GMAT Question of the Day: Daily via email | Daily via Instagram New to GMAT Club? Watch this Video

 It is currently 16 Feb 2020, 19:55 ### GMAT Club Daily Prep

#### Thank you for using the timer - this advanced tool can estimate your performance and suggest more practice questions. We have subscribed you to Daily Prep Questions via email.

Customized
for You

we will pick new questions that match your level based on your Timer History

Track

every week, we’ll send you an estimated GMAT score based on your performance

Practice
Pays

we will pick new questions that match your level based on your Timer History

#### Not interested in getting valuable practice questions and articles delivered to your email? No problem, unsubscribe here.  # The number of water lilies on a certain lake doubles every

Author Message
TAGS:

### Hide Tags

Intern  Joined: 10 Jun 2012
Posts: 8
The number of water lilies on a certain lake doubles every  [#permalink]

### Show Tags

5
42 00:00

Difficulty:   95% (hard)

Question Stats: 43% (01:48) correct 57% (01:34) wrong based on 497 sessions

### HideShow timer Statistics

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

Originally posted by rainbooow on 21 Nov 2012, 21:18.
Last edited by Bunuel on 09 Mar 2014, 05:49, edited 1 time in total.
Math Expert V
Joined: 02 Sep 2009
Posts: 61189
Re: The number of water lilies on a certain lake doubles every  [#permalink]

### Show Tags

4
3
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.

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

Hope it helps.
_________________
##### General Discussion
Intern  Joined: 08 Apr 2012
Posts: 2
GMAT 1: 610 Q47 V27
GMAT 2: 710 Q50 V35
Re: The number of water lilies on a certain lake doubles every  [#permalink]

### Show Tags

1
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.
Manager  Joined: 26 Dec 2011
Posts: 89
Re: The number of water lilies on a certain lake doubles every  [#permalink]

### Show Tags

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?
Math Expert V
Joined: 02 Sep 2009
Posts: 61189
Re: The number of water lilies on a certain lake doubles every  [#permalink]

### Show Tags

1
1
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.

_________________
Manager  Joined: 24 Apr 2013
Posts: 50
Location: United States
Re: The number of water lilies on a certain lake doubles every  [#permalink]

### Show Tags

Bunuel,
would you please illustrate this question using the population formula rule used in the MGMAT.

Thank you
Math Expert V
Joined: 02 Sep 2009
Posts: 61189
Re: The number of water lilies on a certain lake doubles every  [#permalink]

### Show Tags

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
_________________
Manager  Joined: 04 Apr 2013
Posts: 108
Re: The number of water lilies on a certain lake doubles every  [#permalink]

### Show Tags

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
Math Expert V
Joined: 02 Sep 2009
Posts: 61189
Re: The number of water lilies on a certain lake doubles every  [#permalink]

### Show Tags

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
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.
_________________
Manager  Joined: 04 Apr 2013
Posts: 108
Re: The number of water lilies on a certain lake doubles every  [#permalink]

### Show Tags

Bunuel 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
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.
Intern  Joined: 18 Feb 2014
Posts: 4
Re: The number of water lilies on a certain lake doubles every  [#permalink]

### Show Tags

That is pretty easy one.
Full = 60 days, knowing that the number of lilies doubles each 2 days we can deduce that the half of the lake was full at 58 days.
Taking initial information that we have 2 lilies at day 1 we can just simply multiply 2 lilies by 1/2 of the lake which means that the lake will be full at 58 days.
Manager  Joined: 17 Jul 2013
Posts: 69
Re: The number of water lilies on a certain lake doubles every  [#permalink]

### Show Tags

1
I thought this way :
30 days will take to complete the pond with lillies count as 2^30 (since it takes 2 days to double hence will take 30 days of 60)
on first day - 2^0 =1 lilly
on day 2 - 2^1 = 2
on day 3 - 2^2 = 4 so on ...
now since the there are two lillies already it will take 2^30/ 2^1 = 2^29 ...this will take complete 2* 29 days i.e 58 days

I hope it is clear .....
Intern  Joined: 23 Apr 2014
Posts: 9
Re: The number of water lilies on a certain lake doubles every  [#permalink]

### Show Tags

1
2
I am going by this formula : y(t) = y(0) x K^t
where
y(t) = desired value after t period
y(0) = initial value
k = multiplier (or the factor by which the value increases every t period)
t = time period

Given - # of lilies doubles every two days
==> t= 2 days
k^t = k^2 = 2
==> k = sqrt(2)
Now,
it takes 60 days for a lake to be fully covered with water lilies starting from 1 lily
so, y(0) = 1
t = 60 days
y(t) i.e no. of lilies after 60 days
y(t) = 1 x sqrt(2)^60

now, we have the final count of lilies after 60 days if we start from 1 lily.
we can calculate the time period if we start from 2 lilies ( the # of lilies after 60 days will not change as the multiplier is constant)

1 x sqrt(2)^60 = 2 x sqrt(2)^t

Solving this will give t= 58 days.

I hope it helps.
Intern  Joined: 15 Jul 2012
Posts: 32
Re: The number of water lilies on a certain lake doubles every  [#permalink]

### Show Tags

Bunuel wrote:

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.

Hope it helps.

