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A person paid a total amount of $P to purchase a musical instrument.

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A person paid a total amount of $P to purchase a musical instrument.  [#permalink]

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New post Updated on: 28 Mar 2019, 01:19
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Difficulty:

  65% (hard)

Question Stats:

44% (01:53) correct 56% (02:23) wrong based on 32 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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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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Re: A person paid a total amount of $P to purchase a musical instrument.  [#permalink]

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New post 14 Mar 2019, 01:43
EgmatQuantExpert wrote:
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


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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Re: A person paid a total amount of $P to purchase a musical instrument.  [#permalink]

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New post 14 Mar 2019, 02:40
- 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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Re: A person paid a total amount of $P to purchase a musical instrument.  [#permalink]

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New post 17 Mar 2019, 22:57
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Re: A person paid a total amount of $P to purchase a musical instrument.  [#permalink]

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New post 18 Mar 2019, 23:00
EgmatQuantExpert wrote:
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.


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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Re: A person paid a total amount of $P to purchase a musical instrument.   [#permalink] 18 Mar 2019, 23:00
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