GMAT Question of the Day - Daily to your Mailbox; hard ones only

 It is currently 20 Nov 2019, 15:01

### GMAT Club Daily Prep

#### Thank you for using the timer - this advanced tool can estimate your performance and suggest more practice questions. We have subscribed you to Daily Prep Questions via email.

Customized
for You

we will pick new questions that match your level based on your Timer History

Track

every week, we’ll send you an estimated GMAT score based on your performance

Practice
Pays

we will pick new questions that match your level based on your Timer History

# If the sum of n (n>1) consecutive positive integers is 75. What is the

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
12
00:00

Difficulty:

95% (hard)

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

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.
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
1
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

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
1
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
2
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)+(n-1)d)/2 * n
d = 1 (consecutive numbers)
S = (2a(1)+n-1)/2 * n = 75
So (2a(1)+n-1)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
GMAT 1: 700 Q50 V33
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
1
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 $$AP = (n/2)[2a+(n-1)d]$$

Now, we have -

$$n (2a+n-1) = 25*6$$

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
GMAT 1: 710 Q50 V34
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
1
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
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+n-1)
second (when d = -1): 150 = n(2a-n+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.
_________________
Thanks for Kudos
Re: If the sum of n (n>1) consecutive positive integers is 75. What is the   [#permalink] 08 Dec 2018, 13:05
Display posts from previous: Sort by