What is the value of positive integer N? (1) Sum of N consecutive po

Question

What is the value of positive integer N?

(1) Sum of N consecutive positive integers is 90.

(2) 5 < N < 10.

u1983 · Accepted Answer

(1) Sum of N consecutive positive integers is 90. ==> what ever odd number divides 90 completely...in other words all odd factors of 90. N=1 ... the only one is 90 .... as we require consequtive int ... this is not a valid case N=3 .....the set is 29,30,31 N=5 .....the set is 16,17,18,19,20 N=9 ........the set is 6,7,8,9,10,11,12,13,14 N=15 ........the set is 1-,0,1,2,3,4,5,6,7,8,9,10,11,12,13...and so on ........................(NS) (2) 5 < N < 10 ===> N= 6 or 7 or 8 or 9 .......................................(NS) (1) + (2) ==> the only possible case is N=9 ........the set is 6,7,8,9,10,11,12,13,14...................(S) Thus I would go for option C .

ColumbiaEMBA · Answer

Still not seeing the OA for this, but my guess is C. I chose A first, but I realized that there are 2 sets of integers that add to 90.

1:
2 + 3 + 4 + 5 + 6 + 7 + 8 + 9 + 10 + 11 + 12 + 13 (N = 12)

2: 
6 + 7 + 8 + 9 + 10 + 11 + 12 + 13 + 14 (N = 9)

We need (b) to arrive at 1 answer.

I'm sure there is a better way to do this, but I'm lost. Any advice?

pushpitkc · Answer

Hey  strivingFor800

The easiest way to find out the various combinations with sum = 90 is as follows: 
Since  90 = 2*3^2*5 , the various factors possible are 1,2,3,5,6,9,10,15,18,30,45,90

For the even number of consecutive integers, the mean/median is the average of the two 
middle integers - which cannot be an integer.

For an odd number of consecutive integers, we will have a middle term that is an integer.
If N = 9, the middle term has a value of  \frac{90}{9} = 10  
The consecutive terms are from 6 to 14(9 in number with 10 as the middle term)

If N = 15, the middle term has a value of  \frac{90}{15} = 6  
The consecutive terms are from -1 to 13(15 in number with 6 as the middle term)

1. N could be 3 - 29,30,31(which adds up to give us 90)
N could be 9 - 6,7,8,9,10,11,12,13,14(again adds up to give us 90)  (Insufficient)

2. 5 < N < 10. N could take values 6,7,8,or 9.  (Insufficient)

Combining the information from both the statements and testing the other 
values(N=6,7,8) we have a unique value of N.  (Sufficient - Option C)

akadiyan · Answer

What is the value of positive integer N?

(1) Sum of N consecutive positive integers is 90 - Insufficient - We could have more than one set of numbers that could yield 90.

(2) 5 < N < 10 = N = 6,7 or 8. More than 1 value - Insufficient.

Both (1) and (2) together - we have unique value of N.

Ans:   C

push12345 · Answer

Here is my approach

I) instead of counting or calculating let's do it other way

90=2*3*3*5

Now if we make pairs
Eg 15*6 means 6 numbers will give 90 i.e. N=6 whose average is 15 which will ultimately give 90.

So all pairs
15*6. N=6
18*5. N=5
30*3. N=3
45*2. N=2
90*1. N=1

We are not concerned the value of numbers as we are only concerned with value of N
So multiple values so Insufficient

II) n ranges from 6 to 9
Insufficient

Combining both
Only N=6 qualify

C is answer

Give kudos if it helps

Posted from my mobile device

@s · Answer

Hi Pushpitkc

i understood the solution provided by you. But i was thinking even sum of 90 can have 4 consecutive numbers (21, 22, 23, 24) which is even. So, in that case, how can we be sure that it is only an odd number.

Thank you.

pushpitkc · Answer

Hi  @s

The answer to this problem is Option C meaning that both statements are needed to answer the question. Statement 2 says that N is a value between 5 and 10. That's the reason the case you have presented does not work.

Hope this helps you!

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What is the value of positive integer N? (1) Sum of N consecutive po

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