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 1 The number of distinct integer solutions \((x, y)\) of the equation \(|x+y|+|x-y|=2\), is

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Video Explanation

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Explanatory Answer

We are thinking about two scenarios where \(x \geq y\) and \(x \geq-y\). When \(x \geq y\), \[ \begin{array}{l} x+y+x-y=2 \\ 2 x=2 \\ x=1 \end{array} \] So, the possibilities are ( 1,1 ), ( 1,0 ) and ( \(1,-1\) )
When \(x=0\),
The possibilities are \((0,1)\) and \((0,-1)\)
When \(x=-1\)
The possibilities are ( \(-1,1\) ), ( \(-1,0\) ) and ( \(-1,-1\) )
So, the number of distinct integer solutions \(=8\)

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The question is "The number of distinct integer solutions \((x, y)\) of the equation \(|x+y|+|x-y|=2\), is"

Hence, the answer is '8'

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