Competition problem — Algebra — Maths Olympiad Prep

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Algebra Difficulty 2.7 Junior Find the answer

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

Pick one

Solution

$\dfrac{2+4+6}{1+3+5} - \dfrac{1+3+5}{2+4+6} = \dfrac{12}{9} - \dfrac{9}{12} = \dfrac{4}{3} - \dfrac{3}{4} = \boxed{\dfrac{7}{12}\; \textbf{(C)}}$

Note: This exact problem was reused in 2013 AMC 10B:
https://artofproblemsolving.com/wiki/index.php/2013_AMC_10B_Problems/Problem_1

Want a route through all this instead of an archive? The track puts 2,000 problems in a working order, from AMC 10 level to the IMO shortlist.

Source: NuminaMath-1.5, licensed Apache-2.0. Statement and solution reproduced as published; topic and difficulty added by this site.