2005 AMC 10A Problem 16

Problem 16 of 25IntermediateNumber Theory Arithmetic

The sum of the digits of a two-digit number is subtracted from the number. The units digit of the result is

6.

How many two-digit numbers have this property?

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Solution

If the number is

10a + b,

then

(10a + b) - (a + b) = 9a.

The units digit of

9a

6

only when

a = 4,

since

9 \cdot 4 = 36.

The digit

b

can then be anything from

0

9,

giving the ten numbers

40

through

49.

Thus, the correct answer is D.

Tagged: digits · place value · units digit