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

hey Bunuel,

i have a doubt in the first part of the problem it is given that if there is one lily it will take 60 days and number of water lillies double every 2 days.

so, it is in GP and the terms will be a, ar, ar^2, ar^3 etc. here it is 1,2,4,8....

we need to find the 30th term which will be ar^n-1 gives us ar^29 that leads to 1(2^29) but you got it as 2^30

what is wrong with what i did?
Math Expert V
Joined: 02 Sep 2009
Posts: 61189
Re: The number of water lilies on a certain lake doubles every  [#permalink]

### Show Tags

saggii27 wrote:
Bunuel wrote:

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.

Hope it helps.

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

hey Bunuel,

i have a doubt in the first part of the problem it is given that if there is one lily it will take 60 days and number of water lillies double every 2 days.

so, it is in GP and the terms will be a, ar, ar^2, ar^3 etc. here it is 1,2,4,8....

we need to find the 30th term which will be ar^n-1 gives us ar^29 that leads to 1(2^29) but you got it as 2^30

what is wrong with what i did?

If you take first term as 1, then you'd have 31 terms: 1st day plus 30 divisions.
_________________
Board of Directors P
Joined: 17 Jul 2014
Posts: 2471
Location: United States (IL)
Concentration: Finance, Economics
GMAT 1: 650 Q49 V30 GPA: 3.92
WE: General Management (Transportation)
Re: The number of water lilies on a certain lake doubles every  [#permalink]

### Show Tags

since it doubles every 2 days..
on day 2 - we have 2
on day 4 - we have 4 or 2^2
on day 6 - we have 8, or 2^3
as we see, the power is nr of days/2
so in 60 days, we'll have 2^30 lilies.

so on day2 - we have 4
on day 4 - we have 8...
day 6 -> 2^4
day 8 -> 2^5
day 10 -> 2^6
day 12 -> 2^7

we can notice a pattern, that when # of days is divisible by 2, the power is +3 than for the last nr of days divisible by 6.
so: day 54 -> 4+3+3+3+3+3+3+3 -> so 28th power.
on day 56 - we'll have 2^29
on day 58 - we'll have 2^30 - the number we need.
so 58 days.
Veritas Prep GMAT Instructor V
Joined: 16 Oct 2010
Posts: 10097
Location: Pune, India
Re: The number of water lilies on a certain lake doubles every  [#permalink]

### Show Tags

4
mvictor wrote:
since it doubles every 2 days..
on day 2 - we have 2
on day 4 - we have 4 or 2^2
on day 6 - we have 8, or 2^3
as we see, the power is nr of days/2
so in 60 days, we'll have 2^30 lilies.

so on day2 - we have 4
on day 4 - we have 8...
day 6 -> 2^4
day 8 -> 2^5
day 10 -> 2^6
day 12 -> 2^7

we can notice a pattern, that when # of days is divisible by 2, the power is +3 than for the last nr of days divisible by 6.
so: day 54 -> 4+3+3+3+3+3+3+3 -> so 28th power.
on day 56 - we'll have 2^29
on day 58 - we'll have 2^30 - the number we need.
so 58 days.

1 lily on Day 1 beginning,
get 2 by Day 2 end (or Day 3 beginning ),
get 4 by Day 4 end
get 8 by Day 6 end and so on
till you get pond full of lilies by Day 60 end.

If there are already 2 water lilies, you are just starting with Day 3 beginning and skipping the first 2 days. So to cover the pond you will need 2 days less i.e. 60 - 2 = 58 days.
_________________
Karishma
Veritas Prep GMAT Instructor

Manager  B
Joined: 08 Sep 2015
Posts: 62
Re: The number of water lilies on a certain lake doubles every  [#permalink]

### Show Tags

1
I found this formula to be easy to apply and it consistently gives me the right answer on questions like this.

Final population = S * P ^ (t/l)
S = starting population
P = progression (doubles = 2, triples = 3 etc.)
t/l = total amount of iterations
t = time
I = intervals

Let X be final number of lilies that covered the lake after 60 days, which means that x = 1 lily * 2 ^ ( 60 days /2 days)
From here => x = 2 ^30 = that is the final number of lilies needed to cover the lake
now if we start with 2 lilies => 2 ^ 30( which is the total number of lilies needed to cover the lake ) = 2 * 2 ^ t/ 2

=> 30 = t/2 +1 => 29 = t/2 => t = 58 - is the time needed to cover the lake when starting with 2 lilies
Manager  G
Joined: 07 Jun 2017
Posts: 159
Location: India
Concentration: Technology, General Management
GMAT 1: 660 Q46 V38
GPA: 3.6
WE: Information Technology (Computer Software)
Re: The number of water lilies on a certain lake doubles every  [#permalink]

### Show Tags

Every 2 days it doubles
Senior Manager  P
Status: Whatever it takes!
Joined: 10 Oct 2018
Posts: 381
GPA: 4
The number of water lilies on a certain lake doubles every  [#permalink]

### Show Tags

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

Could someone evaluate whether I did it right?
2^60 =$$\frac{2^n}{2}$$
60=n-2
n=58 option D The number of water lilies on a certain lake doubles every   [#permalink] 22 Jul 2019, 22:39
Display posts from previous: Sort by

# The number of water lilies on a certain lake doubles every  