Each of the 20 employees at Company J is to receive an end-of-year bon

Question

Each of the 20 employees at Company J is to receive an end-of-year bonus this year. Agnes will receive a larger bonus than any other employee, but only $500 more than Cheryl will receive. None of the employees will receive a smaller bonus than Cheryl. If the amount of money to be distributed in bonuses at Company J this year totals $60,000, what is the largest bonus Agnes can receive?

A. $3,250
B. $3,325
C. $3,400
D. $3,475
E. $3,500

PS97190.02

A. $3,250
B. $3,325
C. $3,400
D. $3,475
E. $3,500

PS97190.02

Bunuel · Accepted Answer

We know that Agnes received the largest bonus and Cheryl received the smallest bonus. If we try values like Agnes = 3,499 and Cheryl = 2,999 with the other 18 employees also at 2,999, the total would exceed 60,000.

To maximize Agnes’s bonus, we need to minimize what the other employees receive. The smallest they can get is what Cheryl gets. Let Cheryl’s bonus be x. Then the other 18 employees also receive x, and Agnes receives x + 500. The total is

19x + (x + 500) = 60,000.

x = 2,975.

That means 19 employees, including Cheryl, received 2,975 each, and Agnes received 2,975 + 500 = 3,475.

lacktutor · Answer

Agnes = Cheryl + 500 
The remaining 18 employees >= Cheryl 
Total = 60000
—> in order Agnes to get the largest bonus, the any other employees should get the same as Cheryl gets.

19Ch + Ch + 500 = 60000
20 Ch = 59500
Ch = 2975 
—> Agnes = 2975 + 500 = 3475

Answer ( D)

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Archit3110 · Answer

given
total employees = 20
A received 500+ C
and all 18 other receive same salary as C ; 
so we have 
19c+500+c = 60,000
solve for c= 2975
a salary ; 2975+500 ; 3475
OPTION D

Amit17nov · Answer

Each of the 20 employees at Company J is to receive an end-of-year bonus this year. Agnes will receive a larger bonus than any other employee, but only $500 more than Cheryl will receive. None of the employees will receive a smaller bonus than Cheryl. If the amount of money to be distributed in bonuses at Company J this year totals $60,000, what is the largest bonus Agnes can receive?

A. $3,250
B. $3,325
C. $3,400
D. $3,475
E. $3,500

Now, if everybody had got the same amount in bonus, then each would have got $60,000/20 = $3000
but since Agnes must receive only $500 more than Cheryl and none of the employees must take less than Cheryl, Agnes' bonus gets max if all other than Agnes receive bonus equal to Cheryl. Since there are 20 employees, all including Agnes must take a cut of $500/20 = $25. So, Agnes takes $3000 + $500 - $25 = $3475. Hence, D is the answer

ScottTargetTestPrep · Answer

We can let the bonus of Cheryl and the other employees = 19x and Agnes’s bonus = x + 500; thus:

20x + 500 = 60,000

20x = 59,500

x = 2,975

Thus, Agnes will receive 2,975 + 500 = $3,475 in bonus.

Answer: D

Sabby · Answer

Hi, 
As Agnes' bonus is 500$ more than Cheryl, let's call it A=C+500
For Agnes to have the max bonus, all the other must have the same minimum, therefore all the 18 other employees and Cheryl must have the same bonus amount: we get 19C

60000=19C+C+500
59500=20C
C=2975$

Now as Agnes = C+500, Agnes will get 2975+500= 3475$ max

Answer D)

JoeSal · Answer

Hi, I wanted to check on the line "None of the employees will receive a smaller bonus than Cheryl". Why did we not take this into account in solving the answer?

saynchalk · Answer

Hi JoeSal,

It is taken into account, but it basically means that the employees will recieve a bonus in this order

Agnes > 19 other employees >or= Cheryl

Basically, whatever bonus amount Cheryl recieves is the lowest limit for what the other 19 employees may recieve.

So, the employees can recieve at the very least the amount that Cheryl has recieved.

Since this is the case, it can also be that the amount recieved by Cheryl is the amount recieved by the 18 other employees apart from Agnes (since Agnes = Cheryl + 500)

KarishmaB · Answer

This means that Cheryl has the smallest bonus and others could have it too. But Agnes has the highest bonus (more than all others) and it is $500 more than Cheryl's bonus. Say Cheryl's bonus is $c.

If we arrange all bonuses in increasing order, we could get something like:
$c, $c, $(c + 10), $(c + 200), ... $(c + 500)

If we want to maximise Agnes' bonus we should minimize that of all others so that Agnes can get the biggest part of $60,000.

So 19 people can get $c while Agnes gets $(c + 500).

19c + c + 500 = 60,000
c = 2975

c + 500 = $3475

Answer (D)

Check out this blog post for  another question on mean, median and range .

justinioane · Answer

Why can't E work for this?
Agnes = 3500
Cheryl = 2500
18 employees = 3000 each

Krunaal · Answer

It seems you missed -  "   Agnes will receive a larger bonus than any other employee,    but only $500 more than Cheryl will receive   "  => A = C + 500

balajiramakrishnan · Answer

One small doubt, not sure if my understanding is correct, 
why cant it be 3499 for Agnes and 2999 for Cheryl and the rest for all emp, since they have not mentioned if rest of the employees have received the same money or not. This way A(C+500)>18E>C right, Was it because there was no answer with this option ?

balajiramakrishnan · Answer

i just ran through the calculations again, my bad, all clear.

Thanks a lot Bunuel !

etaireia · Answer

Hi, my interpretation: $60000/20 =3,000/- per head. Now Agnes needs to get max and $500 more than Cheryl. So why can't we take 500 from Cheryl and give it to Agnes? This would make Agnes's bonus $3,500, Cheryl's $2,500 and rest of the employees get $3,000 each. Cheryl still has the lowest bonus amount. Not sure where I made a mistake in the interpretation. Could you please help me rectify my error?

Bunuel · Answer

Each of the 20 employees at Company J is to receive an end-of-year bonus this year. Agnes will receive a larger bonus than any other employee, but only $500 more than Cheryl will receive. None of the employees will receive a smaller bonus than Cheryl. If the amount of money to be distributed in bonuses at Company J this year totals $60,000, what is the largest bonus Agnes can receive?

A. $3,250
B. $3,325
C. $3,400
D. $3,475
E. $3,500

PS97190.02

We are told that " Agnes will receive ... $500 more than Cheryl will receive. "

How is your distribution with Agnes = $3,500 and Cheryl = $2,500 satisfy this?

etaireia · Answer

Omg... careless mistake on my behalf! Thank you

Each of the 20 employees at Company J is to receive an end-of-year bon

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Each of the 20 employees at Company J is to receive an end-of-year bon

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