CAT (QA) PYQs

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

The average of three distinct real numbers is 28. If the smallest number is increased by 7 and the largest number is reduced by 10, the order of the numbers remains unchanged, and the new arithmetic mean becomes 2 more than the middle number, while the difference between the largest and the smallest numbers becomes 64. Then, the largest number in the original set of three numbers is

Suppose hospital $A$ admitted $21$ less Covid infected patients than hospital $B$, and all eventually recovered. The sum of recovery days for patients in hospitals $A$ and $B$ were $200$ and $152$, respectively. If the average recovery days for patients admitted in hospital $A$ was $3$ more than the average in hospital $B$ then the number admitted in hospital $A$ was