DS question on Sum of consecutive postive integers

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

(1) n is even

(2) n < 9

OA is E. What will be the quickest way to solve this?
Last edited by Auzbee on Wed Jan 02, 2008 5:26 pm, edited 1 time in total.

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by StarDust845 » Tue Jan 01, 2008 7:05 pm
OA must be wrong. I am getting an answer E.

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by samirpandeyit62 » Tue Jan 01, 2008 8:36 pm
I agree with Calista

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

(1) n is even

Now 45 is an odd nos

so if n is even, it must have half even nos & half odd nos which will when summed up will lead to an odd nos, there are many possibilities like 22,23 5,6,7,8,9,10 etc INSUFF

(2) n < 9

again the above possibilities will arise and we can have odd value of n also
as 14,15,16 INSUFF

Combine again n can assume odd as well as even vals below 9 INSUFF

E
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Samir

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by Auzbee » Tue Jan 01, 2008 9:21 pm
Samir, MGMAT explanation is quite long and complex for this question. Attached is their explanation.

Image

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by StarDust845 » Tue Jan 01, 2008 9:37 pm
The sum of n consecutive positive integers is 45. What is the value of n?

(1) n is even

(2) n < 9


22 + 23 = 45; here n = 2 which is even and less than 9.
5+6+7+8+9+10 = 45; here n = 6 which is even and less than 9.

Simple. Answer must be E and hence MGMAT is wrong.

Calista.

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by sirikesav » Wed Jan 02, 2008 6:12 am
The Most easy way to solve this equation is
1) as the elements are consecutive integer they are in AP

hence Sum of n consecutive elements is = a(2a+n-1)/2

Hence we can form the Equation as
a(2a+n-1)/2 = 45

Where a--- the First integer in the series.
n-- no of integers in the series.

as it is equation of two variables unless you get the value of the a we can solve the problems.Hence both the conditions are insufficient.

E
Hope this will help you understand easily

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by StarDust845 » Wed Jan 02, 2008 10:30 am
Auzbee,

I checked the MGMAT explanation just now, they too say that the answer is E.

However in your first post, you gave the OA as D.

That's why this confusion.

Calista.

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by Auzbee » Wed Jan 02, 2008 5:26 pm
[quote]Auzbee,

I checked the MGMAT explanation just now, they too say that the answer is E.

However in your first post, you gave the OA as D.

That's why this confusion.
[/quote]
My apologies for being in a haste while replying. Let me correct my previous post on this thread.