# CAT 2023 Set-3 | Quantitative Aptitude | Question: 1

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Section: Quantitative Aptitude
Q. 1)

If $x$ is a positive real number such that $x^{8}+\left(\frac{1}{x}\right)^{8}=47$, then the value of $x^{9}+\left(\frac{1}{x}\right)^{9}$ is

1. $34 \sqrt{5}$
2. $40 \sqrt{5}$
3. $36 \sqrt{5}$
4. $30 \sqrt{5}$

If $x$ is a positive real number such that $x^{8}+\left(\frac{1}{x}\right)^{8}=47$, then the value of $x^{9}+\left(\frac{1}{x}\right)^{9}$ is$34 \sqrt{5}$$40 \sqrt{5}$$36... 0 votes 0 answers 2 116 views Let$n$and$m$be two positive integers such that there are exactly$41$integers greater than$8^{m}$and less than$8^{n}$, which can be expressed as powers of$2$. Th... 0 votes 0 answers 3 109 views Q. 3)For some real numbers$a$and$b$, the system of equations$x+y=4$and$(a+5) x+\left(b^{2}-15\right) y=8 b$has infinitely many solutions for$x$and$y$. Then, the... 0 votes 0 answers 4 148 views Q. 4)For a real number$x$, if$\frac{1}{2}, \frac{\log _{3}\left(2^{x}-9\right)}{\log _{3} 4}$, and$\frac{\log _{5}\left(2^{x}+\frac{17}{2}\right)}{\log _{5} 4}$are in... 0 votes 1 answer 5 169 views Q. 5)A quadratic equation$x^{2}+b x+c=0$has two real roots. If the difference between the reciprocals of the roots is$\frac{1}{3}\$, and the sum of the reciprocals of t...