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

CAT Questions | Algebra | Linear Equations - Integer Solutions

The question is about Possible pairs of Solutions of a Linear Equation. 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.

Question 7: 2x + 5y = 103. Find the number of pairs of positive integers x and y that satisfy this equation?

  1. 9
  2. 10
  3. 12
  4. 20

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Explanatory Answer

Method of solving this CAT Question from CAT Algebra - Linear Equations: Possible solutions of two varible linear equations!

Rearranging the equation, we get:
2x = 103 – 5y

This says that when you subtract a multiple of 5 from 103, you get an even number. You have to subtract an odd multiple of 5 from 103 in order to get an even number. There are 20 multiples of 5 till 100, ten of which are odd. (Note that you cannot subtract 105, or higher multiples as they result in a negative value for x.)

So, y can have ten integer values. x also has 10 integer values, each corresponding to a particular value of y.
y = 1, gives us a potential value for x, so do y = 3, 5, 7….19. y can take 10 values totally.

The question is "Find the number of pairs of positive integers x and y that satisfy this equation? "

Hence the answer is "10"

Choice B is the correct answer.


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