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

CAT Questions | Algebra | Linear Equations - Counting

The question is about Possible pairs of Solutions. We need to find out the possible pairs that satisfy the given linear equation which contains modulus. Framing and solving equations is an integral part of this topic. 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. Counting question with modulus also thrown in. Worry about all those negative possibilities as well.

Question 2: (|x| - 3) (|y| + 4) = 12. How many pairs of integers (x,y) satisfy this equation?

  1. 4
  2. 6
  3. 10
  4. 8

Rs. 2500 off on 2IIM Ultimate DI LR Course for CAT 2019. Offer valid till March 24th.


Signup to sample the Best CAT Online Coaching


Video Explanation


Best CAT Coaching in Chennai


Starts Sat, Mar 23, 2019


Explanatory Answer

Method of solving this CAT Question from CAT Algebra - Linear Equations: Counting question with modulus also thrown in. Worry about all those negative possibilities as well.

If x and y are integers, so are |x| –3 and |y| + 4. So, we start by finding out in how many ways 12 can be written as the product of two integers.
12 can be written as 12 * 1, or 6 * 2, or 3 * 4. To start with, we can eliminate the possibilities where the two terms are negative as |y| + 4 cannot be negative.

Further, we can see that |y| + 4 cannot be less than 4. So, among the values, we can have |y| +4 take values 4, 6 or 12 only, or |y| can take values 0, 2 and 8 only.
When |y| = 0, |x| - 3 = 3, |x| = 6, x can be +6 or -6. Two pairs of values are possible: (6, 0) and (-6, 0)
When |y| = 2, |x| - 3 = 2, |x| = 5, x can be +5 or --5. There are four possible pairs here: (5, 2) , (-5, 2), (5, -2), (-5, -2)
When |y| = 8, |x| - 3 = 1, |x| = 4, x can be +4 or --4. There are four possible pairs here: (4, 8) , (-4, 8), (4, -8), (-4, -8)

The question is "(|x| - 3) (|y| + 4) = 12. How many pairs of integers (x,y) satisfy this equation?"

Hence the answer is "10"

Choice C is the correct answer.

 

Online CAT Coaching
Try it free!

Register in 2 easy steps and start learning in 30 seconds!

★ Sign up for Free

Already have an Account?

★ Login to Continue

CAT Coaching in Chennai

Next Weekend Batch Starts Sat, Mar 23rd, 2019

★ CAT Coaching Info

Best CAT Coaching in Chennai

Sign up for a Free Demo of our CAT Coaching in Chennai

★ Schedule Demo

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,
10-C, Kalinga Colony, Bobbili Raja Salai
K.K.Nagar, Chennai. India. Pin - 600 078

How to reach 2IIM?

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