WAEC 2020 · Paper 1 · Q6

If $101_{\text{two}} + 12_y = 23_{\text{five}}$ , find the value of $y$ .

Worked solution (try it first)

Change to base ten: $101_{\text{two}} = 4 + 1 = 5$ and $23_{\text{five}} = 10 + 3 = 13$ .
In base $y$ , $12_y = y + 2$ , so $5 + y + 2 = 13$ .
So $y + 7 = 13$ and $y = 6$ , option C.