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Each of the bottles mentioned in this question contains $50 \; \text{ml}$ of liquid. The liquid in any bottle can be $100 \%$ pure content $\text{(P)}$ or can have certain amount of impurity $\text{(I)}.$ Visually it is not possible to distinguish between $\text{P}$ and $\text{I}.$ There is a testing device which detects impurity, as long as the percentage of impurity in the content tested is $10 \%$ or more.

For example, suppose bottle $1$ contains only $\text{P},$ and bottle $2$ contains $80 \% \; \text{P}$ and $20 \% \; \text{I}.$ If content of bottle $1$ is tested, it will be found out that it contains only $\text{P}.$ If content of bottle $2$ is tested, the test will reveal that it contains some amount of  $\text{I}.$ If $10 \; \text{ml}$ of content from bottle $1$ is mixed with  $20 \; \text{ml}$ content from bottle $2,$ the test will show that the mixture has impurity, and hence we can conclude that at least one of the two bottles has $\text{I}.$ However, if $10 \; \text{ml}$ of content from bottle $1$ is mixed with  $5 \; \text{ml}$ of content from bottle $2.$ the test will not detect any impurity in the resultant mixture.

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

1. $1$
2. $4$
3. $2$
4. $3$

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2
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