What is the value of the following expression? (2+4+6)/(1+3+5) - (1+3+5)/(2+4+6)

2013 AMC 10B Problem 1 — Solution

2013 AMC 10B Problem 1

Attempt Problem 1 of the 2013 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 2013 AMC 10B solutions, or check the answer key.

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What is the value of the following expression? $\frac{2+4+6}{1+3+5} - \frac{1+3+5}{2+4+6}$

$-1$

$\dfrac{5}{36}$

$\dfrac{7}{12}$

$\dfrac{49}{20}$

$\dfrac{43}{3}$

Answer: C

Concepts:fraction

Difficulty rating: 560

Small Hint:

Compute the even and odd sums separately

Big Hint:

Convert both fractions to a common denominator after simplifying

Solution:

$\begin{aligned} &\frac{2+4+6}{1+3+5} - \frac{1+3+5}{2+4+6} \\ \ &= \dfrac {12}9 - \dfrac 9{12} \\ &= \dfrac 43 - \dfrac 34 \\ &= \dfrac 7{12} \end{aligned}$

Thus, the correct answer is C.

Full Exam

Problem 2#2

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