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

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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.

 

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