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

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Joined: 02 Sep 2009
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The sum of n consecutive positive integers is 45. What is the value of  [#permalink]

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11 Apr 2018, 08:21
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Difficulty:

75% (hard)

Question Stats:

44% (01:43) correct 56% (01:42) wrong based on 66 sessions

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

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

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Joined: 17 Jan 2017
Posts: 61
The sum of n consecutive positive integers is 45. What is the value of  [#permalink]

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11 Apr 2018, 09:01
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1
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)
Intern
Joined: 28 Apr 2014
Posts: 49
GMAT 1: 640 Q50 V25
Re: The sum of n consecutive positive integers is 45. What is the value of  [#permalink]

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11 Apr 2018, 09:31
St1 gives lot of options
St2: unique set of 1 to 9
IMO B
Senior Manager
Joined: 29 Dec 2017
Posts: 386
Location: United States
Concentration: Marketing, Technology
GMAT 1: 630 Q44 V33
GMAT 2: 690 Q47 V37
GMAT 3: 710 Q50 V37
GPA: 3.25
WE: Marketing (Telecommunications)
The sum of n consecutive positive integers is 45. What is the value of  [#permalink]

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11 Apr 2018, 10:39
1
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

The sum of n consecutive positive integers is 45. What is the value of &nbs [#permalink] 11 Apr 2018, 10:39
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