If the number 756534P57Q is divisible by 72, then find the value of 2P + Q.
18
The correct answer is 18.
Other common composite divisors include 6 (check divisibility by 2 and 3), 12 (check by 3 and 4), 15 (check by 3 and 5), etc. In this problem, applying the divisibility rule of 8 first helped narrow down the possible value of Q quickly, which then made it easier to find P using the divisibility rule of 9. This systematic approach is useful for solving such problems involving unknown digits in large numbers.
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