Latest Elitmus Aptitude Question SOLUTION: 7880 ball are there of diameter 2 cm, if these ball are arranged in a form of pile such that top has 1 ball,2nd layer has 3,3rd has 6,4th has 10,5 has 10 and so on.how many level

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(#M40037909) ELITMUS Category question Keep an EYE

7880 ball are there of diameter 2 cm, if these ball are arranged in a form of pile such that top has 1 ball,2nd layer has 3,3rd has 6,4th has 10,5 has 10 and so on.how many levels are there.
Options are
a. 34
b. 33
c. 31
d. 32

Asked In Elitmus Gaurav Malhotra (10 years ago)

Unsolved Read Solution (8)

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Read Solution (8) :

puja singh  (10 years ago)

its a series of 1,3,6,10,15,21, so on
here, each term varies in series like +2,+3,+4,+5,+6 so on
so, sum upto n terms i.e. 1+3+6+10+15+21+... upto n terms =7880
here after solving this AP, n= 34

Is this solution Helpfull? Yes (2) | No (6)  

AB  (10 years ago)

are idiot uetion post karne ka man hi hai to thik s post karo naa

Is this solution Helpfull? Yes (1) | No (2)  

Liti  (10 years ago)

@puja

its not in AP, then how to get the sum ?

Is this solution Helpfull? Yes (1) | No   

Arindam Ghosh  (7 years ago)

actually the ques is wrong ..ques is
There are 7880 balls, each with a radius of 2 cm stacked in a pile with 1 ball on top,3 balls in the second layer,6 in the 3rd layer,10 in the fourth and so on, the number of horizontal layers in the pile is ?

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SWATI TANMAYA RATH  (7 years ago)

The given series is this: 1, 3, 6, 10, 15....
Note, every nth term is the sum of first n positive integers i.e. 3rd term is 1+2+3 = 6 and so on.

Therefore t(n) = n(n+1)/2 = (n^2)/2 + n/2
Sum of n terms of this series will be S(n) = ∑t(n) = (1/2)∑n^2 + (1/2) ∑n (summation of the terms)
This gives us S(n) = (1/2) n(n+1)(2n+1)/6 +(1/2)n(n+1)/2
Take n(n+1) common from the two terms and simplify the rest to get S(n) = n(n+1)(n+2)/6

Now n(n+1)(n+2)/6 = 8436
or n(n+1)(n+2) = 8436 x 6
At this point, use options. If n = 34, product of 34, 35, 36 will end in 0, not 6, so not possible.
If n = 36, product of 36,37 and 38 will end in 6. This is the only possibility. None of the other products will end in 6 so answer must be 36.

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farahan  (10 years ago)

we find h.c.f of 7880 so ans is 32.....

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potani manikumar  (10 years ago)

pls explain

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Mithun Kumar Kesari  (10 years ago)

this link help you guys
http://gmatclub.com/forum/sum-of-series-103317.html

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