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Problem 200

AMC 10/12, early questions

Number theory Difficulty 3.8 Find the answer South African Mathematics Olympiad · South Africa

One of the factors of $48$ is chosen at random. What is the probability that the chosen factor is NOT a multiple of $4$ ?

(A) $40\%$
(B) $30\%$
(C) $25\%$
(D) $20\%$
(E) $10\%$

Your answer

Official solution

There are ten factors: $1$ , $2$ , $3$ , $4$ , $6$ , $8$ , $12$ , $16$ , $24$ , $48$ . Four of them are not multiples of $4$ , viz. $1$ , $2$ , $3$ , $6$ . The probability is therefore $\frac{4}{10}$ or $40\%$ .

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