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$686,000 in bonus money is to be divided among 6 employees. No employe [#permalink]

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26 Nov 2010, 14:52

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$686,000 in bonus money is to be divided among 6 employees. No employee is to receive a bonus more than 20% greater than the bonus received by any other employee. What is the minimum possible bonus that an employee can receive?

Re: $686,000 in bonus money is to be divided among 6 employees. No employe [#permalink]

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26 Nov 2010, 15:03

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The question stem states that the difference between the minimum and maximum bonus may not exceed 20%. To determine the minimum possible bonus for an employee you have to assume that the other 5 employees obtain the maximum possible bonus.

If x denotes the minimum possible bonus and 1.2x denotes the maximum possible bonus you can set up the equation as follows:

x + 5*1.2x = $686,000 => 7x = $686,000 => x = $98'000

Stanford2012 has explained the solution perfectly. The only thing I want to highlight here is the concept.

Let's say you have a fixed sum of $100 that needs to be distributed among 5 people. If you want to maximize one person's share, you need to give everyone else the minimum that you can. e.g. the question says each person must receive at least $10, what is the maximum one person can receive? Since you want to maximize one person's share, you should give everyone else the minimum possible i.e. $ 10. You give $10 to each of the other 4 people and are left with $60, the maximum that you can give to one guy. Similarly, if you want to minimize someone's share, you should give everyone else the maximum possible.

In your question here, a fixed amount has to be distributed among 6 people and one person's minimum share needs to be found. A person will receive minimum (say $x) , when everyone else gets the maximum that they can (that will be $6x/5).
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$686,000 in bonus money is to be divided among 6 employees [#permalink]

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13 Feb 2012, 20:34

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$686,000 in bonus money is to be divided among 6 employees. No employee is to receive a bonus more than 20% greater than the bonus received by any other employee. What is the minimum possible bonus that an employee can receive?

A. $96,000 B. $97,000 C. $98,000 D. $99,000 E. $100,000

I often struggle with such questions. I can understand that for minimum value , we need to consider highest salary 20%, however I cannot understand how to put other 4 intermediate values. When I read the explanation I understand, but do not seem to apply it while solving. Can someone pls help in how to think through such problems.

$686,000 in bonus money is to be divided among 6 employees. No employee is to receive a bonus more than 20% greater than the bonus received by any other employee. What is the minimum possible bonus that an employee can receive?

A. $96,000 B. $97,000 C. $98,000 D. $99,000 E. $100,000

I often struggle with such questions. I can understand that for minimum value , we need to consider highest salary 20%, however I cannot understand how to put other 4 intermediate values. When I read the explanation I understand, but do not seem to apply it while solving. Can someone pls help in how to think through such problems.

Thanks.

Since "no employee is to receive a bonus more than 20% greater than the bonus received by any other employee", then the bonuses of 6 employees must be in the range: \($x\) and \($1.2x\).

So we want to minimize \(x\). To minimize \(x\) we should make only one employee to receive that bonus (minimum possible) and the rest 5 employees to receive \(1.2x\) bonus (maximum possible).

\(x+5*1.2x=686\) --> \(7x=686\) --> \(x=98\).

Answer: C.

General rule for such kind of problems: to maximize one quantity, minimize the others; to minimize one quantity, maximize the others.

Re: $686,000 in bonus money is to be divided among 6 employees [#permalink]

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12 Jun 2014, 21:11

Hi Bunuel,

I am confused. Why are we minimizing 1 persons bonus and maxing out all the other 5?? Shouldnt we be minimizing 1 persons bonus, maxing only 1 other persons bonuses and keeping the 4 in the middle at 1/6 of the total bonus. So let 686,000/6=@ @ is what everyone should get in an even world. So for the first guy, whom we eant to minimize, i am going to deduct x from his @. For the 6th guy, the guy we want to max out where going to give him x, but such that the following condition is met.

(@-x)1.2=(@+x) .2@=2.2x .2(686,000/6)/2.2=10393.0=x Now the first guy, the minimum bonus guy is going to get @-x=114333-10393=103,940 Where am I going wrong?

I am confused. Why are we minimizing 1 persons bonus and maxing out all the other 5?? Shouldnt we be minimizing 1 persons bonus, maxing only 1 other persons bonuses and keeping the 4 in the middle at 1/6 of the total bonus. So let 686,000/6=@

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Questions asks: what is the minimum possible bonus that an employee can receive?

If we maximize the bonuses of 5 people the remaining 6th one will get the minimum bonus.
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Re: $686,000 in bonus money is to be divided among 6 employees [#permalink]

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