After her birthday, Fiona had D dollars in gift money.

Question

After her birthday, Fiona had D dollars in gift money. She spent 3/5 of this on an electric skateboard. The next day, she spent 1/3 of what was left on a movie passcard, and then finally put the last $80 in the bank. If she made no other purchases with that money, then what was the value of D?

A. $240
B. $300
C. $320
D. $360
E. $480

A. $240
B. $300
C. $320
D. $360
E. $480

BrentGMATPrepNow · Accepted Answer

One option is to WORK BACKWARDS

The next day, she spent 1/3 of what was left on a movie passcard, and then finally put the last $80 in the bank.  
If she spent 1/3 of her money on a movie passcard, then 2/3 of her money remained (which she put in the bank). 
This means 2/3 of her money = $80
We can also say that 1/3 of her money = $40
 So, she spent $40 on a movie passcard and saved $80
In other words, at the beginning of that day, she had  $120

After her birthday, Fiona had D dollars in gift money. She spent 3/5 of this on an electric skateboard.  
If she spent 3/5 of her money (on a skateboard), then 2/5 of her money remained (to be spent on a movie passcard the following day). 
In other words, 2/5 of D =  $120 
Or we can write: (2/5)D =  $120 
Multiply both sides by 5 to get: 2D = $600
Divide both sides by 2 to get: D = $300

Answer: B

Cheers,
Brent

Bismarck · Answer

OA: B

Initial amount = D 
Amount remaining after buying Electric Skateboard = D- \frac{3D}{5} 
Amount remaining after buying movie ticket = D- \frac{3D}{5} -\frac{1}{3}  (D- \frac{3D}{5})=D*\frac{2}{5}*\frac{2}{3} 
As per question stem, D*\frac{2}{5}*\frac{2}{3}=80 
 D=300

adkikani · Answer

Bismarck

Can you please comment on text in RED?

Initial amount = D 
Amount remaining after buying Electric Skateboard = D- \frac{3D}{5} 
 OK, I simplified this to get  \frac{2D}{5}

Amount remaining after buying movie ticket = D- \frac{3D}{5} -\frac{1}{3}  (D- \frac{3D}{5})=D*\frac{2}{5}*\frac{2}{3} 
 I directly multiplied 1/3 *(2D/5) and then took 1-(2D/15) to equate to 80  
Where did I go wrong?

Bismarck · Answer

Can you please comment on text in RED?

Initial amount = D

Purchase 1  
Amount remaining after buying Electric Skateboard = D- \frac{3D}{5} 
 OK, I simplified this to get  \frac{2D}{5}  
 After buying Electric Skateboard,She has now    \frac{2D}{5}    remaining with her, instead of   D

Purchase 2 
Amount remaining after buying movie ticket = D- \frac{3D}{5} -\frac{1}{3}  (D- \frac{3D}{5})=D*\frac{2}{5}*\frac{2}{3} 
 I directly multiplied 1/3 *(2D/5) and then took 1-(2D/15) to equate to 80  
Where did I go wrong?

Movie ticket price  =  \frac{1}{3} *(\frac{2D}{5})  
 Money remaining after Purchase 2  =  Money remaining after Purchase 1  -  Movie ticket price  =  \frac{2D}{5}   -   \frac{1}{3} *(\frac{2D}{5})  
 Money remaining after Purchase 2  =   \frac{2D}{5}    -    \frac{1}{3} *(\frac{2D}{5})   =80

AkshdeepS · Answer

Answer choices seem easy :

Start with B as it seems easiest to work with:

Say D = $ 300

Expense on skate boards = 3/5 * 300 = $ 180

Balance amount = 300 - 180 = $ 120

Expense on smart card = 1/3 * 120 = $ 40

Total expense = 180 + 40 = $ 220

Amount left to put in the bank = 300 - 220 = $ 80 (perfect match)

(B)

maxmayr · Answer

can somebody explain to me why this approach is incorrect:

I assume that Fiona has in total x dollars.

After the first purchase she is left with 5/3 of x and from this remaining amount she makes a second purchase which is 1/3 of the this amount.

