value of n?

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sanju09: GMAT Instructor; Posts: 3650; Joined: Wed Jan 21, 2009 4:27 amFollowed by: 80 members; Location: India; Thanked: 267 times; GMAT Score:760

by sanju09 » Sat Aug 14, 2010 3:02 am

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

(1) n is even.
(2) n < 9.

[spoiler]Source: Picked from some source unknown to www.avenuesabroad.org[/spoiler]

The mind is everything. What you think you become. -Lord Buddha

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Lucknow-226001

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Source: Beat The GMAT — Data Sufficiency | Sat Aug 14, 2010 3:02 am

kvcpk: Legendary Member; Posts: 1893; Joined: Sun May 30, 2010 11:48 pmFollowed by: 7 members; Thanked: 215 times

by kvcpk » Sat Aug 14, 2010 3:49 am

sanju09 wrote:The sum of n consecutive positive integers is 45. What is the value of n?

(1) n is even.
(2) n < 9.

[spoiler]Source: Picked from some source unknown to www.avenuesabroad.org[/spoiler]

n(n+1)/2 = 45
n^2+n-90=0n=-10 or 9

n cannot be -10. hence n=9

(n+10)(n-9)=0

Question doesnt require any of the statements.

I am not sure what to choose in this case.
Probably D.

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don't be afraid of failure and don't abandon it.
People who work sincerely are the happiest."
Chanakya quotes (Indian politician, strategist and writer, 350 BC-275BC)

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HPengineer: Master | Next Rank: 500 Posts; Posts: 165; Joined: Wed Mar 24, 2010 8:02 amFollowed by: 1 member; Thanked: 2 times

by HPengineer » Sat Aug 14, 2010 4:01 am

can you shed some more light on this forumla?

n(n+1)/2 = 45

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kvcpk: Legendary Member; Posts: 1893; Joined: Sun May 30, 2010 11:48 pmFollowed by: 7 members; Thanked: 215 times

by kvcpk » Sat Aug 14, 2010 4:05 am

HPengineer wrote:can you shed some more light on this forumla?

n(n+1)/2 = 45

Sum of first n consecutive positive integers is given by n(n+1)/2

Example: sum of 1,2,3 is 6
Here n=3
By formula: 3(3+1)/2 = 3*2 = 6

Hope this helps!!

Last edited by kvcpk on Sat Aug 14, 2010 4:14 am, edited 1 time in total.

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sanju09: GMAT Instructor; Posts: 3650; Joined: Wed Jan 21, 2009 4:27 amFollowed by: 80 members; Location: India; Thanked: 267 times; GMAT Score:760

by sanju09 » Sat Aug 14, 2010 4:11 am

kvcpk wrote:
HPengineer wrote:can you shed some more light on this forumla?

n(n+1)/2 = 45
Sum of n consecutive positive integers is given by n(n+1)/2

Example: sum of 1,2,3 is 6
Here n=3
By formula: 3(3+1)/2 = 3*2 = 6

Hope this helps!!

The sum of n consecutive positive integers is not always same as the sum of first n consecutive positive integers.

The mind is everything. What you think you become. -Lord Buddha

Sanjeev K Saxena
Quantitative Instructor
The Princeton Review - Manya Abroad
Lucknow-226001

www.manyagroup.com

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kvcpk: Legendary Member; Posts: 1893; Joined: Sun May 30, 2010 11:48 pmFollowed by: 7 members; Thanked: 215 times

by kvcpk » Sat Aug 14, 2010 4:13 am

sanju09 wrote:
kvcpk wrote:
HPengineer wrote:can you shed some more light on this forumla?

n(n+1)/2 = 45
Sum of n consecutive positive integers is given by n(n+1)/2

Example: sum of 1,2,3 is 6
Here n=3
By formula: 3(3+1)/2 = 3*2 = 6

Hope this helps!!
The sum of n consecutive positive integers is not always same as the sum of first n consecutive positive integers.

Dont know How I missed that. Thanks for correcting.

