ABC26GN1671 · Problems on Numbers
Subject: General Aptitude · Chapter: Problems on Numbers · Exam: · Marks: · Difficulty:
The sum of a number and its reciprocal is one-eighth of 34. What is the product of the number and its square root?
(a)8
(b)27
(c)32
(d)None of these
Answer
Explanation
Let the number be $x$. Then, $x+\frac{1}{x}=\frac{34}{8} \Leftrightarrow \frac{x^{2}+1}{x}=\frac{34}{8}$ $$\begin{aligned} & \Leftrightarrow 8 x^{2}-34 x+8=0 \\ & \Leftrightarrow 4 x^{2}-17 x+4=0 \\ & \Leftrightarrow(4 x-1)(x-4)=0 \\ & \Leftrightarrow x=4 . \end{aligned} \therefore \quad \text { Required number }=4 \times \sqrt{4}=4 \times 2=8 .$$
Explanation as extracted from the printed page; notation may be imperfect.
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