CAT 2024 Question Paper | Quant Slot 1

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 :If $x$ is a positive real number such that $4 \log _{10} x+4 \log _{100} x+8 \log _{1000} x=13$, then the greatest integer not exceeding $x$, is

---

---

Video Explanation

---

---

Explanatory Answer

$$\begin{array}{l} 4(\log x / \log 10)+4(\log x / 2 \log 10)+8(\log x / 3 \log 10)=13 \\ 4 \log x+2 \log x+(8 / 3) \log x=13 \\ \log x(4+2+8 / 3)=13 \\ (26 / 3) \log x=13 \\ \log x=3 / 2 \\ x=10^{1.5}=31.62 \end{array}$$ The greater integer not exceeding $x=31$

---

The question is "If $x$ is a positive real number such that $4 \log _{10} x+4 \log _{100} x+8 \log _{1000} x=13$, then the greatest integer not exceeding $x$, is"

Hence, the answer is '31'

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