2010 AMC 8 Problem 2 — Solution | LIVE by Po-Shen Loh

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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.

All problems are used with official legal permission of the Mathematical Association of America (MAA).

2.

If $a * b = \dfrac{a\times b}{a+b}$ for $a,b$ positive integers, then what is $5 *10?$

$\ \dfrac{3}{10}$

$\ 1$

$\ 2$

$\ \dfrac{10}{3}$

$\ 50$

Answer: D

Concepts:custom operation fraction

Difficulty rating: 610

Solution:

Given our definition of $a*b,$ we have $5 *10 = \dfrac{5 \times 10}{5 + 10} = \dfrac{50}{15} = \dfrac{10}{3}.$

Thus, the answer is D .

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