Jennifer has 60 dollars more than Brian. If she were to give

Question

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

I got the answer wrong and the correct answer is B. I worked to get to B but I have the doubt which I highlighted below. Why it will be 75% and not 25%?

If we denote the amount of money owned by Jennifer as j and that owned by Brian as b, we can create two equations based on the information in the problem. First, Jennifer has 60 dollars more than Brian: j = b + 60.

Second, if she were to give Brian 1/5 of her money, she would have j – (1/5)j = (4/5)j dollars. Brian would then have b + (1/5)j dollars. Therefore, since Brian’s amount of money would be  75%  of Jennifer’s, we can create another equation: b + (1/5)j = (0.75)(4/5)j, which can be simplified as follows:
b + (1/5)j = (0.75)(4/5)j
b + (1/5)j = (3/4)(4/5j)
b + (1/5)j = (3/5)j
b = (3/5)j – (1/5)j
b = (2/5)j

Substitute this expression for b back into the first equation, then solve for j:
j = b + 60
j = (2/5)j + 60
j – (2/5)j = 60
(3/5)j = 60
j = (60)(5/3) = 100
Therefore, Jennifer has 100 dollars.

Bunuel · Accepted Answer

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

Jennifer has 60 dollars more than Brian --> J=B+60;

If Jennifer were to give Brian 1/5 of her money,  she would have 4/5*J  and Brian would have  B+1/5*J=(J-60)+1/5*J ;

After that Brian would have 25%  less  than the amount that Jennifer would then have, so Brian would have 100%-25%=75% (3/4th) of the amount that Jennifer would then have --> 3/4*(4/5*J)=(J-60)+4/5*J --> 3J/5=6J/5-60 --> 3J=6J-300 --> J=100.

Answer: B.

Hope it's clear.

P.S. Notice that this question is a good candidate for backsolving.

Stoneface · Answer

This is how I did it. Could someone tell me if it is flawed or if you can do it this way?

J-60 = Brian's money
J(.2) = Amount given to Brian
J(.8) = Jennifer after giving away money
J(.75) = Percentage of Jennifer's money that Brian's is after she gave him .25 of her money

Brian + Money Jennifer gave to Brian = Jennifer's money after giving to brign * Percentage of Jennifer's money that Brian's money is equal to.

J-60+J(.2)=J(.8)(.75)
J-60+J(.2)=J(.6)
J-60=J(.6)-J(.2)
J-60=J(.4)
J-J(.4)=60
J(.6)=60
J=100

Bunuel · Answer

Your approach is correct, basically it's the same as mine: you just use decimals instead of fractions.

pbull78 · Answer

assume B = x
J= x +60
1/5J = x/5 +12
J= 4/5X+48
B x+x/5+12
now 25/100*4/5x +25/100*48
 x/5+12
implies 4/5x +48- x/5-12
implies 6/5x+12= 3/5X36
implies X = 40 
we are looking for jenifer its x +60 so jenifier is 100

gladiator999 · Answer

My Way of doing it :-

Brian= x
Jenifer= 60+x
When jenifer gave one fifth of her money to brian ,then money with brian will be equal to 75% of the money that is remaining with Jenifer. So we can make the following equation :

x+1/5(60+x)= 75%[60+x-1/5(60+x)
Solve it and you will get:

x= 40 
and amount with jenifer will be = 60+x
 = 60+40= 100

I hope the simple explanation helps.

sidhu09 · Answer

If B = x
J = B + 60 = x + 60 ----(1)

(75%)(4/5)(J) = B + (1/5)(J)

We get (2/5)*J = B ----(2)

Substitute (2) in (1)

J = 100; B = 40

I hope I am clear with the solution

KarishmaB · Answer

You can do this question by assuming values too (as long as you know the situations in which you can assume values).
Start from the last step and work upwards.

"Brian would have 25% less than the amount that Jennifer would then have " - Say Jennifer has $100 after giving then Brian would have $75 (25% less than Jennifer).
Jennifer gave 1/5 of her money and was left with $100 so she must have had $125 to begin with. Since Brian now has $75, we must have had $50 to begin with. In this case, Jennifer has $75 more than Brian. But actually she has $60 more than Brian which is (4/5) of 75. So instead of $125, she has (4/5)*125 = $100 right now.

Answer (B)

ScottTargetTestPrep · Answer

We can let the amount of money Jennifer has = J and the amount of money that Brian has = B and create the equation:

J = B + 60

B = J - 60

If Jennifer gives 1/5 of her money to Brian, she would have:

(4/5)J

and Brian would have:

B + (1/5)J = J - 60 + (1/5)J

Since Brian would now have 25% less money than Jennifer, we have:

J - 60 + (1/5)J = (3/4)

J - 60 + (1/5)J = (3/5)J

Multiplying the equation by 5, we have:

5J - 300 + J = 3J

3J = 300

J = 100
 
Answer: B

BrentGMATPrepNow · Answer

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

blawp · Answer

Plugging in answer choices got me this question in 2 minutes. I started with 120, failed high, then chose 100, and was right.

adityasuresh · Answer

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

This can be answered quicker if we assume values from the POV of Jennifer.
Stem: Jennifer has 60 dollars more than Brian implies Amount of money Jennifer has = J & Amount of money Brian has = J - 60
If she were to give Brian 1/5 of her money, Brian would have 25% less than the amount that Jennifer would then have. 
So J -  1/5J  = J +  1/5J  - 60
 4/5J  =  6/5J  - 60
Now the second condition
 6/5J  - 60 =  3/4 * 4/5J 
 6/5J  - 3/5J  = 60
 3/5J  = 60
J = 300/3  =100
 B

Legallyblond · Answer

how do you know the level of these questions?

bumpbot · Answer

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Jennifer has 60 dollars more than Brian. If she were to give

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Jennifer has 60 dollars more than Brian. If she were to give

Prep Toolkit

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