CAT (QA) PYQs

The strength of a salt solution is $\mathrm{p} \%$ if $100 \mathrm{ml}$ of the solution contains $p$ grams of salt. Each of three vessels $\mathrm{A}, \mathrm{B}, \mathrm{C}$ contains $500 \mathrm{ml}$ of salt solution of strengths $10 \%, 22 \%$, and $32 \%$, respectively. Now, $100 \mathrm{ml}$ of the solution in vessel A is transferred to vessel B. Then, $100 \mathrm{ml}$ of the solution in vessel $B$ is transferred to vessel $C$. Finally, $100 \mathrm{ml}$ of the solution in vessel $C$ is transferred to vessel $A$. The strength, in percentage, of the resulting solution in vessel $A$ is

There are four bottles. It is known that three of these bottles contain only P, while the remaining one contains 80% P and 20% I. What is the minimum number of tests required to definitely identify the bottle containing some amount of I?

There are four bottles. It is known that either one or two of these bottles contain(s)only P, while the remaining ones contain 85% P and 15% I. What is the minimum number of tests required to ascertain the exact number of bottles containing only P?