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# One filter decreases the concentration of harmful substances in water

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One filter decreases the concentration of harmful substances in water [#permalink]

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25 Dec 2014, 13:52
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One filter decreases the concentration of harmful substances in water by half. If water that contains less than 0.1 percent of harmful substances is considered clean, how many filters are required to clean 200 liters of water containing 0.5 liters of harmful substances ?

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[Reveal] Spoiler: OA

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Re: One filter decreases the concentration of harmful substances in water [#permalink]

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25 Dec 2014, 15:26
First calculate the concentration of the contaminated water:
0.5l/200l * 100 = 0.25%

Every filter then reduces the concentration by half:
The first filter will bring the concentration down to 0.125%. A second one will bring it down to 0.0625%. A concentration that is below the 0.1% that is considered save. Answer A is correct.
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Re: One filter decreases the concentration of harmful substances in water [#permalink]

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25 Dec 2014, 20:02
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o.1% of 200 litres is 0.2litres. We are given that current harmful substances is 0.5l. using 1st filter will reduce it to 0.25l and using the second will bring it down to 0.25l.

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Re: One filter decreases the concentration of harmful substances in water [#permalink]

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26 Dec 2014, 07:42
One filter decreases the concentration of harmful substances in water by half. If water that contains less than 0.1 percent of harmful substances is considered clean, how many filters are required to clean 200 liters of water containing 0.5 liters of harmful substances ?

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

Initially, the concentration of harmful substances in the water is $$\frac{0.5}{200}*100\% = 0.25\%$$. One filter will reduce this concentration to $$0.125\%$$. Two filters will reduce the concentration to $$0.0625\%$$ which is less than $$0.1\%$$.

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Re: One filter decreases the concentration of harmful substances in water [#permalink]

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02 Jan 2015, 02:48
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.

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One filter decreases the concentration of harmful substances in water [#permalink]

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17 Aug 2017, 21:12
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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Re: One filter decreases the concentration of harmful substances in water [#permalink]

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17 Aug 2017, 21:19
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Expert's post
leanhdung wrote:
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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Re: One filter decreases the concentration of harmful substances in water [#permalink]

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22 Aug 2017, 11:13
One filter decreases the concentration of harmful substances in water by half. If water that contains less than 0.1 percent of harmful substances is considered clean, how many filters are required to clean 200 liters of water containing 0.5 liters of harmful substances ?

2

3

5

6

8

the liters of water is irrelevant her becuase it simply say that the filer halves the concentration.. so initially is it .5 then after one filter it is .25 and then after second it is .125 which is equal to .1 so two is the answer... simply.

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Re: One filter decreases the concentration of harmful substances in water   [#permalink] 22 Aug 2017, 11:13
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