What is the smallest positive single-digit integer x such that the five-digit number 56x42 is divisible by 9?
Answer and explanation
Correct answer: A. 1
- Step 1: A number is divisible by 9 if and only if the sum of its digits is divisible by 9. Step 2. Sum of digits: 5 + 6 + x + 4 + 2 = 17 + x. The smallest single digit making 17 + x a multiple of 9 (18) is x = 1. Answer: 1. Why not the others: 2 gives sum 19; 0 gives sum 17; 4 gives sum 21 (divisible by 3 but not 9).
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