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Sequence

by guerrero » Thu Apr 04, 2013 7:02 am
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


Need help to solve it algebraically...OA D
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by Brent@GMATPrepNow » Thu Apr 04, 2013 7:11 am
guerrero 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


Need help to solve it algebraically...OA D
If there is exactly one water lily on the lake, it takes 60 days for the lake to be fully covered with water lilies.

Day 0: 1 lily
Day 2: 2 lilies
Day 4: 4 lilies
Day 6: 8 lilies
.
.
.
Day 58: Lake half full
Day 60: Lake full

In how many days will the lake be fully covered with lilies, if initially there were two water lilies on it?
Here's we are essentially starting on Day 2 of the above scenario.
If we're starting on Day 2, then it will take only 58 days to reach Day 60.

Answer: D

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Brent
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by srcc25anu » Thu Apr 04, 2013 11:50 am
# Water lilies on Day 0 = x
# Water lilies on Day 0+2 = 2*x

on Day 0, # water lilies = 1
Day 2 - 2
Day 4 - 4
Day 6 will be 8 and so on

Let suppose for simplicity the pond is full with 8 lilies only in 6 days (instead of 60 days in Question)
so if we start with 1 lily, the pond has 8 lilies on DAY 6 (6 days)
Suppose we started with 2 lilies on Day 0
Day 2 we would have 4 lilies and
Day 4 we would have 8 lilies the pond has 8 liles on DAY 4.

Therefore the pond is NOW full in only 4 days if we start with 2 (instaed of 1) . i.e. TWO lESS DAys. WHY? Because it takes exactly 2 days to double from 1 to 2 lilies.

the same logic would also apply for the given question. it would take 2 less days if we start with 2 lilies than if we start with 1 lily. since origianlly it takes 60 days to fill the pond if we start with 1 lily on Day 0, The number of days will reduce by 2 if we had instead started with 2 liles.
Hence Answer D

And likewise just suppose we were to start with 4 lilies instead of 1, guess how many days will it take to fill the pond?
[spoiler]60 - 4 = 56 (since it takes 4 days to grow from 1 lily to 4)[/spoiler]
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by vipulgoyal » Thu Apr 04, 2013 10:12 pm
algeb ans

1*2^30 = 2*2^x
x+1 = 30
x = 29
since x is no of 2 days period 29x2=58 days
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