What is (2+4+6)/(1+3+5) - (1+3+5)/(2+4+6) ?

2011 AMC 10B Problem 1 — Solution

2011 AMC 10B Problem 1

Attempt Problem 1 of the 2011 AMC 10B 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 2011 AMC 10B solutions, or check the answer key.

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What is $\dfrac{2+4+6}{1+3+5} - \dfrac{1+3+5}{2+4+6} ?$

$-1$

$\dfrac{5}{36}$

$\dfrac{7}{12}$

$\dfrac{147}{60}$

$\dfrac{43}{3}$

Answer: C

Concepts:fraction order of operations

Difficulty rating: 660

Solution:

Simply solving directly: $\begin{align*} &\dfrac{2+4+6}{1+3+5} - \dfrac{1+3+5}{2+4+6} \\ &= \dfrac{12}9 - \dfrac 9{12} \\ &= \dfrac {16}{12} - \dfrac 9{12} \\ &=\dfrac 7{12}.\end{align*}$

Thus, the correct answer is C .

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