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 ?
339
349
369
Data inadequate
Explanation:
$ x $ = 13$ p $ + 11 and $ x $ = 17$ q $ + 9
$\therefore$ 13$ p $ + 11 = 17$ q $ + 9
$\Rightarrow$ 17$ q $ - 13$ p $ = 2
$\Rightarrow$ q=$ \dfrac{2 + 13p}{17} $
The least value of $ p $ for which q =$\dfrac{2 + 13 p }{17}$ is a whole number is $ p $ = 26
$\therefore x $ = $ \left(13 \times 26 + 11\right)$
= 338 + 11
= 349