2010 AMC 8 Problem 2

Attempt Problem 2 of the 2010 AMC 8 below, then check your answer against the professionally curated solution from LIVE by Po-Shen Loh. You can also try the full timed exam, view all 2010 AMC 8 solutions, or check the answer key.

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2.

If a∗b=a×ba+ba \ast b = \dfrac{a\times b}{a+b} for a,a, bb positive integers, then what is 5∗10?5 \ast 10?
 310 \ \dfrac{3}{10}
 1 \ 1
 2 \ 2
 103 \ \dfrac{10}{3}
 50 \ 50
Answer: D
Concepts:custom operationfraction
Small hint:
Reduce 5015\frac{50}{15} after adding the denominator.
Big hint:
Substitute the two given numbers into the definition of a∗ba\ast b.
Solution:
Given our definition of a∗b,a\ast b, we have 5∗10=5×105+10=5015=103.5 \ast 10 = \dfrac{5 \times 10}{5 + 10} = \dfrac{50}{15} = \dfrac{10}{3}.
Thus, the answer is D .
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