What is the value of\[Z\]?
A) \[1\frac{17}{60}\]
B) \[1\frac{7}{12}\]
C) \[2\frac{47}{60}\]
D) \[3\frac{47}{60}\]
Correct Answer: C
Solution :
Observing the given pattern, we find that the two fractions in a row add up to the one on its top row \[i.e.,\]\[\frac{1}{2}+\frac{1}{4}=\frac{3}{4}\]and\[\frac{1}{4}+\frac{1}{5}=\frac{9}{20}\]. So, similarly, \[X=\frac{1}{3}+\frac{1}{2}=\frac{2+3}{6}=\frac{5}{6}\] \[Y=\frac{5}{6}+\frac{3}{4}=\frac{10+9}{12}=\frac{19}{12}\] and \[Z=\frac{19}{12}+1\frac{1}{5}=2\frac{47}{60}\]
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