JAMB 2017 · UTME · Q10

Find $x$ and $y$ respectively in the subtraction below, carried out in base 5.

$\begin{array}{rcccc} & 4 & 2 & 4 & 3 \\ - & 1 & 3 & x & 4 \\ \hline & y & 3 & 4 & 4 \end{array}$

Worked solution (try it first)

Units: $3 - 4$ needs a borrow of 5, and $8 - 4 = 4$ , which matches.
Fives: after lending, the 4 is 3, and $3 - x = 4$ needs another borrow.
So $8 - x = 4$ and $x = 4$ .
Twenty-fives: after lending, the 2 is 1, and $1 - 3$ needs a borrow: $6 - 3 = 3$ , which matches.
Hundred-and-twenty-fives: after lending, the 4 is 3, and $3 - 1 = 2$ , so $y = 2$ .
That is $x = 4$ and $y = 2$ , option C.