Hence I calculated:

3/5x+1/3(3/5x)+80 = x
--> 9/15x + 3/15x+80 = x
--> 12/15x+80=x
--> 4/5x+80=x
-->80 = 1/5x
--> x = 400

Where is my logical flaw? From the post above it doesn't come clear to me.

Thanks in advance.

Max

BrentGMATPrepNow · Answer

Another approach is to use algebra.

After her birthday, Fiona had D dollars in gift money. She spent 3/5 of this on an electric skateboard.  
If Fiona SPENT 3/5 of D dollars, then 2/5 of D dollars REMAINED
In other words, the amount remaining at the end of the day =  2D/5  dollars

The next day, she spent 1/3 of what was left on a movie passcard, and then finally put the last $80 in the bank.  
If Fiona SPENT 1/3 of her remaining  2D/5  dollars, then she must have SAVED 2/3 of  2D/5  dollars
2/3 of  2D/5  = (2/3)( 4D/5 ) =  4D/15 
So, after spending 1/3 of her money that day,  4D/15  dollars remained (which she put in the bank)
In other words,  4D/15 = $80

What was the value of D?  
Take:  4D/15 = $80 
Multiply both sides by 15 to get: 4D = 1200
Divide both sides by 4 to get: D = $300

Answer: B

Cheers,
Brent

EMPOWERgmatRichC · Answer

Hi All,

We're told that after her birthday, Fiona had D dollars in gift money. She spent 3/5 of this on an electric skateboard, then she spent 1/3 of what WAS LEFT on a movie passcard, and then finally put the last $80 in the bank. Assuming she made no other purchases with that money, we're asked for the value of D. This question can be solved in a number of different ways, including by TESTing THE ANSWERS. Based on the given Answers, it looks like Answer B would be the easiest to work with, so let's start there...

Answer B: $300 
IF.... D = $300.... 
Fiona spent (3/5)($300) = $180 on a skateboard, leaving her with $300 - $180 = $120 
She then spent (1/3)($120) = $40 on a movie passcard, leaving her with $120 - $40 = $80 
This is an exact match for what we were told, so this must be the answer!

Final Answer:  B

GMAT assassins aren't born, they're made, 
Rich

CareerGeek · Answer

She spent 3/5 of this on an electric skateboard.
—> Spent = 3D/5
—> Remaining = 2D/5

she spent 1/3 of what was left 
—> Remaining = 2/3*2D/5 = 4D/15

Given, 4D/15 = 80
—> D = 80*15/4 = 300 $

IMO Option B

Posted from my mobile device

nkr037 · Answer

Answer:

3/5x is spent on skateboard
remaining is 2/5x
one-third of 2.5x is 1/3*2/5x = 2/15x spent on Movie pass
Remaining amount is $80. To find out the fraction of the remaining amount, we need to find a common denominator of 3/5 and 2/15
We can re-write 3/5 as 9/15 and add this to 2/15 which gives us 11/15
So whatever amount is remaining must be of fraction 4/15x. 
Its given that 4/15x = 80
which gives us x=300

Kimberly77 · Answer

Hi Brent  BrentGMATPrepNow , if I haven't thought of saving of 2/3 after Fiona SPENT 1/3 of her remaining  2D/5  dollars but calculate it as 1/3 * 2/5D = 2/15 D. Does it mean the calculation is wrong? As my thoughts was to find D rather than saving here. If the calculation is possible, could you show how to calculate it this way? Thanks Brent

BrentGMATPrepNow · Answer

In order to use the fact that Fiona put $80 in the bank, we must calculate the amount of money left over after Fiona spent 1/3 of her remaining  2D/5  dollars.

So, before spending 1/3 of her money, Fiona had  2D/5  dollars. 
According to your calculations, Fiona spent 2D/15 dollars. 
So, the amount left over =  2D/5  - 2D/15 dollars
In other words, the amount left over =  6D/15  - 2D/15 dollars
Simplify to get: the amount left over = 4D/15 dollars

This means 4D/15 = $80 which we can solve for D

btsaami · Answer

We know that answer D is a multiple of 15.

Therefore, can eliminate C. Among A, B D and E, subtract 80 from each.

240-80=160, 220, 280, 400

D-80= (11/15)*D. As we can see from above D= 220*15/11= 20*15= 300.

bumpbot · Answer

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After her birthday, Fiona had D dollars in gift money.

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