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

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After her birthday, Fiona had D dollars in gift money.  [#permalink]

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New post 15 Jul 2018, 05:43
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Question Stats:

79% (01:23) correct 21% (02:12) wrong based on 56 sessions

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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

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Re: After her birthday, Fiona had D dollars in gift money.  [#permalink]

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New post 15 Jul 2018, 06:52
adkikani 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


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,\(D*\frac{2}{5}*\frac{2}{3}=80\)
\(D=300\)
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Re: After her birthday, Fiona had D dollars in gift money.  [#permalink]

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New post 15 Jul 2018, 06:59
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?
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Re: After her birthday, Fiona had D dollars in gift money.  [#permalink]

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New post 15 Jul 2018, 07:23
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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\(=\)\(\frac{2D}{5}\) \(-\) \(\frac{1}{3} *(\frac{2D}{5})\)\(=80\)
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After her birthday, Fiona had D dollars in gift money.  [#permalink]

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New post 21 Jul 2018, 04:52
adkikani 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


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)
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Re: After her birthday, Fiona had D dollars in gift money.  [#permalink]

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New post 13 Aug 2018, 08:02
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
Re: After her birthday, Fiona had D dollars in gift money. &nbs [#permalink] 13 Aug 2018, 08:02
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