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A will was written such that an estate would be divided among five ben

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A will was written such that an estate would be divided among five ben  [#permalink]

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A will was written such that an estate would be divided among five beneficiaries with the remainder donated to charity. One stipulation in the will is that no one beneficiary can receive an amount within 20% of another's amount. If one of the beneficiaries received $10,000, what is the smallest possible range between the highest and lowest amounts (rounded to the nearest dollar) among the five beneficiaries?

A. $4096
B. $5904
C. $7892
D. $10736
E. $20736

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Re: A will was written such that an estate would be divided among five ben  [#permalink]

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New post 09 Oct 2014, 04:21
aadikamagic wrote:
A will was written such that an estate would be divided among five beneficiaries with the remainder donated to charity. One stipulation in the will is that no one beneficiary can receive an amount within 20% of another's amount. If one of the beneficiaries received $10,000, what is the smallest possible range between the highest and lowest amounts (rounded to the nearest dollar) among the five beneficiaries?

A. $4096
B. $5904
C. $7892
D. $10736
E. $20736


Not a fan of the wording. Anyway:

1st - 10,000.
2nd - 0.8*10,000 = 8,000
3rd - 0.8*8,000 = 6,400
4th - 0.8*6.400 = ~5,100
5h - 0.8*5,100 = ~4,000

Range = 10,000 - 4,000 = 6,000.

Answer: B.
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Re: A will was written such that an estate would be divided among five ben  [#permalink]

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New post 09 Oct 2014, 10:38
I feel like a kid asking this but Bunuel can you please tell me what this question is trying to ask? The question was a bummer to me.
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Re: A will was written such that an estate would be divided among five ben  [#permalink]

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New post 10 Oct 2014, 01:18
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AmoyV wrote:
I feel like a kid asking this but Bunuel can you please tell me what this question is trying to ask? The question was a bummer to me.


The question asks to find the smallest possible range between the highest and lowest amounts received by five people, while giving some constraints. It says that no one can receive an amount within 20% of another's amount. For example, if one has $10, then no one else can get amount from 8 (10 - 20%) to 12 (10+20%).
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Re: A will was written such that an estate would be divided among five ben  [#permalink]

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New post 11 Oct 2014, 05:18
Hello Bunuel. can you please explain why did u assume that $10K is the highest value of the range. It could also be the lowest value in the range right?

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Re: A will was written such that an estate would be divided among five ben  [#permalink]

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New post 11 Oct 2014, 06:01
p2bhokie wrote:
Hello Bunuel. can you please explain why did u assume that $10K is the highest value of the range. It could also be the lowest value in the range right?

Posted from my mobile device


In order to minimize the range 10k should be considered as the largest share.
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Re: A will was written such that an estate would be divided among five ben  [#permalink]

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New post 11 Oct 2014, 06:56
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AmoyV wrote:
I feel like a kid asking this but Bunuel can you please tell me what this question is trying to ask? The question was a bummer to me.


It was mentioned in the question that none of the beneficiaries can receive an amount with in 20% of another's amount.

If the 10000 becomes max amount, then the other amounts can be
0.8 * 10000 = 8000
0.8 * 8000 = 6400
0.8 * 6400 = 5120
0.8 * 5120 = 4096

Here, the next value decreases by 20% from previous value(as the shares keep on decreasing their 20% also decreases)
range = 10000 - 4096 = 5904

If we think that the amount 10000 is the least share then the second share will be a minimum of 12500(should not consider 12000 as 80% of 12000 = 9600 i.e 10000 is with in the reach of 20% of 12000) and similarly, each value increase by 25% from its previous values... the shares keep on increasing 25% also increases... resulting in the increase of range.

Hope this clarifies.
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Re: A will was written such that an estate would be divided among five ben  [#permalink]

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New post 24 Oct 2014, 12:54
Bunuel wrote:
aadikamagic wrote:
A will was written such that an estate would be divided among five beneficiaries with the remainder donated to charity. One stipulation in the will is that no one beneficiary can receive an amount within 20% of another's amount. If one of the beneficiaries received $10,000, what is the smallest possible range between the highest and lowest amounts (rounded to the nearest dollar) among the five beneficiaries?

