JAMB 2000 · UME · Q10

Number bases

If $P344_6 - 23P2_6 = 2PP2_6$ , find the value of the digit $P$ .

Worked solution (try it first)

Units: $4 - 2 = 2$ , which matches.
Sixes: $4 - P$ must end in $P$ .
Without a borrow, $4 - P = P$ gives $P = 2$ .
But then the 36s column is $3 - 3 = 0$ , not 2, so that fails.
With a borrow of 6: $10 - P = P$ (in base ten), so $P = 5$ .
Check the 36s: $2 + 6 - 3 = 5$ , and the 216s: $4 - 2 = 2$ .
Both match.
So $P = 5$ , option D.

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