CAT 2024 Question Paper | Quant Slot 2

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 21 If \(x\) and \(y\) are real numbers such that \(4 x^2+4 y^2-4 x y-6 y+3=0\), then the value of \((4 x+5 y)\) is

---

---

Video Explanation

---

---

Explanatory Answer

\[ 4 x^2+4 y^2-4 x y-6 y+3=\left(4 x^2+y^2-4 x y\right)+\left(3 y^2-6 y+3\right) \] We know that \(4 x^2+y^2-4 x y=(2 x-y)^2\) \[ 3 y^2-6 y+3=3\left(y^2-2 y+1\right)=3(y-1)^2 \] Therefore, \(4 x^2+4 y^2-4 x y-6 y+3=(2 x-y)^2+3(y-1)^2=0\).
The equation is satisfied only when \(y=1\) and \(x=1 / 2\).
The value of \((4 x+5 y)=4(1 / 2)+5(1)=2+5=7\).

---

The question is "If \(x\) and \(y\) are real numbers such that \(4 x^2+4 y^2-4 x y-6 y+3=0\), then the value of \((4 x+5 y)\) is"

Hence, the answer is '7'

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