A. $4096
B. $5904
C. $7892
D. $10736
E. $20736


Not a fan of the wording. Anyway:

1st - 10,000.
2nd - 0.8*10,000 = 8,000
3rd - 0.8*8,000 = 6,400
4th - 0.8*6.400 = ~5,100
5h - 0.8*5,100 = ~4,000

Range = 10,000 - 4,000 = 6,000.

Answer: B.



Hi Bunuel,

If you compare 10000 and 4000, 4000 is outside the range of 20 percent of 10000. Why it is not considered?
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Re: A will was written such that an estate would be divided among five ben  [#permalink]

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New post 25 Oct 2014, 05:10
Bambaruush wrote:
Bunuel wrote:
aadikamagic wrote:
A will was written such that an estate would be divided among five beneficiaries with the remainder donated to charity. One stipulation in the will is that no one beneficiary can receive an amount within 20% of another's amount. If one of the beneficiaries received $10,000, what is the smallest possible range between the highest and lowest amounts (rounded to the nearest dollar) among the five beneficiaries?

A. $4096
B. $5904
C. $7892
D. $10736
E. $20736


Not a fan of the wording. Anyway:

1st - 10,000.
2nd - 0.8*10,000 = 8,000
3rd - 0.8*8,000 = 6,400
4th - 0.8*6.400 = ~5,100
5h - 0.8*5,100 = ~4,000

Range = 10,000 - 4,000 = 6,000.

Answer: B.



Hi Bunuel,

If you compare 10000 and 4000, 4000 is outside the range of 20 percent of 10000. Why it is not considered?


Not sure I can follow you... We are told that no one can receive an amount within 20% of another's amount. 4000 is not within 20% range from 10000.
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Re: A will was written such that an estate would be divided among five ben  [#permalink]

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New post 12 Jul 2015, 11:47
I am trying to reason out why we need to take 10,000 as the largest number and why can't we take it as the smallest number - is it because if we take 20% of larger and larger numbers will make the numbers more far apart than if we were to go downwards, because 20% of a smaller quantity would be a smaller number?
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Re: A will was written such that an estate would be divided among five ben  [#permalink]

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New post 31 Oct 2017, 15:05
Bunuel wrote:
AmoyV wrote:
I feel like a kid asking this but Bunuel can you please tell me what this question is trying to ask? The question was a bummer to me.


The question asks to find the smallest possible range between the highest and lowest amounts received by five people, while giving some constraints. It says that no one can receive an amount within 20% of another's amount. For example, if one has $10, then no one else can get amount from 8 (10 - 20%) to 12 (10+20%).



Hi Bunuel

If the question says no one can receive an amount within 20% of another's amount, why we decrease 10,000 by 20% and so on...?
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Re: A will was written such that an estate would be divided among five ben  [#permalink]

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New post 31 Oct 2017, 20:05
1
soodia wrote:
Bunuel wrote:
AmoyV wrote:
I feel like a kid asking this but Bunuel can you please tell me what this question is trying to ask? The question was a bummer to me.


The question asks to find the smallest possible range between the highest and lowest amounts received by five people, while giving some constraints. It says that no one can receive an amount within 20% of another's amount. For example, if one has $10, then no one else can get amount from 8 (10 - 20%) to 12 (10+20%).



Hi Bunuel

If the question says no one can receive an amount within 20% of another's amount, why we decrease 10,000 by 20% and so on...?


Not sure what to add to the post you are quoting...

In order to minimize the range 10k should be considered as the largest share. Since no one can receive an amount within 20% of another's amount, then the next amount cannot be more than 8k and so on.
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Re: A will was written such that an estate would be divided among five ben  [#permalink]

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New post 01 Nov 2017, 06:47
Bunuel wrote:
aadikamagic wrote:
A will was written such that an estate would be divided among five beneficiaries with the remainder donated to charity. One stipulation in the will is that no one beneficiary can receive an amount within 20% of another's amount. If one of the beneficiaries received $10,000, what is the smallest possible range between the highest and lowest amounts (rounded to the nearest dollar) among the five beneficiaries?

A. $4096
B. $5904
C. $7892
D. $10736
E. $20736


Not a fan of the wording. Anyway:

1st - 10,000.
2nd - 0.8*10,000 = 8,000
3rd - 0.8*8,000 = 6,400
4th - 0.8*6.400 = ~5,100
5h - 0.8*5,100 = ~4,000

Range = 10,000 - 4,000 = 6,000.

