Problem: The reciprocal of (12+13)\left(\dfrac{1}{2}+\dfrac{1}{3}\right)(21+31) is
Answer Choices:
A. 16\dfrac{1}{6}61 B. 25\dfrac{2}{5}52 C. 65\dfrac{6}{5}56 D. 52\dfrac{5}{2}25 E. 555
Solution:
12+13=56\dfrac{1}{2}+\dfrac{1}{3}=\dfrac{5}{6}21+31=65 and its reciprocal is 65\dfrac{6}{5}56.
Answer: C\boxed{C}C.
The problems and solutions on this page are the property of the MAA's American Mathematics Competitions