CAT 2024 Question Paper | Quant Slot 2

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 If \(x\) and \(y\) satisfy the equations \(|x|+x+y=15\) and \(x+|y|-y=20\), then \((x-y)\) equals

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Video Explanation

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Explanatory Answer

\[ |x|+x+y=15 \text { and } x+|y|-y=20 \] Let's assume \(|x|=\) negative, \(|x|+x+y=15\) makes \(y=15\).
If we substitute \(y=15\) in \(x+|y|-y=20\), we get \(x=20\) which is positive.
Hence \(x\) cannot be negative.
Now let's assume \(y=\) positive. \(x+|y|-y=20\) becomes \(x=20\) In equation \(|x|+x+y=15,20+20-y=15 . y=-25\) which is negative. Hence \(y\) cannot be positive.
Therefore, \(x\) is positive and \(y\) is negative,
\[ \begin{array}{l} 2 x+y=15-----(1) \\ x-2 y=20----(2) \\ 4 x+2 y=30----(1) \star 2 \end{array} \] Adding we get \(5 x=50, x=10\)
Sub \(x=10\), we get \(y=-5\)
The value of \(x-y=10-(-5)=15\)

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The question is "If \(x\) and \(y\) satisfy the equations \(|x|+x+y=15\) and \(x+|y|-y=20\), then \((x-y)\) equals "

Hence, the answer is '15'

Choice D is the correct answer.

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