Question

If for any natural number $p$ and $q$, $p$ is divided by $q$, then the maximum possible difference between the minimum possible and maximum possible remainder can be?

• A. $p-q$
• B. $p-1$
• C. $q-1$
• D. None of these

Answer 1

Answer: (C)

$q-1$

Solution:- (C) $q-1$

If $q$ divides $p$, i.e.,

$\frac{p}{q}$

Minimum possible remainder $=0$; when $q$ exactly divides $p$.

Maximum possible remainder $=q-1$

$\therefore$ maximum possible difference between the minimum possible and maximum possible remainder $=(q-1)-0=q-1$

Hence the correct answer is $q-1$.