28)=112 .

Answer: B.

Those are not averages, but the sums of the numbers in each column.

MHIKER · Answer

Why will we multiply the sum of column by 7?

fluke · Answer

Take 1 row at a time

1st row: Total = Average*Number of elements = 4*7
2nd row: Total = Average*Number of elements = -8*7
3rd row: Total = Average*Number of elements = 12*7
4th row: Total = Average*Number of elements = -16*7
5th row: Total = Average*Number of elements = 20*7
6th row: Total = Average*Number of elements = -24*7
7th row: Total = Average*Number of elements = 28*7

Add them up:
4*7+(-8)*7+12*7+(-16)*7+20*7+(-24)*7+28*7
Take 7 common:
7(4-8+12-16+20-24+28)

subhashghosh · Answer

I went for a different approach, the sum of every coulmn came as a multiple of 4, starting from 4, and there are 7 columns.

So sum = 4 + 8 + 12 + 16 + 20 + 24 + 28

= 112

Answer - B

Spidy001 · Answer

=(1+2+3+4+5+6+7)(1-2+3-4+5-6+7)
=112

Answer B.

amit2k9 · Answer

Each row - ( 1+2+3+4+5+6+7) = 28
 Let that be a constant A = 28.
 Now, visual analysis shows that each row is a multiple of A,
 as
 row 1 = A
 row 2 = -2(A)
 row 3 = 3(A)
 
 and so on.

Hence, we get A- 2A + 3A-4A+5A-6A+7A = 4A => 4* 28
 = 112.
 Thanks.

YuraK · Answer

Guys,
what do you thing is the level of a difficulty of the such question? Anyone knows?
Thanks

Bunuel · Answer

I'd say it's 600 level question. Check similar one to practice: https://gmatclub.com/forum/what-is-the- ... 26125.html

keiraria · Answer

Hello Fluke 
just to make sure I understood 
as thoses questions look tricky and time consuming

first each line is a AP Progression 
you use the average formula in reverse to find the sum
since in an AP Progression the mean or average is the same as median number 
and then you factorise by 7 to complete the sum and multiply it by 7 as each line is a multiple of 7

right ?

Thanks for help

best regards

keiraria · Answer

hello 
why do you have added all the average plz explain

thanks for your help

best regards

BDSunDevil · Answer

Let X be the sum of 1 to 7 = 28
1st row = x
2nd row=-2x
3rd row=3x
4th row = -4x
5th row = 5x
6th row = -6x
7th row = 7x
Total =  
 = 4x=4*28=112

pqhai · Answer

B is correct. Here is my solution:

blitzkriegxX · Answer

Took a slighly different approach!

If u observe carefully, in each column-- 
(sum of 7th number and the 3rd number) - (sum of 6th number and 4th number ) = 0

This pattern is same for all the columns. Now all u have to do is  add only the units digit  of the remaining numbers and u have the answer!

IMO  fluke  gave the best approach, though i could not come up with it immediately when i saw the question!

RenB · Answer

I used the same approach.  Bunuel   chetan2u  is it correct?

kingbucky · Answer

Looking carefully, the sum of all the numbers is just equal to (sum of numbers in first row) *(sum of numbers in first column) as the structure of the table is like a multiplication table.

Sum = (1+2+3...+7)*(1-2+3-4..+7) =(7*8/2)*4 = 112

Ngocanhvy · Answer

The pattern is: The sum of 2nd, 3rd, 4th, 5th... row is: -2, 3,- 4, 5... * SUM(row 1)  
 SUM(row 1)= (7*8)/2 = 28  
 SUM(table) = 28*(1+3+5+7) - 28*(2+4+6) = 28*16 - 28*12 = 28*4 = 112

P.S: 28*(1+3+5+7) = SUM(row1) + SUM(row3) + SUM(row5) + SUM(row7)

totaltestprepNick · Answer

B https://www.youtube.com/watch?v=Fuq6o_0RU0w Nick Slavkovich, GMAT/GRE tutor with 20+ years of experience tutoring@totaltestprep.net

What is the sum of the integers in the table above?

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