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Bunuel
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On Monday, Millie puts a quart of seeds, 25% of which are millet, into 29 Mar 2019, 00:24
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95% (hard)

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21% (04:03) correct 79% (02:50) wrong based on 29 sessions

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On Monday, Millie puts a quart of seeds, 25% of which are millet, into a bird feeder. On each successive day she adds another quart of the same mix of seeds without removing any seeds that are left. Each day the birds eat only 25% of the millet in the feeder, but they eat all of the other seeds. On which day, just after Millie has placed the seeds, will the birds find that more than half the seeds in the feeder are millet?

(A) Tuesday
(B) Wednesday
(C) Thursday
(D) Friday
(E) Saturday
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vgabrov
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On Monday, Millie puts a quart of seeds, 25% of which are millet, into 07 Apr 2019, 03:28
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Let m be the millet. Then on Tuesday, there will be 3/16 m. Continuing like this, we see that on Thursday there will be 111/256, which is slightly smaller than 1/2. Thus, Friday.
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georgethomps
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On Monday, Millie puts a quart of seeds, 25% of which are millet, into 07 Apr 2019, 08:50
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vgabrov
Let m be the millet. Then on Tuesday, there will be 3/16 m. Continuing like this, we see that on Thursday there will be 111/256, which is slightly smaller than 1/2. Thus, Friday.
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How would I do this in under two minutes? There has to be a better way. The concept is easy but the mental math is too tedious.
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vgabrov
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On Monday, Millie puts a quart of seeds, 25% of which are millet, into Updated on: 07 Apr 2019, 23:38
Originally posted by vgabrov on 07 Apr 2019, 09:03.
Last edited by vgabrov on 07 Apr 2019, 23:38, edited 1 time in total.
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georgethomps
How would I do this in under two minutes? There has to be a better way. The concept is easy but the mental math is too tedious.
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To me the longer part was putting down the correct formula and understanding that the "other" seeds dont matter. So, yes, I also did not do it in two minutes.
The calculations are just 3 operations with ratios, and its a 700 level question.
I'm not sure. Lets see what people say.

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On Monday, Millie puts a quart of seeds, 25% of which are millet, into Updated on: 07 Apr 2019, 10:13
Originally posted by georgethomps on 07 Apr 2019, 09:52.
Last edited by georgethomps on 07 Apr 2019, 10:13, edited 3 times in total.
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Wait I'm having a problem working through this with a calculator. The amount of seed is reaching a limit of 33.33.

1 Day: 25 * .25 + 25 = 31.25
2 Days: 31.25 * .25 + 25 = 32.8125
3 Days: 32.8125 * .25 + 25 = 33.203
.....

LIMIT EXPLAINED:

Assume a quart has 100 seeds, so there will be 25 millet seeds in each quart of feeder.

The math for 1 day would be: (25 * .25 + 25) -> 25(.25 + 1)
The math for 2 days would be: (25 * .25 + 25) * .25 + 25 -> (.25^2 * 25 + .25 * 25) + 25 -> 25(.25 + .25^2 + 1)
The math for 3 days would be: 25(.25 + .25^2 + .25^3 + 1)

This infinitely repeating pattern S can be approximated with the following math (this is more accurate the more days millet is laid):

S = .25 + .25^2 + .25^3 + .25^4 ...

.25*S = .25^2 + .25^3 + .25^4 + .25^5 ...

Focusing on the term S, we can eliminate the infinitely repeating part of the equations by subtracting .25 * S from S. Subtracting both equations equals .25!

Solve for S: S - .25*S = .25 -> S(1 - .25) = .25 -> S(.75) = .25 -> S = .33

RETURN TO THE EQUATIONS ABOVE:

The equations above can be simplified to the following: 25(S + 1) = 25(1.33) = 33.25, which is why the amount of Millet reaches a limit of approximately 33.33.
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vgabrov
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On Monday, Millie puts a quart of seeds, 25% of which are millet, into 07 Apr 2019, 09:59
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Are you calculating the amount of millet eaten instead of millet left over?

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georgethomps
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On Monday, Millie puts a quart of seeds, 25% of which are millet, into 07 Apr 2019, 10:14
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vgabrov
Are you calculating the amount of millet eaten instead of millet left over?

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Yep, wow did I overcomplicate this. Oh well, the math is interesting. This is much easier now.

Monday: 25 * .75 = 18.75 Left over
Tuesday: (18.75 + 25) * .75 = 32.81
Wednesday: (32.81 + 25) * .75 = 43.36 Left over
Thursday: (43.37 + 25) * .75 > 50 Left Over

The birds will then find the amount left over on Friday. It's important to assume the birds will start eating on Monday and that they eat after the millet is laid. This lead to a lot of confusion on my end even after my initial mistake.
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