Minimum Bonus : GMAT Problem Solving (PS)

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Minimum Bonus [#permalink]

26 Nov 2010, 14:52

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Question Stats:

33% (01:01) correct

66% (03:53) wrong

based on 0 sessions

Source: Knewton

$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

[Reveal] Spoiler: OA

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Re: Minimum Bonus [#permalink]

26 Nov 2010, 15:03

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

Hence, solution c is correct.

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Re: Minimum Bonus [#permalink]

26 Nov 2010, 20:15

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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