Question

$x$ is an integer such that it leaves a remainder of $2$ when divided by $3$, leaves a remainder of $3$ when divided by $5$, and leaves a remainder of $5$ when divided by $7$. What could be a possible value of $x$ from among the following options?

• A. $53$
• B. $68$
• C. $74$
• D. $83$

Answer 1

The correct option is B $68$

When positive integer $x$ is divided by $3$ it leaves $2$

$\therefore x=3q+2$ .....(1)

When positive integer $x$ is divided by $5$ it leaves $$

$\therefore x=5q+3$ .......(2)

When positive integer $x$ is divided by $7$ it leaves $5$

$\therefore x=7q+5$ ........(3)

On substituting $x=68$ it satisfies all the three equations.

Hence,$x=68$.