Consider the following multiplication problem : (PQ)×3 = RQQ, where P, Q and R are different digits and R≠ 0. What is the value of (P+R)÷Q?
1
2
5
Cannot be determined due to insufficient data
PQ × 3 = RQQ Or (10P + Q) × 3 = 100R + 10Q + Q Or 30P + 3Q = 100R + 11Q Or 30P = 100R + 8Q The last digit of 30P will be 0, as well as that of 100R. So, the last digit of 8Q must also be 0. So, the value of Q must be 5. Hence, 30P = 100R + 8Q = 100R + 40 Or 3P = 10R + 4 If R = 1, then P = 14/3 (not an integer) If R = 2, then P = 24/3 = 8 If R = 3, then P = 34/3 (not an integer, and in double digits) So, P = 8, Q = 5, and R = 2 That is, 85 × 3 = 255 So, (P + R)/Q = (8 + 2)/5 = 10/5 = 2
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