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# Water lily grows at such a rate that it covers double the

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VP
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Water lily grows at such a rate that it covers double the [#permalink]  25 Sep 2007, 00:12
Water lily grows at such a rate that it covers double the surface that it covered the day before. It takes 30 days for a water lily to cover the entire surface of the pond. How long would it take for two water lilies of the same size to cover the entire surface of the same pond?

A) 8.33
B) 12.5
C) 15
D) 20
E) 29

I like this question. Thought to repost it for our newcomers.

Have Fun.

P.S - ywilfred , let them try before you solve this Thanks

GMAT Club Legend
Joined: 07 Jul 2004
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Yes, my lord
Manager
Joined: 27 Jul 2007
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Is it E?

2^29.x = 2. 2^(y-1).x
=> y=29.
Senior Manager
Joined: 27 Aug 2007
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I think it is E,

Since on 29th day 1/2 of pool will be covered (when there is one water lily), when there are two of the water lilies than pool will be covered on 29th day.

for example on 25th day, one flower would cover 1/32 of pool if there are two of them it will be done on 24th day since 1/64+1/64 = 1/32.

(if has hesitation or do not believe than you can other numbers (days) take with one flower take two flowers and you will see that there is only one day difference)

So it will take 29 days to cover pool for two lowers.

Ans: E

P.S. one of the weaknesses of mine, cannot explain well
VP
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The OA is (E)

Thanks

Director
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Re: Water lily [#permalink]  25 Sep 2007, 08:43
KillerSquirrel wrote:
Water lily grows at such a rate that it covers double the surface that it covered the day before. It takes 30 days for a water lily to cover the entire surface of the pond. How long would it take for two water lilies of the same size to cover the entire surface of the same pond?

A) 8.33
B) 12.5
C) 15
D) 20
E) 29

I like this question. Thought to repost it for our newcomers.

Have Fun.

P.S - ywilfred , let them try before you solve this Thanks

Logically I can determine the answer is 29. (One lily covers 1/2 on the 29th day. If there is one more lily it will also cover 1/2 on the 29th day. Therefore, the whole pool will be covered).

However, mathematically I cannot come up with a solution; I don't understand the above 2 solutions either. Can someone explain it mathematically?
VP
Joined: 08 Jun 2005
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Re: Water lily [#permalink]  25 Sep 2007, 08:58
GK_Gmat wrote:

Logically I can determine the answer is 29. (One lily covers 1/2 on the 29th day. If there is one more lily it will also cover 1/2 on the 29th day. Therefore, the whole pool will be covered).

However, mathematically I cannot come up with a solution; I don't understand the above 2 solutions either. Can someone explain it mathematically?

As I understand it:

one lily

surface of pond = n

first day = 2x = 2^1*x
second day = 4x= 2^2*x
third day = 8x = 2^3*x
fourth day = 16x= 2^4*x

so after 30 days

n = 2^30*x

two lilies

n/2 = (2^30*x)/2

n = 2^29*x

29 days

Manager
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Nice question, Killersquirrel! I like it!
CEO
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Re: Water lily [#permalink]  25 Sep 2007, 19:34
KillerSquirrel wrote:
Water lily grows at such a rate that it covers double the surface that it covered the day before. It takes 30 days for a water lily to cover the entire surface of the pond. How long would it take for two water lilies of the same size to cover the entire surface of the same pond?

A) 8.33
B) 12.5
C) 15
D) 20
E) 29

I like this question. Thought to repost it for our newcomers.

Have Fun.

P.S - ywilfred , let them try before you solve this Thanks

Nice Q. I say E. b/c the water lilly will cover 1/2 the pond on day 29.

However, w/ two lillys then on day 28 they each cover 1/4 the pond. So next day---> 1/2+1/2 =1.
Re: Water lily   [#permalink] 25 Sep 2007, 19:34
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