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# If the sum of 9 consecutive integers is 90, what is the sum of the fol

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Math Expert
Joined: 02 Sep 2009
Posts: 58427
If the sum of 9 consecutive integers is 90, what is the sum of the fol  [#permalink]

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28 Sep 2016, 02:56
1
5
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Difficulty:

35% (medium)

Question Stats:

76% (02:19) correct 24% (02:21) wrong based on 127 sessions

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If the sum of 9 consecutive integers is 90, what is the sum of the following 9 consecutive integers?

A. 99
B. 135
C. 145
D. 171
E. 180

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Math Expert
Joined: 02 Aug 2009
Posts: 8006
Re: If the sum of 9 consecutive integers is 90, what is the sum of the fol  [#permalink]

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28 Sep 2016, 03:08
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5
Bunuel wrote:
If the sum of 9 consecutive integers is 90, what is the sum of the following 9 consecutive integers?

A. 99
B. 135
C. 145
D. 171
E. 180

Ways to do it..
1) greatest of each will have a difference of 9 and next greatest too will have a difference of 9 and so on..
Therefore all nine terms will have a term MORE by 9..
Sum =90+(9*9)=171

2) if sum is 90, the average= median=90/9=10..The median of next 9 will be 10+9=19..
And ssum would be 19*9=171

D
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Posts: 55
Location: India
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Re: If the sum of 9 consecutive integers is 90, what is the sum of the fol  [#permalink]

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29 Apr 2019, 23:11
1
Although the methods explained above by Chetan2u are quicker but this is how i approached:

let first term=x then 9th term = x+8

we know, sum = n/2 [first term + last term]
substituting values--->

$$\frac{9}{2}[x+x+8]=90$$ ----> x=6

so the two ends are x=6 and x+8=14

Now the next 9 consecutive integers will lie between 15 and 23

substituting in formula

$$\frac{n}{2}[first + last ] = sum$$

$$\frac{9}{2}[15+23] ----> 171$$ (D)
Re: If the sum of 9 consecutive integers is 90, what is the sum of the fol   [#permalink] 29 Apr 2019, 23:11
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