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

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MHIKER
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What is the sum of the integers in the table above? [#permalink] New post  06 Apr 2011, 14:21
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What is the sum of the integers in the table above?

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

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fluke
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Re: What is the sum of the integers in the table above? [#permalink] New post  06 Apr 2011, 14:26
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Baten80 wrote:
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"
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Bunuel
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What is the sum of the integers in the table above? [#permalink] New post  17 May 2012, 01:43
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keiraria wrote:
fluke wrote:
Baten80 wrote:
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




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.


keiraria wrote:
subhashghosh wrote:
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


Those are not averages, but the sums of the numbers in each column.
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Re: What is the sum of the integers in the table above? [#permalink] New post  06 Apr 2011, 14:36
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fluke wrote:
Baten80 wrote:
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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fluke
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Re: What is the sum of the integers in the table above? [#permalink] New post  06 Apr 2011, 14:43
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Baten80 wrote:
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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Re: What is the sum of the integers in the table above? [#permalink] New post  06 Apr 2011, 18:11
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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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Re: What is the sum of the integers in the table above? [#permalink] New post  06 Apr 2011, 18:37
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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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Re: What is the sum of the integers in the table above? [#permalink] New post  07 Apr 2011, 23:25
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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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Re: What is the sum of the integers in the table above? [#permalink] New post  11 May 2012, 01:00
Guys,
what do you thing is the level of a difficulty of the such question? Anyone knows?
Thanks
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Bunuel
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What is the sum of the integers in the table above? [#permalink] New post  11 May 2012, 04:05
Expert Reply
YuraK wrote:
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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Re: What is the sum of the integers in the table above? [#permalink] New post  17 May 2012, 00:43
fluke wrote:
Baten80 wrote:
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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keiraria
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Re: What is the sum of the integers in the table above? [#permalink] New post  17 May 2012, 00:52
subhashghosh wrote:
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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Re: What is the sum of the integers in the table above? [#permalink] New post  17 May 2012, 10:23
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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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Re: What is the sum of the integers in the table above? [#permalink] New post  02 Jul 2013, 16:45
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B is correct. Here is my solution:
Attachments

Sum of integers.png
Sum of integers.png [ 25.72 KiB | Viewed 42234 times ]

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What is the sum of the integers in the table above? [#permalink] New post  06 Jan 2019, 02:18
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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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