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345X is divisible by 15. What is the value of X?

Question

345X is divisible by 15. What is the value of X?

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Solution

A number is divisible by 15 if it is divisible by both 3 and 5.

  1. Check for divisibility by 3: A number is divisible by 3 if the sum of its digits is divisible by 3. In this case, the sum of the digits is 3+4+5+X = 12+X. For 12+X to be divisible by 3, X could be 0, 3, 6, or 9.

  2. Check for divisibility by 5: A number is divisible by 5 if its last digit is either 0 or 5. So, X could be 0 or 5.

Therefore, considering both conditions, the only possible value for X is 0.

This problem has been solved

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