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Tree

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by heshamelaziry » Mon Nov 23, 2009 8:34 pm
If each day a tree loses half of its remaining leaves, what fraction of its leaves will it have lost after 5 days ?

1/32

1/16

9/10

15/16

31/32


What is the logic behind this? I picked 80 and cut half for 5 days, btu didin't work. [spoiler]OA 31/32[/spoiler]
Last edited by heshamelaziry on Mon Nov 23, 2009 9:08 pm, edited 1 time in total.
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Source: — Problem Solving |

by thephoenix » Mon Nov 23, 2009 9:03 pm
imo a)
with 80 your no. we will have 2.5 lost on 5th day
and fraction is 2.5/80=1/32

days actual lost remaining
1 x x/2 x/2
2 x/2 x/4 x/4
3 x/4 x/8 x/8
4 x/8 x/16 x/16
5 x/16 x/32 x/32

hence 1/32 is the req fraction
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by papgust » Mon Nov 23, 2009 9:57 pm
This can be approached in a more simple way.

Assume tree leaf = 1 (Intial stage)

Half of the remaining leaves is lost per day --> 1/2
so for 5 days --> 1/2^5 = 1/32

Now, subtract lost leaves from the initial stage of the tree to get the current number of leaves.
1 - 1/32 = 31/32
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by heshamelaziry » Mon Nov 23, 2009 10:00 pm
papgust wrote:This can be approached in a more simple way.

Assume tree leaf = 1 (Intial stage)

Half of the remaining leaves is lost per day --> 1/2
so for 5 days --> 1/2^5 = 1/32

Now, subtract lost leaves from the initial stage of the tree to get the current number of leaves.
1 - 1/32 = 31/32

But what is the difference between choosing 1 or any other number ? if i choose any other number it wil not work. this why I am too confused.
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by papgust » Mon Nov 23, 2009 10:09 pm
You can choose any number that is comfortable for you. For me, it was comfortable using 1 which is helpful in the calculation of this problem i've shown
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by heshamelaziry » Mon Nov 23, 2009 10:15 pm
papgust wrote:You can choose any number that is comfortable for you. For me, it was comfortable using 1 which is helpful in the calculation of this problem i've shown
If you can,please whow how to do it with 80
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by Testluv » Mon Nov 23, 2009 10:52 pm
heshamelaziry wrote:
papgust wrote:You can choose any number that is comfortable for you. For me, it was comfortable using 1 which is helpful in the calculation of this problem i've shown
If you can,please whow how to do it with 80
You don't want to pick 80 here. Before you pick a number, reason with the problem a little bit. When picking numbers you want to pick numbers that are permissible and manageabe. So, you always want to think about what kind of numbers will be manageable given the specific conditions of the problem. Here, whatever number we pick, we are going to be dividing it by 2 over and over again. So, be sure to pick a number that can divide 2 over and over again nicely. Ideally, you want to pick a power of 2. Since we will be dividing it by 2 five times, you can pick something like 2^5 or 2^6.

If you pick 2^6 = 64, then original number of leaves is 64. We half it once, giving us 32, half it again giving us 16, and then half it three more times arriving at 2. So when we start with 64 leaves, we are left with 2. Therefore, we have lost 62. So, the proportion lost is 62/64 = 31/32.
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by heshamelaziry » Tue Nov 24, 2009 9:13 am
Thank you Testluv.
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