Answer: B.



Hi, can't we take the 5 values as x1, x2, x3, x4, x5; take x5 = 10000 , take x4= 10000/1.2 instead of 10000*.8
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Re: A will was written such that an estate would be divided among five ben  [#permalink]

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New post 17 Jan 2019, 18:25
Hi All,

We're told that a will was written such that an estate would be divided among FIVE beneficiaries with the remainder donated to charity, with one stipulation in the will is that no one beneficiary can receive an amount within 20% of another's amount. One of the beneficiaries received $10,000 - and we're asked for the SMALLEST possible range between the highest and lowest amounts (rounded to the nearest dollar) among the five beneficiaries. This question comes down to a certain amount of Arithmetic, but the answers are sufficiently 'spaced out' that we can do a little estimation along the way.

To start, since percentages are calculated from a 'base value', to MINIMIZE the RANGE, we want to DECREASE the values from the initial $10,000 (as opposed to increasing those values, which would increase the actual difference between each pair of values).

20% of $10,000 = $2000, so the 2nd beneficiary could receive close to $10,000 - $2,000 = $8,000
20% of $8,000 = $1600, so the 3rd beneficiary could receive close to $8,000 - $1,6000 = $6,400
20% of $6,400 = approximately $1300, so the 4th beneficiary could receive close to $6,400 - $1,300 = $5,100
20% of $5,100 = approximately $1,000, so the 5th beneficiary could receive close to $5,100 - $1,000 = $4,100

The range of these values is approximately $10,000 - $4,100 = approximately $5,900

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Re: A will was written such that an estate would be divided among five ben  [#permalink]

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New post 21 Jan 2019, 18:08
aadikamagic wrote:
A will was written such that an estate would be divided among five beneficiaries with the remainder donated to charity. One stipulation in the will is that no one beneficiary can receive an amount within 20% of another's amount. If one of the beneficiaries received $10,000, what is the smallest possible range between the highest and lowest amounts (rounded to the nearest dollar) among the five beneficiaries?

A. $4096
B. $5904
C. $7892
D. $10736
E. $20736


Since we want the smallest possible range, we should let $10,000 be the highest amount. Since we want the smallest possible range between the highest and lowest amounts, we should make every other beneficiary receive as much as possible. Therefore, the next (or second) highest amount is no more than 10,000 x 0.8 = $8000. The third highest amount is no more than 8,000 x 0.8 = $6,400. The fourth highest amount is no more than 6,400 x 0.8 = $5,120 and the last (or fifth or least) amount is no more than $5,120 x 0.8 = $4,096. Therefore, the smallest possible range is 10,000 - 4,096 = $5,904 (when rounded to the nearest dollar).

Answer: B
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Re: A will was written such that an estate would be divided among five ben  [#permalink]

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New post 26 Jan 2019, 12:30
aadikamagic wrote:
A will was written such that an estate would be divided among five beneficiaries with the remainder donated to charity. One stipulation in the will is that no one beneficiary can receive an amount within 20% of another's amount. If one of the beneficiaries received $10,000, what is the smallest possible range between the highest and lowest amounts (rounded to the nearest dollar) among the five beneficiaries?

A. $4096
B. $5904
C. $7892
D. $10736
E. $20736


1. If someone recieve "X" dollars, so nobody can recieve an amount from "0.8X to 1.2X".
2. If "X" should be $100, the least amount greater than X that another one can recieve is 121 and the greatest amount less than X that another one can receive 79.
3. One of the beneficiaries recieve $10000.
4. We have to calculate the SMALLEST possible range between the HIGHEST and LOWEST amount, so we don't have to calculate amounts greater than $10000 because the range increase.

5. According to the first 4 points:

Let Xn=Beneficiary n

X1=10000
X2<0.8*(10000)---> X2=7999
X3<0.8*(7999) ----> X3=6399
X4<0.8*(6399) ----> X4=5119
X5<0.8*(5119) ----> X5=4095

Hence, the smallest range is 5905 (10000-4095)

ANSWER (B)
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Re: A will was written such that an estate would be divided among five ben   [#permalink] 26 Jan 2019, 12:30
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