Find largest integer x for which another integer n exists with nx = n + 12x

Hi Abhishek,

Rearrange the given equation, and we have:

x(n-12) = n

Or x = n/(n-12).

Now we have to find the largest x --------- (So we will assume x to be positive, since if it is negative, then it cannot be the largest).

So x = n/(n-12).

So we have to maximise n/(n-12).

Now, x = n/(n-12) = 1 + 12/(n-12).

This will clearly be maximum when (n-12) = 1..... ie n = 13.

So the maximum value of x will be 13.

Hope this helps.

Wish you all the best.

Regards,

Ashwin (IIT Madras).

Approved

I thought the maximum value for it will be 12 because:

As  x = n/(n-12)

When n=12, x=12/0=Infinity.......

Thus it should be 12 na?

Satyaram,

No n cant be 12.

Put n=12 in the original eqn,

You will get 12x = 12+12x....

Which is absurd.

Hence x = 13, fon n=13.

Regards,

Ashwin (IIT MadraS).