Question

When a number is divided by $13$, the remainder is $11$. When the same number is divided by $17$, then remainder is $9$. What is the number?

• A. $339$
• B. $349$
• C. $369$
• D. Data inadequate

Answer 1

The correct option is B $349$

$x=13p+11$ and $x=17q+9$
$\therefore$ $13p+11=17q+9$
$\Rightarrow$ $17q-13p=2$
$\Rightarrow$ $q=\frac{2+13p}{17}$
The least value of $p$ for which $q=\frac{2+13p}{17}$ is a whole number is $p=26$
$\therefore$ $x=(13\times 26+11)$
$=(338+11)$
$=349$