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$686,000 in bonus money is to be divided among 6 employees. No employe [#permalink] ### Show Tags 26 Nov 2010, 13:52 3 This post was BOOKMARKED 00:00 Difficulty: 55% (hard) Question Stats: 67% (02:54) correct 33% (02:25) wrong based on 199 sessions ### HideShow timer Statistics 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 _________________ I appreciate the kudos if you find this post helpful! +1 Manager Joined: 02 Apr 2010 Posts: 103 Followers: 5 Kudos [?]: 120 [0], given: 18 Re:$686,000 in bonus money is to be divided among 6 employees. No employe [#permalink]

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26 Nov 2010, 14:03
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. Veritas Prep GMAT Instructor Joined: 16 Oct 2010 Posts: 7177 Location: Pune, India Followers: 2161 Kudos [?]: 13985 [0], given: 222 Re:$686,000 in bonus money is to be divided among 6 employees. No employe [#permalink]

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26 Nov 2010, 19:15
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). _________________ Karishma Veritas Prep | GMAT Instructor My Blog Get started with Veritas Prep GMAT On Demand for$199

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$686,000 in bonus money is to be divided among 6 employees [#permalink] ### Show Tags 13 Feb 2012, 19:34 2 This post was BOOKMARKED$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. Math Expert Joined: 02 Sep 2009 Posts: 37036 Followers: 7230 Kudos [?]: 96127 [1] , given: 10707 Re:$686,000 in bonus money is to be divided among 6 employees [#permalink]

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13 Feb 2012, 20:45
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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).

$$x+5*1.2x=686$$ --> $$7x=686$$ --> $$x=98$$.

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

Similar questions:
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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.
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12 Jun 2014, 20:11
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?

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16 Jun 2015, 11:13
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Re: $686,000 in bonus money is to be divided among 6 employees. No employe [#permalink] ### Show Tags 15 May 2016, 12:01 Hello from the GMAT Club BumpBot! Thanks to another GMAT Club member, I have just discovered this valuable topic, yet it had no discussion for over a year. I am now bumping it up - doing my job. I think you may find it valuable (esp those replies with Kudos). Want to see all other topics I dig out? Follow me (click follow button on profile). You will receive a summary of all topics I bump in your profile area as well as via email. _________________ Re:$686,000 in bonus money is to be divided among 6 employees. No employe   [#permalink] 15 May 2016, 12:01
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