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Arithmetic

by BTGmoderatorRO » Sun Oct 08, 2017 11:45 am
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
QA is b.

Can anyone help me out here, i hate word problems :oops:
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by Jay@ManhattanReview » Sun Oct 08, 2017 9:57 pm
Roland2rule 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
QA is b.

Can anyone help me out here, i hate word problems :oops:
Two things first...

1. Since the question asks us to find out the value of the smallest possible range, we must assume that the share $10,000 is the highest.

2. Since no beneficiary can receive an amount within 20% of another's amount, we assume that share of a beneficiary is less than 80% of that of others.
  • Highest share (share of 5th beneficiary) = $10,000;
    Share of 4th beneficiary < 80% of $10,000 < $8000;
    Share of 3rd beneficiary < 80% of $8,000 < $6400;
    Share of 2nd beneficiary < 80% of $6,400 < ~$5100;
    Lowest share (share of 1st beneficiary) < 80% of ~$5,100 < ~$4000
Smallest possible range = 10,000 - ~4,000 = ~6,000 => [spoiler]$5904[/spoiler]

The correct answer: B

Hope this helps!

-Jay

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by Scott@TargetTestPrep » Sun Nov 24, 2019 5:45 pm
BTGmoderatorRO 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
QA is b.

Can anyone help me out here, i hate word problems :oops:
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 the other beneficiaries 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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by [email protected] » Mon Nov 25, 2019 10:14 am
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

Final Answer: B

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