CAT 2023 Question Paper | Quant Slot 3

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

Video Explanation

Explanatory Answer

\( \frac { A + B + C } { 3 } = y \)
\( A + B + C = 3 y \)
\( \frac { A + B + C + D } { 4 } = y - x \)
\( A + B + C + D = 4 y - 4 x \)
\( D = y - 4 x \)
\( \frac { A + B + C + E } { 4 } = y + 2 x \)
\( A + B + C + C = 4 y + 8 x \)
\( E = y + 8 x \)
\( E - D = 12 \)
\( ( y + 8 x ) - ( y - 4 x ) = 12 \)
\( 12 x = 12 \)
\( x = 1 \)

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 "

The answer is '1'

Choice D is the correct answer.