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

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)

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

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

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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.

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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