Maths Olympiad Prep

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Algebra Difficulty 3.8 AMC 10/12 Find the answer Italy

How many two-digit numbers are there such that, if you subtract the sum of the digits from the original number, you get 45?

Pick one

Solution

The answer is (D). A number that has aa as the tens digit and bb as the units digit can be expressed as 10a+b10a + b; the exercise asks to count the two-digit numbers for which 10a+b(a+b)=4510a + b - (a + b) = 45, that is, such that 9a=459a = 45. Such numbers are all those that have 5 as the tens digit: the integers from 50 to 59, which are 10.

Want a route through all this instead of an archive? The track puts 2,000 problems in a working order, from AMC 10 level to the IMO shortlist.

Source: MathNet, licensed CC-BY-4.0. Statement translated into English from it; metadata (topic, difficulty) added by this project.