CAT 2020 Question Paper | Quants Slot 3

CAT Previous Year Paper | CAT Quants Questions | Question 15

This question is about checking for the consistency of the given equations. Knowing a few equations, we can find whether the equations have a unique solution or infinite solutions, or no solution. 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 during your CAT Preparation.

Question 15 : Let k be a constant. The equations kx + y = 3 and 4x + ky = 4 have a unique solution if and only if

  1. |k| = 2
  2. k ≠ 2
  3. |k| ≠ 2
  4. k = 2

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Explanatory Answer

Two generic equations, a1x + b1y + c1 = 0 and a2x + b2y + c2 = 0, will have a unique solution if and only if, \\frac{a_{1}}{a_{2}}) ≠ \\frac{b_{1}}{b_{2}}).

We have the equations kx + y = 3 and 4x + ky = 4,
For them to have unique solutions, they must satisfy the condition
\\frac{k}{4}) ≠ \\frac{1}{k})
k2 ≠ 4
k ≠ ±2
|k| ≠ 2


The question is "Let k be a constant. The equations kx + y = 3 and 4x + ky = 4 have a unique solution if and only if"

Hence, the answer is, "|k| ≠ 2"

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