Edited mypost above to HP engineer.

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HPengineer: Master | Next Rank: 500 Posts; Posts: 165; Joined: Wed Mar 24, 2010 8:02 amFollowed by: 1 member; Thanked: 2 times

by HPengineer » Sat Aug 14, 2010 4:17 am

so now i have two formulas to work with when it comes to finding sums etc of consecutive integers??

N(N+1)/2 = sum and N*(avg of set) = sum just apply them accordingly based off the info given in problem stem?

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selango: Legendary Member; Posts: 1460; Joined: Tue Dec 29, 2009 1:28 amFollowed by: 7 members; Thanked: 135 times

by selango » Sat Aug 14, 2010 4:17 am

Praveen,

Its not given sum of first n consecutive integers.

Sum of n consecutive integers.

n is even and n<9

n=2,4,6,8

n=2;22 and 23

n=6;sum of 5 to 10

n=2 and 6 satisfy.

As there are 2 values its Insuff.

Please correct me If I am wrong.

Last edited by selango on Sat Aug 14, 2010 4:46 am, edited 1 time in total.

--Anand--

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kvcpk: Legendary Member; Posts: 1893; Joined: Sun May 30, 2010 11:48 pmFollowed by: 7 members; Thanked: 215 times

by kvcpk » Sat Aug 14, 2010 4:40 am

sanju09 wrote:The sum of n consecutive positive integers is 45. What is the value of n?

(1) n is even.
(2) n < 9.

[spoiler]Source: Picked from some source unknown to www.avenuesabroad.org[/spoiler]

a + a+1 + a+2...a+(n-1) = 45
an+1+2+..n-1 = 45
an + n(n-1)/2 = 45
n(a+ (n-1)/2) = 45
2a+(n-1) = 90/n
n,a are positive integers

n=1, a=45 is possible
n=2, a=22 is possible
n=3, a=14 is possible
n=4, a is not integer
n=5, a=7 is possible
n=6, a=5 is possible
n=7, a i snot integer
n=8, a is not integer
n=9, a=1 is possible

(1) n is even.
n can be either 2 or 6.. INSUFF
(2) n < 9.
7 values of n are possible. INSUFF

Combining:
still n can be either 2 or 6..INSUFF

pick E.

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sanju09: GMAT Instructor; Posts: 3650; Joined: Wed Jan 21, 2009 4:27 amFollowed by: 80 members; Location: India; Thanked: 267 times; GMAT Score:760

by sanju09 » Sat Aug 14, 2010 4:41 am

The sum of n consecutive positive integers is given by n/2 {2 x + n - 1}, where x is the smallest of all positive integers that we don't know. And until we don't know x, we cannot answer n.

We cannot answer n using either statement alone, for sure; but can we fix a value for x, if the two statements are taken together?

[spoiler]I hope NOT

E[/spoiler]

The mind is everything. What you think you become. -Lord Buddha

Sanjeev K Saxena
Quantitative Instructor
The Princeton Review - Manya Abroad
Lucknow-226001

www.manyagroup.com

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kvcpk: Legendary Member; Posts: 1893; Joined: Sun May 30, 2010 11:48 pmFollowed by: 7 members; Thanked: 215 times

by kvcpk » Sat Aug 14, 2010 4:42 am

selango wrote:Praveen,

Its not given sum of first n consecutive integers.

Sum of n consecutive integers.

n is even and n<9

n=2,4,6,8

n=2;22 and 23

n=4;sum of 5 to 10

n=2 and 4 satisfy.

As there are 2 values its Insuff.

Please correct me If I am wrong.

Hi Anand, I misread in the beginning.
I think n=2,6 satisfy. not 2,4.
Check my above post.

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selango: Legendary Member; Posts: 1460; Joined: Tue Dec 29, 2009 1:28 amFollowed by: 7 members; Thanked: 135 times

by selango » Sat Aug 14, 2010 4:47 am

Yes praveen..n=2 and 6 only..typo mistake..edited it..

--Anand--

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