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

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%).

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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In order to minimize the range 10k should be considered as the largest share.

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.

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.

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?

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.

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

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:

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

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

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)

For all those asking why take 10K as the highest, see what happens if you take 10K as the lowest (range gets bigger):

10*1.2 = 12
12*1.2 = 14.4
14.4*1.2 = 17.8
17.8*1.2 = 20.7

20,700-10,000 = 10, 700

For all those asking why take 10K as the highest, see what happens if you take 10K as the lowest (range gets bigger):

10*1.2 = 12
12*1.2 = 14.4
14.4*1.2 = 17.8
17.8*1.2 = 20.7

20,700-10,000 = 10, 700

Can someone explain why this method is giving wrong answer:

lowest amount=x
2nd=1.2*x
3rd=1.2^2*x
4th=1.2^3*x
5th=1.2^4*x=10000

This gives range of 5177

Hi SanjaySrini,

The prompt asks for the SMALLEST possible range and based on what the prompt tells us, we can calculate a range in 2 ways:

-starting at $10,000 with 20% increases
-starting at $10,000 with 20% decreases

With the first option, by increasing your values, the individual numbers will become farther and farther apart, so this range will be larger than the other range of the second option (in which the individual values become closer and closer together).

With 20% decreases, the calculations would be:

Highest value = X = $10,000
2nd value = (.8)(X)
3rd value = (.8^2)(X)
4th value = (.8^3)(X)
5th value = (.8^4)(X)

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