CAT Quantitative Aptitude Questions | CAT Algebra - Linear Equations; Quadratic Equations

CAT Questions | Algebra | Quadratic Equations - Sum of the variables

The question is about finding Value of variables of a Quadratic Equation. Two different equations involving two variables are given and we need to find out x + y. Framing and solving equations is an integral part of Linear Equations and Quadratic Equations. Get as much practice as you can in these two topics because the benefits of being good at framing equations will be useful in other concepts.

Question 13: If (3x+2y-22)2 + (4x-5y+9)2 = 0 and 5x-4y = 0. Find the value of x+y?

  1. 7
  2. 9
  3. 11
  4. 13

🎉 Ace XAT 2025 with 2IIM's Crash Course - Enrol now


Best CAT Online Coaching
Try upto 40 hours for free
Learn from the best!


2IIM : Best Online CAT Coaching.


Best CAT Coaching in Chennai


CAT Coaching in Chennai - CAT 2022
Limited Seats Available - Register Now!


Explanatory Answer

Method of solving this CAT Question from CAT Algebra - Quadratic Equations: What is the value of x+y ?

Do not jump and start expanding the squares.

In equation (1), both the squares will yield either positive number or 0. Since sum of two positive number cannot be 0, each of the term must be 0

∴ 3x + 2y -22 = 0

Multiplying by 2, and adding both equation
6x + 4y - 44 = 0
5x - 4y = 0

=> x = 4
Putting the value of x in the equation
5 x 4 – 4y = 0
y = 5
∴ x+y = 9

The question is "If (3x+2y-22)2 + (4x-5y+9)2 = 0 and 5x-4y = 0. Find the value of x+y?"

Hence the answer is "9"

Choice B is the correct answer.

 

CAT Online Preparation | CAT Algebra Videos On YouTube


Other useful sources for Algebra Questions | Linear Quadratic Sample Questions



CAT Questions | CAT Quantitative Aptitude

CAT Questions | CAT DILR

CAT Questions | Verbal Ability for CAT


Where is 2IIM located?

2IIM Online CAT Coaching
A Fermat Education Initiative,
58/16, Indira Gandhi Street,
Kaveri Rangan Nagar, Saligramam, Chennai 600 093

How to reach 2IIM?

Phone: (91) 44 4505 8484
Mobile: (91) 99626 48484
WhatsApp: WhatsApp Now
Email: prep@2iim.com