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imc

number theory intermediate

Problem

The sum of the digits of a two-digit number is subtracted from the number. The units digit of the result is . How many two-digit numbers have this property?
(A)
(B)
(C)
(D)
Solution
Let the number be where and are the tens and units digits of the number. So must have a units digit of This is only possible if , so is the only way this can be true. So the numbers that have this property are . Therefore the answer is
Final answer
D