Question

If $a$ and $b$ are positive integers, $x$ and $y$ are non negative integers and $a=bx+y$, then which one of the following is correct?

• A. $0\le y<a$
• B. $0<y\le b$
• C. $0<y<a$
• D. $0\le y<b$

Answer 1

The correct option is C $0<y<a$

$a\ge 0$ & $b\ge 0$

Also, $x>0$ & $y>0$ (given)

It is given that $a=bx+y$

$\Rightarrow a>b,a>x$ & $a>y$ ($\because a,b,c,d$ are all positive)

But, $y>0$

Therefor, $0<y<a$