Problem Solving

VJesus12 wrote: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

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

VJesus12 wrote: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

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

Hi VJesus12,

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

VJesus12 wrote: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

[spoiler]OA=B[/spoiler]

Source: Magoosh

We can create the equation:

3D/5 + 1/3(2D/5) + 80 = D

3D/5 + 2D/15 + 80 = D

Multiplying by 15, we have:

9D + 2D + 1,200 = 15D

1,200 = 4D

300 = D

Alternate Solution:

After spending 3/5 of her money, Fiona had 2/5 of her money left. After spending 1/3 of what's left, she had 2/3 of 2/5 of her money; in other words, she had 2/3 x 2/5 = 4/15 of her money left. Since we are given that this amount is equal to 80, she had 80/(4/15) = (80 * 15)/4 = 20 * 15 = 300 dollars to begin with.

Answer: B