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EgmatQuantExpert
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A person paid a total amount of $P to purchase a musical instrument. Updated on: 28 Mar 2019, 01:19
Originally posted by EgmatQuantExpert on 13 Mar 2019, 01:42.
Last edited by EgmatQuantExpert on 28 Mar 2019, 01:19, edited 3 times in total.
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B
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45% (medium)

Question Stats:

66% (02:02) correct 34% (01:59) wrong based on 295 sessions

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A person paid a total amount of $P to purchase a musical instrument. The total amount includes the price of the instrument, a sales tax and a delivery charge. Was the tax paid more than 10% of the price of the instrument?

    1. Sales tax was less than 6% of P.
    2. Sales tax was \(\frac{1}{20}\) of the price of the instrument.

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B
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A person paid a total amount of $P to purchase a musical instrument. 14 Mar 2019, 01:43
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A person paid a total amount of $P to purchase a musical instrument. The total amount includes the price of the instrument, a sales tax of 5% charged on the price and a delivery charge, charged as 5% of the tax paid. Was the tax paid more than 10% of the price of the instrument?

1. The tax paid was $400.
2. P = $80000
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basic price = x
Sales tax = 1.05*x
delivery cost = 1.05x *1.05; 1.1025x

#1
tax paid = 400$
so 5/100*x= 400
x= 400*100/5 ; basic price = 8000 $ ;

10% of 8000 ; 800
so yes tax paid was >400$ ; sufficient

#2
P = 80,000
P = 1.1025x
so
80,000=1.1025x
x= 72562.3$ ; basic price
tax = 72562.3*1.05 = 76190.47
tax paid = ~3628 $
sufficient
IMO D
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A person paid a total amount of $P to purchase a musical instrument. 14 Mar 2019, 02:40
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- shouldn't #1 be no, but still sufficient? - if tax paid for is $400 - isn’t 10% of 8000(the cost), more than $400?

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A person paid a total amount of $P to purchase a musical instrument. 17 Mar 2019, 22:57
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Hi all.

Due to some ambiguity present in the previous version of the question, we have made some changes in the question.

You can give it another try...detailed solution will be posted soon. :)

Regards,
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A person paid a total amount of $P to purchase a musical instrument. 18 Mar 2019, 23:00
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EgmatQuantExpert
A person paid a total amount of $P to purchase a musical instrument. The total amount includes the price of the instrument, a sales tax and a delivery charge. Was the tax paid more than 10% of the price of the instrument?

    1. Sales tax was less than 6% of P.
    2. Sales tax was \(\frac{1}{20}\) of the price of the instrument.
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Solution


Given:
    • A person paid a total amount of $P to purchase a musical instrument.
    • The total amount includes the price of the instrument, a sales tax and a delivery charge.

To find:
    • Whether the tax paid more than 10% of the price of the instrument or not.

Approach and Working:
We can say the total paid amount P = Price + Sales Tax + Delivery Charge
    • Now, to determine whether the tax paid was more than 10% of the price of instrument, we need to know either both the price and tax paid, or the ratio of sales tax and price of the instrument.

Analysing Statement 1
As per the information given in statement 1, sales tax is less than 6% of P.
    • However, from this statement, we cannot determine the relation between sales tax and the price of the instrument.

Hence, statement 1 is not sufficient to answer the question.

Analysing Statement 2
As per the information given in statement 2, sales tax was 1/20 of the price of the instrument.
    • Therefore, sales tax as a percentage of the price = 1/20 x 100 = 5%
    • So, the sales tax paid was less than 10% of the price of the instrument.

Hence, statement 2 is sufficient to answer the question.

Hence, the correct answer is option B.

Answer: B
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A person paid a total amount of $P to purchase a musical instrument. 04 May 2020, 23:58
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EgmatQuantExpert

Why can't we assume a number for Price and solve this question?
I get D as the answer when I do that(assuming P = $1000)

1) Tax is < 6% => Tax is < $60 which is less than 10% of P i.e ($100). Sufficient
2) Tax is 1/20 of 1000 => $50 which is less than $100 . Sufficient.

Can you point out the mistake here please?
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A person paid a total amount of $P to purchase a musical instrument. 10 Nov 2023, 03:18
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Hello from the GMAT Club BumpBot!

Thanks to another GMAT Club member, I have just discovered this valuable topic, yet it had no discussion for over a year. I am now bumping it up - doing my job. I think you may find it valuable (esp those replies with Kudos).

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