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The sum of n consecutive positive integers is 45. What is the value of

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The sum of n consecutive positive integers is 45. What is the value of [#permalink]

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New post 11 Apr 2018, 09:21
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  45% (medium)

Question Stats:

58% (00:53) correct 42% (01:42) wrong based on 24 sessions

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The sum of n consecutive positive integers is 45. What is the value of [#permalink]

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Bunuel wrote:
The sum of n consecutive positive integers is 45. What is the value of n?

(1) n is odd
(2) n >= 9


Five ways to get 45 out of consecutive integers.
n=2: 22+23
n=3: 14+15+16
n=5: 7+8+9+10+11
n=6: 5+6+7+8+9+10
n=9: 1+2+3+4+5+6+7+8+9

(1) n=3, n=5, n=9
INSUFFICIENT

(2) n=9 remains
SUFFICIENT

Ans. (B)
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Re: The sum of n consecutive positive integers is 45. What is the value of [#permalink]

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New post 11 Apr 2018, 10:31
St1 gives lot of options
St2: unique set of 1 to 9
IMO B
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The sum of n consecutive positive integers is 45. What is the value of [#permalink]

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New post 11 Apr 2018, 11:39
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Bunuel wrote:
The sum of n consecutive positive integers is 45. What is the value of n?

(1) n is odd
(2) n >= 9


S = ( a(1)+a(n) )*n / 2 ==> 2a(1) + n - 1 = 90/n ==> a(1)= (90/n-n+1)/2


1)n is odd.

If n=5, then a(1)= (90/5-5+1)/2 = 7, check 7+8+9+10+11 = 45

If n=9, then a(1)= (90/9-9+1)/2 = 1, check 1+2+3+4+5+6+7+8+9 = 45 (NOT SUFF)

2)n >= 9

If n=9, then a(1)= (90/9-9+1)/2 = 1, check 1+2+3+4+5+6+7+8+9 = 45

If n=10, then a(1)= (90/10-10+1)/2 = 0, but a(1)>0 (SUFF)
For other n>9 a(1) will be <0, which contradicts our condition a(1)>0

Answer (B)
The sum of n consecutive positive integers is 45. What is the value of   [#permalink] 11 Apr 2018, 11:39
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