Question

A $5$- digit number $xy235$ is divisible by $3$ such that $x+y<5$, where $x$ and $y$ are digits , then possible values of $(x,y)$ are ___ .

• A. $(1,1)$ or $(4,0)$
• B. $(1,1)$ or $(2,0)$
• C. $(1,1)$ or $(0,2)$
• D. $(2,0)$ or $(0,2)$

Answer 1

Answer: (B)

$(1,1)$ or $(2,0)$

Given number is $xy235$

For it to be divisible by $3,$ sum of its digits should be divisible by $3$

$\Rightarrow$ $x+y+2+3+5$ $=x+y+10$ is divisible by $3$

Also, $x+y$ $<5$

$\Rightarrow$ $x+y$ $=2$

$\Rightarrow$ Possible sets of $(x,y)$ are $(1,1)$ or $(2,0)$.