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?

Let's break this down - we need to find the minimum tests to determine if there's 1 or 2 pure bottles.

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What we know:

• 4 bottles total
• Either 1 bottle OR 2 bottles contain only $P$ (pure)
• Remaining bottles contain $85\%$ $P$ and $15\%$ $I$ (impure)

We'll do ONE test: mix equal amounts from all 4 bottles and check the impurity level.

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Case 1: Only 1 bottle is pure

• 1 pure bottle + 3 impure bottles
• Take $10ml$ from each bottle (total = $40ml$)
• Impurity calculation:
• Pure bottle contributes: $0ml$ impurity
• Each impure bottle contributes: $10ml \times 15\% = 1.5ml$ impurity
• Total impurity: $3 \times 1.5ml = 4.5ml$

Impurity percentage:

$\dfrac{4.5ml}{40ml} = 11.25\%$

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Case 2: Exactly 2 bottles are pure

• 2 pure bottles + 2 impure bottles
• Take $10ml$ from each bottle (total = $40ml$)
• Impurity calculation:
• Pure bottles contribute: $0ml$ impurity
• Each impure bottle contributes: $10ml \times 15\% = 1.5ml$ impurity
• Total impurity: $2 \times 1.5ml = 3ml$

Impurity percentage:

$\dfrac{3ml}{40ml} = 7.5\%$

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Using a detection threshold of $10\%$:

• If impurity $> 10\%$ → We have 1 pure bottle
• If impurity $< 10\%$ → We have 2 pure bottles

Since the two cases give distinctly different impurity levels ($11.25\%$ vs $7.5\%$), one test tells us exactly which scenario we're in.

Minimum number of tests required: $\boxed{1}$