$686,000 in bonus money is to be divided among 6 employees

Question

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

Bunuel · Accepted Answer

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.

stanford2012 · Answer

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.

KarishmaB · Answer

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).

priyankaparanjape · Answer

$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.

alphabeta1234 · Answer

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?

Posted from my mobile device

Bunuel · Answer

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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$686,000 in bonus money is to be divided among 6 employees

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