Latest TCS Aptitude Question SOLUTION: What is the greatest positive integer n for which n3 + 102 is divisible by n + 10?

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What is the greatest positive integer n for which n3 + 102 is divisible by n + 10?

Asked In TCS mauu (10 years ago)

Solved saranya sankar Read Solution (12)

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Read Solution (12) :

Praveen Vaishnav  (10 years ago)

By division we find that n^3 + 102 = (n + 10) (n^2 - 10n + 100) - 898. Thus, if n + 10 divides n^3 + 102, then it must also divide 898. Moreover, since n is maximized whenever n + 10 is, and since the largest divisor of 898 is 898, we must have n+10 = 898. Therefore, n = 888.

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saranya sankar  (10 years ago)

We can apply the remainder theorem, which is when f(x) is divided by (x-a) the remainder will be f(a)

So, when n ^ 3 is divided by n+10, which is (n-(-10), the remainder will be
(-10) ^ 3 + 102 = -898

So, the remainder is -898, if the number is 898 or a factor of it, the entire expression is divisible .

So, the possible valus of (n+10) is 898
So, the possible values of n is 888

So, the maximum possible value of n is 260

Answer is 888

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navin  (10 years ago)

the greatest will be 4.

Is this solution Helpfull? Yes (2) | No (4)  

Shivangi Nagar  (10 years ago)

answer is 887.....
here after dividing (n^3+102)by n+10 we get
quotient=n^2-10n+100 and remainder as =-898
there fore n+10>-898
by solving this...we get
n+10

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ravi   (10 years ago)

(n^3+102)/n+10=(n^2-10n+100)-898/n+10
so to divide 898 by n+10 maximum integer value of n should be 888

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mounica.jallipalli  (10 years ago)

n value is 2

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Arun Menariya  (10 years ago)

ans is 62.

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mounica.jallipalli  (10 years ago)

sorry it is 62

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Amlan Mohanty  (10 years ago)

Mr Praveen is absolutely correct.

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jaya akula  (10 years ago)

is that 3n or n^3..??

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jaya akula  (10 years ago)

mounica can u explain

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sonali soni  (10 years ago)

Which one is correct.. pls explain...

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