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The number of water lilies on a certain lake doubles every

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The number of water lilies on a certain lake doubles every [#permalink] New post 21 Nov 2012, 21:18
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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?

(A) 15
(B) 28
(C) 30
(D) 58
(E) 59
[Reveal] Spoiler: OA

Last edited by Bunuel on 09 Mar 2014, 05:49, edited 1 time in total.
Added the OA.
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Re: The number of water lilies on a certain lake doubles every [#permalink] New post 21 Nov 2012, 21:29
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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

My approach doesn't work :( Please, share your ideas!


Starting from 1 Water Lilly it takes 60 days.
If there are already two present, it can be taken as the first day is over.
It will take 59 more days.
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Re: The number of water lilies on a certain lake doubles every [#permalink] New post 21 Nov 2012, 21:43
seems too simple for "problem of the week" :o
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Re: The number of water lilies on a certain lake doubles every [#permalink] New post 22 Nov 2012, 04:18
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nawaab wrote:
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

My approach doesn't work :( Please, share your ideas!


Starting from 1 Water Lilly it takes 60 days.
If there are already two present, it can be taken as the first day is over.
It will take 59 more days.


Notice that we are told that "the number of water lilies on a certain lake doubles every two days", thus if initially there were two water lilies instead of one, we can consider that two days are over and therefore only 58 days are left.

Answer: D.

Similar question to practice: it-takes-30-days-to-fill-a-laboratory-dish-with-bacteria-140269.html

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Re: The number of water lilies on a certain lake doubles every [#permalink] New post 22 Nov 2012, 04:29
I also think so. Thanks for the link.
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Re: The number of water lilies on a certain lake doubles every [#permalink] New post 30 Nov 2012, 06:57
I understand the logic, but am not able to solve it algebraically.

since the series is in the geometric progression with the common ration (r) = 2, initial condition can be rewritten as:

a(n) = 1.2^60-1 {a(n = a.r^n-1)} === which gives us total number of lillies in the pool ==>2^59.....no this is equated when the the pool starts with 2 lillies...==> 2^59 = 2.2^n-1 ===>n=59..

Where am I going wrong?
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Re: The number of water lilies on a certain lake doubles every [#permalink] New post 30 Nov 2012, 08:53
Expert's post
pavanpuneet wrote:
I understand the logic, but am not able to solve it algebraically.

since the series is in the geometric progression with the common ration (r) = 2, initial condition can be rewritten as:

a(n) = 1.2^60-1 {a(n = a.r^n-1)} === which gives us total number of lillies in the pool ==>2^59.....no this is equated when the the pool starts with 2 lillies...==> 2^59 = 2.2^n-1 ===>n=59..

Where am I going wrong?


We are told that "the number of water lilies on a certain lake doubles every TWO days".

If there are two lilies, then in order to cover the lake they would need to double one time less than in case with 1 lily. Since lilies double every two days, then 60-2=58 days are needed.


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Re: The number of water lilies on a certain lake doubles every [#permalink] New post 08 Sep 2013, 05:17
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Re: The number of water lilies on a certain lake doubles every [#permalink] New post 08 Sep 2013, 06:33
Bunuel,
would you please illustrate this question using the population formula rule used in the MGMAT.

Thank you
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Re: The number of water lilies on a certain lake doubles every [#permalink] New post 08 Sep 2013, 06:43
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SaraLotfy wrote:
Bunuel,
would you please illustrate this question using the population formula rule used in the MGMAT.

Thank you


Sorry not familiar with that one. The following threads might help:
a-certain-bacteria-colony-doubles-in-size-every-day-for-144013.html
it-takes-30-days-to-fill-a-laboratory-dish-with-bacteria-140269.html
a-certain-culture-of-bacteria-quadruples-every-hour-if-a-52258.html
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Re: The number of water lilies on a certain lake doubles every [#permalink] New post 09 Mar 2014, 04:46
Bunuel or anyone,

Please confirm if my approach is correct.

Sum of lillies for 30 days using Geo Series:
a= 1+2+2^2+2^3..2^30 --(1)
2a = 2+2^2...2^31 -- (2)
Subtract 1 from 2
a=2^31 - 1 (Total lillies in the pond)

Now let x be number of times, both lillies expanded at once
lilly 1 -> a=1+2+2^2...2^x
sum of lilly 1 using Geo series described above = 2^x+1 - 1
lilly 2 -> a=1+2+2^2....2^x
sum of lilly 2 using Geo series described above = 2^x+1 - 1
--> sum of lilly 1 + sum of lilly 2 = 2^31 -1
so 2(2^x+1 -1) = 2^31 - 1
2^x+2 - 2 = 2^31 -1
approximately 2^x+2 = 2^31
x+2 = 31, x= 29 times ....so 58 days as lillies doubles evry 2 days
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Re: The number of water lilies on a certain lake doubles every [#permalink] New post 09 Mar 2014, 06:21
Expert's post
maaadhu wrote:
Bunuel or anyone,

Please confirm if my approach is correct.

