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AMC10 2013b Test Paper
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Sample Question 20:

The number 20132013 is expressed in the form 2013=a1!a2!am!b1!b2!bn!,2013=\frac{a_1!a_2!\cdots a_m!}{b_1!b_2!\cdots b_n!}, where a1a2ama_1\ge a_2\ge\cdots\ge a_m and b1b2bnb_1\ge b_2\ge\cdots\ge b_n are positive integers and a1+b1a_1+b_1 is as small as possible. What is a1b1|a_1-b_1|?

(A) 1(B) 2(C) 3(D) 4(E) 5\textbf{(A)}\ 1\qquad\textbf{(B)}\ 2\qquad\textbf{(C)}\ 3\qquad\textbf{(D)}\ 4\qquad\textbf{(E)}\ 5




Answer Keys

Question 20: B