## DS question on Sum of consecutive postive integers

##### This topic has expert replies
Senior | Next Rank: 100 Posts
Posts: 77
Joined: 09 Jul 2007
Location: US of A

### DS question on Sum of consecutive postive integers

by Auzbee » Mon Dec 31, 2007 7:53 pm
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.

Master | Next Rank: 500 Posts
Posts: 158
Joined: 03 Dec 2007
Thanked: 7 times
by StarDust845 » Tue Jan 01, 2008 7:05 pm
OA must be wrong. I am getting an answer E.

Master | Next Rank: 500 Posts
Posts: 460
Joined: 25 Mar 2007
Thanked: 27 times
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
Regards
Samir

Senior | Next Rank: 100 Posts
Posts: 77
Joined: 09 Jul 2007
Location: US of A
by Auzbee » Tue Jan 01, 2008 9:21 pm
Samir, MGMAT explanation is quite long and complex for this question. Attached is their explanation. Master | Next Rank: 500 Posts
Posts: 158
Joined: 03 Dec 2007
Thanked: 7 times
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.

Junior | Next Rank: 30 Posts
Posts: 22
Joined: 28 Nov 2007
Thanked: 3 times
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

Master | Next Rank: 500 Posts
Posts: 158
Joined: 03 Dec 2007
Thanked: 7 times
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.

Senior | Next Rank: 100 Posts
Posts: 77
Joined: 09 Jul 2007
Location: US of A
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.

• Page 1 of 1