Latest Elitmus Aptitude Question SOLUTION: 7777 books are to be placed in shelves such that the 1st shelf carry 1 book 2nd shelf 3 3rd shelf 6 4th shelf 10 5th shelf 15 books nd so on... how many shelves the books will requ

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(#M40038311) ELITMUS question Keep an EYE

7777 books are to be placed in shelves such that the 1st shelf carry 1 book 2nd shelf 3 3rd shelf 6 4th shelf 10 5th shelf 15 books nd so on... how many shelves the books will require???

Asked In Elitmus Sourav Mitra (9 years ago)

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Saraswathy  (9 years ago)

It should be 7770
1 - 1
3 - (1 + 2)
6 - (1 + 2 + 3)
10 - (1 + 2 + 3 + 4)
.
.
It is of the form n*(n+1)/2
So nth shelf contains n*(n+1)/2 books
Sum of books in all shelf => sum of n*(n+1)/2 terms
Total books = 7770
Sum of n*(n+1)/2 terms = 7770
1/2*sum of [n^2 + n]
Sum of n^2 terms = n(n+1)(2n+1)/6
Sum of n terms = n(n+1)/2
1/2*[n(n+1)(2n+1)/6 + n(n+1)/2] = 7770
n(n+1)(2n+4)/12 = 7770
n(n+1)(2n+4) = 7770*12
n(n+1)(2n+4) = (2*3*5*7*37) * (2*2*3)
n(n+1)(2n+4) = 35(2*2*3*3)(37*2)
So n = 35

Ans : 35

Is this solution Helpfull? Yes (15) | No (1)  

parag  (9 years ago)

1,3,6,10,15---n*(n+1)/2
and the sum of this series is
1,4,10,20,35---n*(n+1)*(n+2)/6
so the number of shelves will be 36 to fill 8436 books.
but I think the question should be '7770 books' so that
'35' shelves will be the answer

Is this solution Helpfull? Yes (2) | No (5)  

raushan kumar  (9 years ago)

the given series is in the form .. (n^2 + n)/2
then sun of(n^2 + n)/2 = 7777. n= 35.

Is this solution Helpfull? Yes (1) | No (4)  

nishant  (9 years ago)

plz confirm that dude wats the total number of book give 7770 or 7777

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