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2003 AMC 10A Problem 15

Problem 15 of 25IntermediateNumber TheoryCounting & Probability

What is the probability that an integer in the set {1,2,3,…,100}\{1, 2, 3, \ldots, 100\} is divisible by 22 and not divisible by 3?3?

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Solution

Of the 100100 integers, 5050 are divisible by 2.2. Among those, the ones also divisible by 33 are the multiples of 6,6, of which there are 16.16. So 50−16=3450 - 16 = 34 qualify, giving probability 34100=1750.\dfrac{34}{100} = \dfrac{17}{50}. Thus, the correct answer is C.

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Concepts: basic probability · multiple · counting integers in a range

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