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value of n?

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value of n?

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]
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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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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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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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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



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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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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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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.
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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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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]
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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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by selango » Sat Aug 14, 2010 4:47 am
Yes praveen..n=2 and 6 only..typo mistake..edited it..
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