CAT 2024 Question Paper | Quant Slot 3

CAT Questions

CAT 2024 Quant was dominated by Algebra followed by Arithmetic. In Arithmetic, the questions were dominated by topics like Speed-time-distance, Mixture and Alligations. This year, there was a surprise. The questions from Geometry were relatively on the lower side as compared to the previous years. There were 8 TITA Qs this year. Overall this section was at a medium level of difficulty.

Question 22 The sum of all distinct real values of \(x\) that satisfy the equation \(10^x+\frac{4}{10^x}=\frac{17}{2}\), is

---

---

Video Explanation

---

---

Explanatory Answer

Let \(10^x=y\)
Then, \(y+\frac{4}{y}=\frac{17}{2}\)
\[ 2 y^2-17 y+8=0 \] After factorising the equation we get, \((2 y-1)(y-8)=0\)
i.e., \(y=8\) or \(y=1 / 2\) \[ \Rightarrow 10^x=8 \text { or } 10^x=1 / 2 \] Taking log on both sides, we get \[ \begin{array}{lrc} \log _{10} 8=x & \text { or } & \log _{10} 1 / 2=x \\ \Rightarrow \log _{10} 2^3=x & \text { (or) } & \log _{10} 2^{-1}=x \\ \Rightarrow x=3 \log _{10} 2 & \text { (or) } & x=-\log _{10} 2 \end{array} \] Sum of these possible values \(=3 \log _{10} 2+\left(-\log _{10} 2\right)=2 \log _{10} 2\)

---

The question is "The sum of all distinct real values of \(x\) that satisfy the equation \(10^x+\frac{4}{10^x}=\frac{17}{2}\), is"

Hence, the answer is '\(2 \log _{10} 2\)'

Choice A is the correct answer.

Verbal Ability for CAT | CAT Reading Comprehension

Verbal Ability for CAT| CAT Para Jumble

Verbal Ability for CAT | CAT Sentence Elimination

Verbal Ability for CAT | CAT Paragraph Completion

Verbal Ability for CAT | CAT Critical Reasoning

Verbal Ability for CAT | CAT Word Usage

Verbal Ability for CAT| CAT Para Summary

Verbal Ability for CAT | CAT Text Completion

Verbal Ability for CAT | CAT Sentence Correction