ABC26GN1082 · Simplification
Subject: General Aptitude · Chapter: Simplification · Exam: 2007 · Marks: · Difficulty:
$\left(\frac{1}{1.4}+\frac{1}{4.7}+\frac{1}{7.10}+\frac{1}{10.13}+\frac{1}{13.16}\right)$ is equal to
(a)$\frac{1}{3}$
(b)$\frac{3}{8}$
(c)$\frac{5}{16}$
(d)$\frac{41}{7280}$
Answer
Explanation
Given $\exp .=\frac{1}{3}\left(1-\frac{1}{4}\right)+\frac{1}{3}\left(\frac{1}{4}-\frac{1}{7}\right)+\frac{1}{3}\left(\frac{1}{7}-\frac{1}{10}\right)$ $$\begin{aligned} & \quad+\frac{1}{3}\left(\frac{1}{10}-\frac{1}{13}\right)+\frac{1}{3}\left(\frac{1}{13}-\frac{1}{16}\right) \\ & =\frac{1}{3}\left[\begin{array}{l} \left(1-\frac{1}{4}\right)+\left(\frac{1}{4}-\frac{1}{7}\right)+\left(\frac{1}{7}-\frac{1}{10}\right) \\ +\left(\frac{1}{10}-\frac{1}{13}\right)+\left(\frac{1}{13}-\frac{1}{16}\right) \end{array}\right] \\ & =\frac{1}{3}\left(1-\frac{1}{16}\right)=\frac{1}{3} \times \frac{15}{16}=\frac{5}{16} . \end{aligned}$$
Explanation as extracted from the printed page; notation may be imperfect.
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