Sum of lillies for 30 days using Geo Series:
a= 1+2+2^2+2^3..2^30 --(1)
2a = 2+2^2...2^31 -- (2)
Subtract 1 from 2
a=2^31 - 1 (Total lillies in the pond)

Now let x be number of times, both lillies expanded at once
lilly 1 -> a=1+2+2^2...2^x
sum of lilly 1 using Geo series described above = 2^x+1 - 1
lilly 2 -> a=1+2+2^2....2^x
sum of lilly 2 using Geo series described above = 2^x+1 - 1
--> sum of lilly 1 + sum of lilly 2 = 2^31 -1
so 2(2^x+1 -1) = 2^31 - 1
2^x+2 - 2 = 2^31 -1
approximately 2^x+2 = 2^31
x+2 = 31, x= 29 times ....so 58 days as lillies doubles evry 2 days


No, that's not correct. Neat algebraic manipulations though...

Notice that the total number of lilies is not 1+2+2^2+2^3..2^30, it's 2^30.

Initially = 1;
After 2 days = 2, not 1+2;
After 4 days = 2^2 = 4, not 1+2+4.
...
After 60 days = 2^30, not 1+2+2^2+2^3+...+2^30.

Similarly, if initially there are 2 lilies, then the total number would be 2*2^x.

So, we'd have that 2^30 = 2*2^x --> x = 29.

Similar questions to practice:
a-certain-bacteria-colony-doubles-in-size-every-day-for-144013.html
it-takes-30-days-to-fill-a-laboratory-dish-with-bacteria-140269.html
a-certain-culture-of-bacteria-quadruples-every-hour-if-a-52258.html
the-population-of-locusts-in-a-certain-swarm-doubles-every-90353.html
the-population-of-a-bacteria-culture-doubles-every-2-minutes-167378.html

Hope it helps.
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DS: 1. DS tough questions; 2. DS tough questions part 2; 3. DS tough questions part 3; 4. DS Standard deviation; 5. Inequalities; 6. 700+ GMAT Data Sufficiency Questions With Explanations; 7 Tough and tricky exponents and roots questions; 8 The Discreet Charm of the DS ; 9 Devil's Dozen!!!; 10 Number Properties set., 11 New DS set.


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Re: The number of water lilies on a certain lake doubles every [#permalink] New post 09 Mar 2014, 18:38
Bunuel wrote:
maaadhu wrote:
Bunuel or anyone,

Please confirm if my approach is correct.

Sum of lillies for 30 days using Geo Series:
a= 1+2+2^2+2^3..2^30 --(1)
2a = 2+2^2...2^31 -- (2)
Subtract 1 from 2
a=2^31 - 1 (Total lillies in the pond)

Now let x be number of times, both lillies expanded at once
lilly 1 -> a=1+2+2^2...2^x
sum of lilly 1 using Geo series described above = 2^x+1 - 1
lilly 2 -> a=1+2+2^2....2^x
sum of lilly 2 using Geo series described above = 2^x+1 - 1
--> sum of lilly 1 + sum of lilly 2 = 2^31 -1
so 2(2^x+1 -1) = 2^31 - 1
2^x+2 - 2 = 2^31 -1
approximately 2^x+2 = 2^31
x+2 = 31, x= 29 times ....so 58 days as lillies doubles evry 2 days


No, that's not correct. Neat algebraic manipulations though...

Notice that the total number of lilies is not 1+2+2^2+2^3..2^30, it's 2^30.

Initially = 1;
After 2 days = 2, not 1+2;
After 4 days = 2^2 = 4, not 1+2+4.
...
After 60 days = 2^30, not 1+2+2^2+2^3+...+2^30.

Similarly, if initially there are 2 lilies, then the total number would be 2*2^x.

So, we'd have that 2^30 = 2*2^x --> x = 29.

Similar questions to practice:
a-certain-bacteria-colony-doubles-in-size-every-day-for-144013.html
it-takes-30-days-to-fill-a-laboratory-dish-with-bacteria-140269.html
a-certain-culture-of-bacteria-quadruples-every-hour-if-a-52258.html
the-population-of-locusts-in-a-certain-swarm-doubles-every-90353.html
the-population-of-a-bacteria-culture-doubles-every-2-minutes-167378.html

Hope it helps.


Thank you Bunuel. My interpretation of question is incorrect.
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Re: The number of water lilies on a certain lake doubles every   [#permalink] 09 Mar 2014, 18:38
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