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The number of water lilies on a certain lake doubles every

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sanjna2023
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Re: The number of water lilies on a certain lake doubles every [#permalink] New post  12 Aug 2020, 08:15
Hi @Bunuel/ BrentGMATPrepNow,

Not sure if my approach is okay but the way I picture this -

For one Lilly -
Day 1 - 1
Day 2 - 2^2*1
Day 3 - 2^2*1
Day 4 - 2^3*1
.
.
.
Day 60 - 2^59*1 (which we know constitutes a filled lake) -----(1)

Thus for 2 lilies increasing at a rate -
Day 1 - 2
Day 2 - 2^2*2
Using (1) => 2 lilies will be same as 2^59 or a filled lake if 2^58*2. This implies it will take 58 days for 2 lilies.

Please advise.
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BrentGMATPrepNow
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Re: The number of water lilies on a certain lake doubles every [#permalink] New post  12 Aug 2020, 08:50
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The number of water lilies on a certain lake doubles every two days. If there is exactly one water lily on the lake, it takes 60 days for the lake to be fully covered with water lilies. In how many days will the lake be fully covered with lilies, if initially there were two water lilies on it?


COVID19butGMAT20 wrote:
Hi @Bunuel/ BrentGMATPrepNow,

Not sure if my approach is okay but the way I picture this -

For one Lilly -
Day 1 - 1
Day 2 - 2^2*1
Day 3 - 2^2*1
Day 4 - 2^3*1
.
.
.
Day 60 - 2^59*1 (which we know constitutes a filled lake) -----(1)

Thus for 2 lilies increasing at a rate -
Day 1 - 2
Day 2 - 2^2*2
Using (1) => 2 lilies will be same as 2^59 or a filled lake if 2^58*2. This implies it will take 58 days for 2 lilies.

Please advise.


That approach works perfectly.
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Re: The number of water lilies on a certain lake doubles every [#permalink] New post  22 Aug 2020, 09:46
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rainbooow wrote:
The number of water lilies on a certain lake doubles every two days. If there is exactly one water lily on the lake, it takes 60 days for the lake to be fully covered with water lilies. In how many days will the lake be fully covered with lilies, if initially there were two water lilies on it?

(A) 15
(B) 28
(C) 30
(D) 58
(E) 59


Solution:

Since 60 days is a “long” period of time in terms of doubling. Let’s say it only takes 6 days for the lake to be fully covered with water lilies. That is,

Day 0 = 1

Day 2 = 2

Day 4 = 4

Day 6 = 8

Now, if initially there are 2 water lilies in the lake, we have:

Day 0 = 2

Day 2 = 4

Day 4 = 8

We see that it takes 2 fewer days for the lake to be fully covered with water lilies had the initial number of lilies been 2. Therefore, it will take 58 days for the lake to be fully covered with water lilies if the initial number of lilies is 2.

Answer: D
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Re: The number of water lilies on a certain lake doubles every [#permalink] New post  28 Feb 2023, 04:52
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Re: The number of water lilies on a certain lake doubles every [#permalink]
28 Feb 2023, 04:52
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