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Official Solution:

A single filter reduces the concentration of harmful substances in water by half. If water with less than 0.1 percent harmful substances is deemed clean, minimum of how many filters are needed to purify 200 liters of water that contains 0.5 liters of these substances?

A. 2
B. 3
C. 5
D. 6
E. 8

At the start, the concentration of harmful substances in the water is \(\frac{0.5}{200}*100\% = 0.25\%\). Using one filter brings this concentration down to \(0.125\%\). After deploying two filters, the concentration falls further to \(0.0625\%\), which is below the \(0.1\%\) threshold.

Therefore, a minimum of two filters is required to bring the concentration of harmful substances below the acceptable limit.

Answer: A.
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If water that contains less than 0.1 percent of harmful substances is considered clean, means

in 1000 litres of water, less than 1.0 bacteria are OK, means

in 200 litres of water, less than 0.2 bacteria are OK(This is ideal condition; benchmark)

Given that 200 liters of water has 0.5 bacteria.

1st filter, bacteria reduced to 0.25

2nd filter, bacteria reduced to 0.125

0.125 < 0.2, so 2 filters are sufficient.

Answer = 2 = A
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In this sentence, i find the term the concentration of harmful substances is rather ambiguous, is it \(\frac{harmful substances}{water}\) or \(\frac{harmful substances}{harmful substances + water}\) ?
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leanhdung
In this sentence, i find the term the concentration of harmful substances is rather ambiguous, is it \(\frac{harmful substances}{water}\) or \(\frac{harmful substances}{harmful substances + water}\) ?

Water = Pure water + Harmful substances, so it's (Harmful substances)/(Water).
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