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Strongt: Senior | Next Rank: 100 Posts; Posts: 51; Joined: Wed Jan 05, 2011 3:32 am; Followed by:1 members

Knewton Q

by Strongt » Tue May 31, 2011 3:50 am

$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

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Source: Beat The GMAT — Problem Solving | Tue May 31, 2011 3:50 am

subhashghosh: Senior | Next Rank: 100 Posts; Posts: 43; Joined: Fri Apr 08, 2011 7:32 am; Thanked: 2 times

by subhashghosh » Tue May 31, 2011 4:26 am

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

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Strongt: Senior | Next Rank: 100 Posts; Posts: 51; Joined: Wed Jan 05, 2011 3:32 am; Followed by:1 members

by Strongt » Tue May 31, 2011 6:12 am

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!:(

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cans: Legendary Member; Posts: 1309; Joined: Mon Apr 04, 2011 5:34 am; Location: India; Thanked: 310 times; Followed by:123 members; GMAT Score:750

by cans » Tue May 31, 2011 6:20 am

$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.

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Strongt: Senior | Next Rank: 100 Posts; Posts: 51; Joined: Wed Jan 05, 2011 3:32 am; Followed by:1 members

by Strongt » Tue May 31, 2011 6:27 am

Perfect! Thank you

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bblast: Legendary Member; Posts: 1077; Joined: Mon Dec 13, 2010 1:44 am; Thanked: 118 times; Followed by:33 members; GMAT Score:710

by bblast » Tue May 31, 2011 8:15 am

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

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cans: Legendary Member; Posts: 1309; Joined: Mon Apr 04, 2011 5:34 am; Location: India; Thanked: 310 times; Followed by:123 members; GMAT Score:750

by cans » Tue May 31, 2011 8:59 am

bblast wrote: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

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bblast: Legendary Member; Posts: 1077; Joined: Mon Dec 13, 2010 1:44 am; Thanked: 118 times; Followed by:33 members; GMAT Score:710