CAT 2023 Quant was dominated by Arithmetic followed by Algebra. 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 12 : There are three persons \(\mathrm{A}, \mathrm{B}\) and \(\mathrm{C}\) in a room. If a person \(\mathrm{D}\) joins the room, the average weight of the persons in the room reduces by \(x \mathrm{~kg}\). Instead of \(\mathrm{D}\), if person \(\mathrm{E}\) joins the room, the average weight of the persons in the room increases by \(2 x \mathrm{~kg}\). If the weight of \(\mathrm{E}\) is \(12 \mathrm{~kg}\) more than that of \(\mathrm{D}\), then the value of \(x\) is

- 1.5
- 2
- 0.5
- 1

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\( \frac { A + B + C } { 3 } = y \)

\( A + B + C = 3 y \)

\( \frac { A + B + C + D } { 4 } = y - x \)

\( A + B + C + D = 4 y - 4 x \)

\( D = y - 4 x \)

\( \frac { A + B + C + E } { 4 } = y + 2 x \)

\( A + B + C + C = 4 y + 8 x \)

\( E = y + 8 x \)

\( E - D = 12 \)

\( ( y + 8 x ) - ( y - 4 x ) = 12 \)

\( 12 x = 12 \)

\( x = 1 \)

The question is **" There are three persons \(\mathrm{A}, \mathrm{B}\) and \(\mathrm{C}\) in a room. If a person \(\mathrm{D}\) joins the room, the average weight of the persons in the room reduces by \(x \mathrm{~kg}\). Instead of \(\mathrm{D}\), if person \(\mathrm{E}\) joins the room, the average weight of the persons in the room increases by \(2 x \mathrm{~kg}\). If the weight of \(\mathrm{E}\) is \(12 \mathrm{~kg}\) more than that of \(\mathrm{D}\), then the value of \(x\) is " **

Choice D is the correct answer.

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