Knewton Q

[Strongt]

$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 know this is a problem where I have to find the minimum value by maximizing the other 5, but I'm confused when it comes to the %20!
OAc

[subhashghosh]

Let minimum Bonus = x

So Bonus given to other five Employees = 1.2x

i.e. x + 20/100 * x

And now, x + 1.2x* 5 = 68600

=> x + 6x = 68600

=> x = 68600/7 = 98,000

Answer - C

Btw, this is very similar to a GMATPrep Problem

[Strongt]

I know I'm missing something, but how did you get 1.2x? the question says that each employee is %20 greater that the other! is that calculated this way?

0.2x + (0.2)0.2x + (0.2)0.04x + (0.2)0.008 + (0.2)0.0016)


I know this is wrong, but can you show me what my mistake is!:(

[cans]

$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?

Notice the words in green above.. If min bonus is x, no one can get more that 1.2x
and as we have to find minimum possible bonus, then bonus to all other employees should be maxmum which is 1.2x.
thus x + 1.2x*5 = 686000 =>x=98000
IMO C
Hope it's clear.

[Strongt]

Perfect! Thank you

[bblast]

Also, the question would be interesting if we would rephrase it as , $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 MAXIMUM possible bonus that an employee can receive?

I think the solution should be :

x+ 0.8*5x = 6,86,000
5x = 6,86,000

x = 1,37,200

[cans]

Also, the question would be interesting if we would rephrase it as , $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 MAXIMUM possible bonus that an employee can receive?

I think the solution should be :

x+ 0.8*5x = 6,86,000
5x = 6,86,000

x = 1,37,200

A minor correction in your solution
it shouldn't be 0.8x..
reason: suppose it is 0.8x. Then any bonus can't be more than 20% of it or max = 1.2*0.8x = .96x
but x>.96x thus wrong.
Correct solution - max bonus = x, and then x+(x/1.2)*5 = 686,000 and then you can solve for x

[bblast]

wooo !!

this turned out to be a better question than the actual one.

BTW thanks for the correction.