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# In a sequence of 8 consecutive integers, how much greater is the sum

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In a sequence of 8 consecutive integers, how much greater is the sum  [#permalink]

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17 Jul 2017, 07:59
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In a sequence of 8 consecutive integers, how much greater is the sum of the last four integers than the sum of the first four integers?

A. 12
B. 14
C. 16
D. 18
E. 20

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Re: In a sequence of 8 consecutive integers, how much greater is the sum  [#permalink]

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17 Jul 2017, 08:04
1
susheelh wrote:
In a sequence of 8 consecutive integers, how much greater is the sum of the last four integers than the sum of the first four integers?

A. 12
B. 14
C. 16
D. 18
E. 20

hi..
1st of the first four would be 4 more ta 1st of last four...
similarly 2nd will be 4 more than 2nd of last four..

four terms with each more by 4..
so total sum more by 4*4=16
C
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In a sequence of 8 consecutive integers, how much greater is the sum  [#permalink]

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17 Jul 2017, 14:43
1
susheelh wrote:
In a sequence of 8 consecutive integers, how much greater is the sum of the last four integers than the sum of the first four integers?

A. 12
B. 14
C. 16
D. 18
E. 20

Method I - sum consecutive integers

$$\frac{[(first term) + (last term)](n)}{2}$$

Sum of first four:
$$\frac{[(x) + (x+3)](4)}{2}$$ =

2(2x + 3)=

4x + 6

Sum of last four:
$$\frac{[(x+4) + (x+7)](4)}{2}$$=

2(2x +11) =

4x + 22

Difference
4x + 22 - (4x + 6) = 16

Method II - use numbers
1, 2, 3, 4, 5, 6, 7, 8

Sum of first four: 10
Sum of last four: 26

Difference: 26 - 10 = 16

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Re: In a sequence of 8 consecutive integers, how much greater is the sum  [#permalink]

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17 Jul 2017, 15:28
1
susheelh wrote:
In a sequence of 8 consecutive integers, how much greater is the sum of the last four integers than the sum of the first four integers?

A. 12
B. 14
C. 16
D. 18
E. 20

sum of first four integers=4x+6
sum of last four integers=4x+22
(4x+22)-(4x+6)=16
C
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Re: In a sequence of 8 consecutive integers, how much greater is the sum  [#permalink]

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15 Mar 2018, 16:20
Or even simpler, realize that each of the 4 numbers is 4 more than its counterpart in the first half and there are 4 of them so the answer is 4*4
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Re: In a sequence of 8 consecutive integers, how much greater is the sum  [#permalink]

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30 Mar 2018, 11:26
susheelh wrote:
In a sequence of 8 consecutive integers, how much greater is the sum of the last four integers than the sum of the first four integers?

A. 12
B. 14
C. 16
D. 18
E. 20

We can let the first 4 numbers be 1, 2, 3, and 4, and the last 4 be 5, 6, 7, and 8, thus the difference is:

26 - 10 = 16

Generally, we see that if the first 4 numbers are a, b, c, and d, the next 4 numbers will be (a + 4), (b + 4), (c + 4), and (d + 4). The sum of the first four numbers is (a + b + c+ d), and the sum of the next four numbers is (a + b + c + d + 16). Thus, the sum of the second group of four numbers is 16 greater than the sum of the first four numbers.

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Re: In a sequence of 8 consecutive integers, how much greater is the sum &nbs [#permalink] 30 Mar 2018, 11:26
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