Question

IN this multiplication problem each letter P, Q and R represents a different digit. What 3 digit number is represented by PQR?

PQR x 3 = QQQ

3xPQR = QQQ = Qx111 ---->

PQR = 37 Q ---->

P0R = 27 Q

You know that 25x4 = 100, so you could try Q = 4, beause you ten get a number slightly larger than 100 which will probably have a zero as the second digit:

27 x 4 = 108

So, Q = 4 and we see that P = 1 and
R = 8.

Answer 1

Since the rightmost digit of the product is always the rightmost digit of the multiplier, R must be 3.
Then $QQQ$ must be divisible by 3, so $Q$ must be one of ${3,6,9}$.
Since $QQQ$ is divisible by 9, $Q=9$.
Then the leftmost digit of the product is the leftmost digit of the multiplier, which is $P$.
Finally, $PQR=\boxed{903}$.