CAT 2024 Question Paper | Quant Slot 3

CAT Questions

CAT 2024 Quant was dominated by Algebra followed by Arithmetic. In Arithmetic, the questions were dominated by topics like Speed-time-distance, Mixture and Alligations. This year, there was a surprise. The questions from Geometry were relatively on the lower side as compared to the previous years. There were 8 TITA Qs this year. Overall this section was at a medium level of difficulty.

Question 2 For some constant real numbers \(p, k\) and \(a\), consider the following system of linear equations in \(x\) and \(y\) : $$ \begin{aligned} & p x-4 y=2 \\ & 3 x+k y=a \end{aligned} $$ A necessary condition for the system to have no solution for \((x, y)\), is

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Video Explanation

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Explanatory Answer

A necessary condition for the system to have no solution for (𝑥,𝑦), is
The condition is \(\frac{a_1}{a_2}=\frac{b_1}{b_2} \neq \frac{c_1}{c_2}\)
i.e., \(\frac{p}{3}=\frac{-4}{k} \neq \frac{2}{a}\)
For \(\frac{p}{3}=\frac{-4}{k} ; \quad p k+12=0\)
For \(\frac{-4}{k} \neq \frac{2}{a} ; \quad-4 a \neq 2 k \Rightarrow 2 a+k \neq 0\)
For \(\frac{p}{3} \neq \frac{2}{a} ; \quad p a-6 \neq 0\)

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The question is "For some constant real numbers \(p, k\) and \(a\), consider the following system of linear equations in \(x\) and \(y\) : $$ \begin{aligned} & p x-4 y=2 \\ & 3 x+k y=a \end{aligned} $$ A necessary condition for the system to have no solution for \((x, y)\), is "

Hence, the answer is '\(2 a+k \neq 0\)'

Choice A is the correct answer.

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