Here's another one that I knew and out-thought myself on.

If you remember "Half Life" concept of radioactive materials then this should not bother you.

After Day1 - Fraction remaining = 1/2
After Day2 - Fraction remaining = 1/2 * 1/2 = 1/4
After Day3 - Fraction remaining = 1/2 * 1/2 * 1/2 = 1/8
After Day4 - Fraction remaining = 1/2 * 1/2 * 1/2 * 1/2 = 1/16
After Day5 - Fraction remaining = 1/2 * 1/2 * 1/2 * 1/2 * 1/2 = 1/32

Fraction lost = 31/32

I get the math, I saw the trick in the answer choices...my problem was the concept of the tree itself. If each day a tree loses half it's remaining leaves, at the end of day 1 I can see the tree having all of it's leaves, and not losing half until day 2. Then at the end of day 5 it has lost 15/16. If, however, it loses half of it's "remaining" leaves on day 1, then it is 31/32.

See what I'm saying?

If the question was worded more like, "If on day 1 a tree loses half of it's leaves, and this progression continues until all of the leaves are gone, how many leaves are remaining at the end of day 5?" I would be fine...

hi microjohn,
To help you with the wordings of the question, consider this. The question speaks of a tree - and it must be a somewhat old tree for it to start shedding its leaves . Now the questions states 'each day the tree loses half of its remaining leaves'. We are not speaking of time from the inception of the tree per se, for this problem. We are only considering the time from when this (somewhat unique) phenomenon of leaves falling started. Thus, it follows that half of the leaves would fall from the tree on the first of the days under consideration. Now count 5 days from this (including this day) and calculate the amount of leaves falling each day. You have your answer:31/32. Hope this helps.

Cheers
Prashrash.

Let the number of leaves be x

1st day it loses = x/2
2nd day it loses = x/4
3rd day it loses = x/8
4th day it loses = x/16
5th day it loses = x/32

total loss = x/2 + x/4 + x/ 8 + x/16 + x/32 = 31x/32

fraction = 31/32

Another way of solving this.

No of days leaves lost =5
rate of loss = 50%/day

Leaves after 5 days= Original * (0.5)^5
% loss = (orig - leaves after 5 days)/orig = orig(1-1/32)/orig = 31/32

To start with the tree has x leaves
D1-lose x/2 remaining x/2
D2-lose x/4 remaing x/4
D3-lose x/8 remaining x/8
D4-lose x/16 remaining x/16
D5-lose x/32 remaining x/32

leaves lost = x -x/32
= 31x/32

Heman