Question

Find the largest integer x for which another integer n exists with nx = n + 12x.
a. 15
b. 17
c. 13
d. 10

Answer 1

Given:

nx = n + 12x.

To find:

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

Solution:

From given, we have,

nx = n + 12x

upon rearranging the given equation, we get,

nx - 12x = n

x (n - 12) = n

x = n / (n - 12).

now we have to find the largest x,

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.

Option c. 13 is correct.