A will was written such that an estate would be divided amon

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

GMAT assassins aren't born, they're made,
Rich

BTGmoderatorDC 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