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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? (A)$96,000
(B) $97,000 (C)$98,000
(D) $99,000 (E)$100,000
[Reveal] Spoiler: OA

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

Thanks.
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Re: $686,000 in bonus money is to be divided among 6 employees [#permalink] ### Show Tags 13 Feb 2012, 21:45 1 This post received KUDOS Expert's post 6 This post was BOOKMARKED priyankaparanjape wrote:$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. Similar questions: a-certain-city-with-population-of-132-000-is-to-be-divided-76217.html?hilit=population#p1035185 shaggy-has-to-learn-the-same-71-hiragana-characters-and-126948.html Other min/max questions: PS: search.php?search_id=tag&tag_id=63 DS: search.php?search_id=tag&tag_id=42 Hope it helps. _________________ GMAT Club Legend Joined: 09 Sep 2013 Posts: 12165 Followers: 538 Kudos [?]: 151 [0], given: 0 Re:$686,000 in bonus money is to be divided among 6 employees [#permalink]

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04 May 2014, 14:33
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13 Jun 2014, 01:56
alphabeta1234 wrote:
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=@

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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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15 May 2016, 13:01
Hello from the GMAT Club BumpBot!

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