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Question of the Week- 14 ( In the year-end clearance sale, a musi...)

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Question of the Week- 14 ( In the year-end clearance sale, a musi...)  [#permalink]

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New post Updated on: 21 Sep 2018, 02:12
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  95% (hard)

Question Stats:

13% (01:07) correct 87% (01:28) wrong based on 101 sessions

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e-GMAT Question of the Week #14

In the year-end clearance sale, a music system is discounted by d%, and then it is discounted by another 3d% on the previous discount amount. The original price of the music system is what percent of the final value, if the initial discount percent is 30?

    A. 23%
    B. 40%
    C. 143%
    D. 233%
    E. 1429%

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Originally posted by EgmatQuantExpert on 14 Sep 2018, 04:09.
Last edited by EgmatQuantExpert on 21 Sep 2018, 02:12, edited 1 time in total.
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Re: Question of the Week- 14 ( In the year-end clearance sale, a musi...)  [#permalink]

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New post 14 Sep 2018, 05:29
If we were to take the initial amount to be '1', and since 'd' is mentioned to be '30%', after the initial discount, it would come to 0.7.

After successive discount of '3d%', which would effectively be '90%', the discounted amount would come to 0.07.

Since the question wanted us to calculate, the original price of the music system is what percent of the final value, we would need to calculate the following.

(1 / 0.07) * 100 %

(100 * 100 ) / 7 %

10000/7 %

1428.5 %

Since we have a 5 in after the decimal point, we can round it off to 1429%. Hence, E would be our answer.
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Re: Question of the Week- 14 ( In the year-end clearance sale, a musi...)  [#permalink]

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New post 19 Sep 2018, 00:23
Hey everyone,

We will be posting the solution soon.

Meanwhile, try to answer the question and post your analysis.

Regards,
Sandeep
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Re: Question of the Week- 14 ( In the year-end clearance sale, a musi...)  [#permalink]

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New post 20 Sep 2018, 09:14
EgmatQuantExpert wrote:
Hey everyone,

We will be posting the solution soon.

Meanwhile, try to answer the question and post your analysis.

Regards,
Sandeep
e-GMAT


Hi Sandeep,

It would probably be a bit too soon to comment, since the explanation is yet to be made available, but here is what I think should be looked into.

After reviewing the OA, which is 'D', and working through the question, here is what I think should be modified.

If you review the question stem, you should see it says the following "...another 3d% on the previous discounted amount...". Here, discounted amount is a bit ambiguous, since it conveys that we are referring to the final amount after applying the discount. If you were to calculate the answer the way I did, you would end up with 'E'. Whereas, if the discount would have been applied on the discount amount, the answer would be 'D'.

My 2 cents here would be that we modify the question statement to say, '...discount amount...' instead of '...discounted amount...'.

Hope this helps to clarify. Please keep me posted as to what are your thoughts on this as well.

Best,
Sayan
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Re: Question of the Week- 14 ( In the year-end clearance sale, a musi...)  [#permalink]

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New post 21 Sep 2018, 02:09

Solution


Given:
    • In the year-end sale, a music system is first discounted by d%
    • And, then it is discounted by another 3d% on the initial discount amount
    • d = 30%

To find:
    • % of Original Price/Final Price

Approach and Working:
    • Let us assume that the Original Selling Price is S
      o Then, the selling price after the first discount of \(d% = S – S*\frac{d}{100}\)

    • Now, a discount of 3d% is given on the previous discounted amount, that is \(S*\frac{d}{100}\)
      o Thus, the final price of the music system = \(S – S*\frac{d}{100} – S * (\frac{d}{100}) * (\frac{3d}{100})\)

    • Therefore, the percentage of original price by final price = \(\frac{S}{[ S – S*d/100 – S * (d/100) * (3d/100)]} *100 = \frac{1}{[ 1 – d/100 – (d/100) * (3d/100)]} * 100\)
      o Substituting the value of d as 30 in the above equation, we get the percentage value = \(\frac{100}{[1 – 0.3 – 0.3*0.9]}= \frac{100}{(1 - 0.57)} = \frac{100}{0.43} ≃ 233%\)

Hence, the correct answer is option D.

Answer: D

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Re: Question of the Week- 14 ( In the year-end clearance sale, a musi...)  [#permalink]

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New post 21 Sep 2018, 02:18
sayankh wrote:

Hi Sandeep,

It would probably be a bit too soon to comment, since the explanation is yet to be made available, but here is what I think should be looked into.

After reviewing the OA, which is 'D', and working through the question, here is what I think should be modified.

If you review the question stem, you should see it says the following "...another 3d% on the previous discounted amount...". Here, discounted amount is a bit ambiguous, since it conveys that we are referring to the final amount after applying the discount. If you were to calculate the answer the way I did, you would end up with 'E'. Whereas, if the discount would have been applied on the discount amount, the answer would be 'D'.

My 2 cents here would be that we modify the question statement to say, '...discount amount...' instead of '...discounted amount...'.

Hope this helps to clarify. Please keep me posted as to what are your thoughts on this as well.

Best,
Sayan


Hey Sayan,

Thanks for pointing it out. Yes the word "discounted amount" is a bit ambiguous, so we have changed it to "discount amount."

Regards,
Sandeep
e-GMAT
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Re: Question of the Week- 14 ( In the year-end clearance sale, a musi...)  [#permalink]

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New post 22 Sep 2018, 10:51
Thanks Sandeep, much appreciated!
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Re: Question of the Week- 14 ( In the year-end clearance sale, a musi...)  [#permalink]

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New post 03 Oct 2018, 12:43
Let original price be P.

1st,it is discounted by 30%---> new price =7P/10.

2nd ,7p/100 is discounted by 90%=> (1/10)*7P/10

Original/Final %=P/(1/10*7P/10)
=100/7

143%

What am i missing here?
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Re: Question of the Week- 14 ( In the year-end clearance sale, a musi...) &nbs [#permalink] 03 Oct 2018, 12:43
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