AMC 8 Daily Practice Round 2
Complete problem set with solutions and individual problem pages
The thousands digit of a four-digit number is less than the ones digit. Then reverse all the digits of the four-digit number to get a new number. Then we subtract the original number from the new four-digit number. What is the ones digit of the result after subtraction?
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Method1: Let the thousands, hundreds, tens, and ones digits of the original four-digit number be , , , and respectively. We are given that . The original four-digit number is equal to . The thousands, hundreds, tens and ones digits of the reversed four-digit number are , , , and , respectively. This number is equal to . Subtracting the original expression from the new one, we get. Thus, the ones digit in the final result is .
Method2:The result must hold for any four-digit number with thousands digit being less than the ones digit. is such a number. Evaluating we get . Thus, the ones digit in the final result is .
