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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