Jennifer

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j_shreyans: Legendary Member; Posts: 510; Joined: Thu Aug 07, 2014 2:24 amFollowed by: 5 members; Thanked: 3 times

by j_shreyans » Sun Sep 21, 2014 7:35 am

Jennifer has 60 dollars more than Brian. If she were to give Brian 1/5 of her money, Brian would have 25% less than the amount that Jennifer would then have. How much money does Jennifer have?

A)40
B)100
C)120
D)140
E)180

OAB

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Source: Beat The GMAT — Problem Solving | Sun Sep 21, 2014 7:35 am

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Brent@GMATPrepNow: GMAT Instructor; Posts: 16207; Joined: Mon Dec 08, 2008 6:26 pmFollowed by: 1268 members; Location: Vancouver, BC; Thanked: 5254 times; GMAT Score:770

by Brent@GMATPrepNow » Sun Sep 21, 2014 9:10 am

j_shreyans wrote:Jennifer has 60 dollars more than Brian. If she were to give Brian 1/5 of her money, Brian would have 25% less than the amount that Jennifer would then have. How much money does Jennifer have?

A)40
B)100
C)120
D)140
E)180

Here's one approach:

Let J = Jennifer's $
Let B = Brian's $

Jennifer has 60 dollars more than Brian.
So, J = B + 60

If Jennifer were to give Brian 1/5 of her money, Brian would have 25% less than the amount that Jennifer would then have.
If Jennifer were to give Brian 1/5 of her money, then Jennifer has (4/5)J dollars, and Brian has B + (1/5)J dollars

If Brian has 25% less than the amount that Jennifer has, then Brian's amount = 3/4 Jennifer's amount.
So, we can write: 3/4(4/5)J = B + (1/5)J
Simplify, to get (3/5)J = B + (1/5)J
Multiply both sides by 5 to get: 3J = 5B + J
Rearrange: 2J = 5B

We now have the system:
J = B + 60
2J = 5B

When we solve it, we get J = 100 (as well as B = 40)

Answer: B

Cheers,
Brent

Brent Hanneson - Creator of GMATPrepNow.com

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GMAT/MBA Expert

Brent@GMATPrepNow: GMAT Instructor; Posts: 16207; Joined: Mon Dec 08, 2008 6:26 pmFollowed by: 1268 members; Location: Vancouver, BC; Thanked: 5254 times; GMAT Score:770

by Brent@GMATPrepNow » Sun Sep 21, 2014 9:14 am

j_shreyans wrote:Jennifer has 60 dollars more than Brian. If she were to give Brian 1/5 of her money, Brian would have 25% less than the amount that Jennifer would then have. How much money does Jennifer have?

A)40
B)100
C)120
D)140
E)180

OAB

We can also test the answer choices here:

A) Jennifer has $40
Hmmm, if Jennifer has 60 dollars more than Brian, then Brian has -20 dollars.
Makes no sense.
ELIMINATE A

B) Jennifer has $100
So, Brian has $40

Then Jennifer gives 1/5 of her money ($20) to Brian.
Now Jennifer has $80, and Brian has $60
So, Brian has 25% less than the amount that Jennifer has.
PERFECT, this matches the condition in the question.

Answer: B

Cheers,
Brent

Brent Hanneson - Creator of GMATPrepNow.com

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