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jmc

number theory junior

Problem

The hundreds digit of a three-digit number is more than the units digit. The digits of the three-digit number are reversed, and the result is subtracted from the original three-digit number. What is the units digit of the result?
(A)
(B)
(C)
(D)
(E)
Solution
Let the hundreds, tens, and units digits of the original three-digit number be , , and , respectively. We are given that . The original three-digit number is equal to . The hundreds, tens, and units digits of the reversed three-digit number are , , and , respectively. This number is equal to . Subtracting this expression from the expression for the original number, we get . Thus, the units digit in the final result is
Final answer
E