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fluke
Baten80
Attachment:
Table.jpg
What is the sum of the integers in the table above?

(A) 28
(B) 112
(C) 336
(D) 448
(E) 784

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"

Why will we multiply the sum of column by 7?
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Baten80
Why will we multiply the sum of column by 7?

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

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

I'd say it's 600 level question.

Check similar one to practice: https://gmatclub.com/forum/what-is-the- ... 26125.html
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fluke
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Why will we multiply the sum of column by 7?

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)

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
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subhashghosh
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

hello
why do you have added all the average plz explain

thanks for your help

best regards
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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 = [x-2x+3x-4x+5x-6x+7x]
= 4x=4*28=112
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B is correct. Here is my solution:
Attachments

Sum of integers.png
Sum of integers.png [ 25.72 KiB | Viewed 47944 times ]

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