CAT (QA) PYQs

The number of coins collected per week by two coin-collectors $A$ and $B$ are In the ratio $3:4$. If the total number of coins collected by $A$ in $5$ weeks is a multiple of $7$, and the total number of coins collected by $B$ in $3$ weeks is a multiple of $24$, then the minimum possible number of coins collected by $A$ in one week is

If $a, b, c$ are three positive integers such that a and b are in the ratio $3 : 4$ while $b$ and $c$ are in the ratio $2:1$, then which one of the following is a possible value of $(a + b + c)$?

The price of a precious stone is directly proportional to the square of its weight. Sita has a precious stone weighing $18$ units. If she breaks it into four pieces with each piece having distinct integer weight, then the difference between the highest and lowest possible values of the total price of the four pieces will be $288000$. Then, the price of the original precious stone is