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On January 1, 2076, Lake Loser contains x liters of water. By Dec 31

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GeminiHeat
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On January 1, 2076, Lake Loser contains x liters of water. By Dec 31 [#permalink] New post   28 Jul 2021, 03:07
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On January 1, 2076, Lake Loser contains x liters of water. By Dec 31 of that same year, 2/7 of the x liters have evaporated. This pattern continues such that by the end of each subsequent year the lake has lost 2/7 of the water that it contained at the beginning of that year. During which year will the water in the lake be reduced to less than 1/4 of the original x liters?

A. 2077

B. 2078

C. 2079

D. 2080

E. 2081
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KarunMendiratta
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Re: On January 1, 2076, Lake Loser contains x liters of water. By Dec 31 [#permalink] New post   28 Jul 2021, 21:07
GeminiHeat wrote:
On January 1, 2076, Lake Loser contains x liters of water. By Dec 31 of that same year, 2/7 of the x liters have evaporated. This pattern continues such that by the end of each subsequent year the lake has lost 2/7 of the water that it contained at the beginning of that year. During which year will the water in the lake be reduced to less than 1/4 of the original x liters?

A. 2077

B. 2078

C. 2079

D. 2080

E. 2081


Since 27th of the water evaporates, we will be left with 57th of water at the end of year

On 1 Jan 2076 = x litres
On 31 Dec 2076 = 57x=0.71x litres
On 31 Dec 2077 = (57)2x=0.51x litres
On 31 Dec 2078 = (57)3x=0.36x litres
On 31 Dec 2079 = (57)4x=0.26x litres
On 31 Dec 2080 = (57)5x=0.18x litres

Hence, option D
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gmatclubot
Re: On January 1, 2076, Lake Loser contains x liters of water. By Dec 31 [#permalink]
28 Jul 2021, 21:07
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