Author 
Message 
TAGS:

Hide Tags

Intern
Joined: 08 Apr 2018
Posts: 4

If the sum of n (n>1) consecutive positive integers is 75. What is the
[#permalink]
Show Tags
Updated on: 21 May 2018, 12:56
Question Stats:
31% (02:57) correct 69% (02:41) wrong based on 153 sessions
HideShow timer Statistics
If the sum of n(n>1) consecutive positive integers is 75. What is the sum of all possible values of n? 1. 5 2. 10 3. 16 4. 26 5. 50
Official Answer and Stats are available only to registered users. Register/ Login.
Originally posted by nitingmat2018 on 21 May 2018, 09:51.
Last edited by pushpitkc on 21 May 2018, 12:56, edited 2 times in total.
OA added



Manager
Joined: 06 May 2018
Posts: 57

Re: If the sum of n (n>1) consecutive positive integers is 75. What is the
[#permalink]
Show Tags
21 May 2018, 10:32
I just "see" 4 different variations. Therefore I would go with A, but I am missing a proper explanation. Pls help.



VP
Joined: 07 Dec 2014
Posts: 1221

If the sum of n (n>1) consecutive positive integers is 75. What is the
[#permalink]
Show Tags
Updated on: 21 May 2018, 13:14
nitingmat2018 wrote: If the sum of n (n>1) consecutive positive integers is 75. What is the sum of all possible values of n?
1. 5 2. 10 3. 16 4. 26 5. 50 start with 2 terms 75/2=37.5 median 2 terms are 37,38 with 3 terms, median will be 25, so terms are 24,25,26 for 5 terms, median will be 15, so terms are 13,14,15,16,17 6 terms are 10,11,12,13,14,15 2+3+5+6=16=sum of all possible values of n  oops! missed the 10 term sequence thank you, pushpitkc
Originally posted by gracie on 21 May 2018, 12:46.
Last edited by gracie on 21 May 2018, 13:14, edited 2 times in total.



Senior PS Moderator
Joined: 26 Feb 2016
Posts: 3308
Location: India
GPA: 3.12

If the sum of n (n>1) consecutive positive integers is 75. What is the
[#permalink]
Show Tags
21 May 2018, 12:59
nitingmat2018 wrote: If the sum of n(n>1) consecutive positive integers is 75. What is the sum of all possible values of n?
1. 5 2. 10 3. 16 4. 26 5. 50 n=2  Terms are 37,38 n=3  Terms are 24,25,26 n=5  Terms are 13,14,15,16,17 n=6  Terms are 10,11,12,13,14,15 n=10  Terms are 3,4,5,6,7,8,9,10,11,12 Therefore, the sum of all possible values of n are 2+3+5+6+10 = 26(Option D)
_________________
You've got what it takes, but it will take everything you've got



Director
Joined: 02 Oct 2017
Posts: 715

Re: If the sum of n (n>1) consecutive positive integers is 75. What is the
[#permalink]
Show Tags
22 May 2018, 09:07
I like "pushpitkc" approach n=2  Terms are 37,38 n=3  Terms are 24,25,26 n=5  Terms are 13,14,15,16,17 n=6  Terms are 10,11,12,13,14,15 n=10  Terms are 3,4,5,6,7,8,9,10,11,12 Therefore, the sum of all possible values of n are 2+3+5+6+10 = 26(Option D) But is There any other way we can deduce the same without making cases Posted from my mobile device
_________________
Give kudos if you like the post



Senior Manager
Joined: 26 Jun 2017
Posts: 397
Location: Russian Federation
Concentration: General Management, Strategy
WE: Information Technology (Other)

Re: If the sum of n (n>1) consecutive positive integers is 75. What is the
[#permalink]
Show Tags
01 Jun 2018, 14:13
nitingmat2018 wrote: If the sum of n(n>1) consecutive positive integers is 75. What is the sum of all possible values of n?
1. 5 2. 10 3. 16 4. 26 5. 50 Formula for sum of arithmetic progression is: S = (a(1) +a(n)/2)*n = (2a(1)+(n1)d)/2 * n d = 1 (consecutive numbers) S = (2a(1)+n1)/2 * n = 75 So (2a(1)+n1)n = 150 a(1)  positive and n is divisable by 150. By checking we can see that fit next values for n: 2, 3, 5, 6, 10 Sum of these values  26  answer D



Director
Joined: 31 Jul 2017
Posts: 510
Location: Malaysia
GPA: 3.95
WE: Consulting (Energy and Utilities)

Re: If the sum of n (n>1) consecutive positive integers is 75. What is the
[#permalink]
Show Tags
02 Jun 2018, 09:16
nitingmat2018 wrote: If the sum of n(n>1) consecutive positive integers is 75. What is the sum of all possible values of n?
1. 5 2. 10 3. 16 4. 26 5. 50 Sum of an \(AP = (n/2)[2a+(n1)d]\) Now, we have  \(n (2a+n1) = 25*6\) So, n can be 2,3,5,6,10.
_________________
If my Post helps you in Gaining Knowledge, Help me with KUDOS.. !!



Intern
Joined: 02 Apr 2018
Posts: 20
GPA: 3.51

Re: If the sum of n (n>1) consecutive positive integers is 75. What is the
[#permalink]
Show Tags
02 Jun 2018, 10:07
I would solve it this way:
Since we need sum of n positive consecutive number to get 75, I can write it as:
n*k + n(n+1)/2 = 75
If I start putting n =1,2,3..., I should get k as integer.
K in integer for n = 2,3,5,6 and 10
So, the sum is 26



Director
Status: Manager
Joined: 27 Oct 2018
Posts: 726
Location: Egypt
Concentration: Strategy, International Business
GPA: 3.67
WE: Pharmaceuticals (Health Care)

Re: If the sum of n (n>1) consecutive positive integers is 75. What is the
[#permalink]
Show Tags
08 Dec 2018, 13:05
nitingmat2018 wrote: If the sum of n(n>1) consecutive positive integers is 75. What is the sum of all possible values of n?
1. 5 2. 10 3. 16 4. 26 5. 50 In my opinion, to find the number of available sequences, we have to remember 2 possibilities: first is ascending consecutive positive integers (where d = 1), second is descending consecutive positive integers (where d = 1). In this case, we have 2 equations: first(when d = 1): 150 = n(2a+n1) second (when d = 1): 150 = n(2an+1) from each equation, n = 2+3+5+6+10 = 26 so the sum = 26*2 = 52 which is not one of the mentioned answers in the question.
_________________




Re: If the sum of n (n>1) consecutive positive integers is 75. What is the
[#permalink]
08 Dec 2018, 13:05






