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 Your Progress

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.

It appears that you are browsing the GMAT Club forum unregistered!

Signing up is free, quick, and confidential.
Join other 500,000 members and get the full benefits of GMAT Club

Registration gives you:

Tests

Take 11 tests and quizzes from GMAT Club and leading GMAT prep companies such as Manhattan GMAT,
Knewton, and others. All are free for GMAT Club members.

Applicant Stats

View detailed applicant stats such as GPA, GMAT score, work experience, location, application
status, and more

Books/Downloads

Download thousands of study notes,
question collections, GMAT Club’s
Grammar and Math books.
All are free!

Thank you for using the timer!
We noticed you are actually not timing your practice. Click the START button first next time you use the timer.
There are many benefits to timing your practice, including:

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

Show Tags

21 Nov 2012, 22:18

1

This post received KUDOS

20

This post was BOOKMARKED

00:00

A

B

C

D

E

Difficulty:

95% (hard)

Question Stats:

44% (02:24) correct
56% (01:27) wrong based on 389 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?

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.

Re: The number of water lilies on a certain lake doubles every [#permalink]

Show Tags

21 Nov 2012, 22:29

1

This post received KUDOS

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.

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.

now, we start with 2... 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.

Or just think about it logically - you start with 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.
_________________

Re: The number of water lilies on a certain lake doubles every [#permalink]

Show Tags

30 Nov 2012, 07:57

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..

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.
_________________

Re: The number of water lilies on a certain lake doubles every [#permalink]

Show Tags

09 Mar 2014, 05:46

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
_________________

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.

Re: The number of water lilies on a certain lake doubles every [#permalink]

Show Tags

09 Mar 2014, 19:38

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.

Re: The number of water lilies on a certain lake doubles every [#permalink]

Show Tags

10 Jun 2014, 13:36

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.

Re: The number of water lilies on a certain lake doubles every [#permalink]

Show Tags

21 Jun 2014, 05:22

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

Re: The number of water lilies on a certain lake doubles every [#permalink]

Show Tags

16 Sep 2014, 04:08

2

This post was BOOKMARKED

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)

Re: The number of water lilies on a certain lake doubles every [#permalink]

Show Tags

05 Oct 2014, 02:34

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

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.
_________________

Re: The number of water lilies on a certain lake doubles every [#permalink]

Show Tags

31 Oct 2015, 13:18

Hello from the GMAT Club BumpBot!

Thanks to another GMAT Club member, I have just discovered this valuable topic, yet it had no discussion for over a year. I am now bumping it up - doing my job. I think you may find it valuable (esp those replies with Kudos).

Want to see all other topics I dig out? Follow me (click follow button on profile). You will receive a summary of all topics I bump in your profile area as well as via email.
_________________

After days of waiting, sharing the tension with other applicants in forums, coming up with different theories about invites patterns, and, overall, refreshing my inbox every five minutes to...

I was totally freaking out. Apparently, most of the HBS invites were already sent and I didn’t get one. However, there are still some to come out on...

In early 2012, when I was working as a biomedical researcher at the National Institutes of Health , I decided that I wanted to get an MBA and make the...