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John bought one book and paid the price marked inside the bo
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18 Nov 2020, 10:22

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John bought one book and paid the price marked inside the book plus sales tax with a $20 bill. He received exact change, which was less than $5. The sales tax was 9% of the book’s marked price. Which of the following must be true?

Indicate all that apply.

A. The marked price of the book was more than $13.50.

B. The marked price of the book was less than $18.50.

C. The sales tax on the book was less than $1.50.

Kudos for the right solution and explanation

Indicate all that apply.

A. The marked price of the book was more than $13.50.

B. The marked price of the book was less than $18.50.

C. The sales tax on the book was less than $1.50.

Kudos for the right solution and explanation

Re: John bought one book and paid the price marked inside the bo
[#permalink]
18 Nov 2020, 22:33

1

here the marked price and tax in total is 20 USD

9% is taxed on the marked price. Now separating,

the two elements i.e. marked price and tax we get

marked price = 20/1.09= 18.35 (approx),

thus the tax amount= 20-18.35=1.65 (approx)

based on the values of marked price and tax we have just calculated, only options A and B remain valid.

therefore, A and B both are correct.

9% is taxed on the marked price. Now separating,

the two elements i.e. marked price and tax we get

marked price = 20/1.09= 18.35 (approx),

thus the tax amount= 20-18.35=1.65 (approx)

based on the values of marked price and tax we have just calculated, only options A and B remain valid.

therefore, A and B both are correct.

John bought one book and paid the price marked inside the bo
[#permalink]
09 Aug 2023, 18:36

1

Given , Total Selling price = Marked Price + 9%of Marked Price (Sales tax as per the question)

if we let the Marked price be x, we can set up a equation based on the constraints given:

20>x+9x/100>15 (the Total sale price will always be less than 20$ since John received a certain amount as change, and the Total sale price should be greater than 15 , since the exact change was less than 5$)

Thus, 20>1.09x>15 --> 20/1.09>x>15/1.09 --> 18.35>x>13.76

Now let us look at the answer choices:

A. The marked price of the book was more than $13.50 - the option looks correct since lower bound value of x (MP) > 13.76

B. The marked price of the book was less than $18.50 - the option looks correct since upper bound value of x (MP) <18.35

C. The sales tax on the book was less than $1.50. - Sales tax is 9% of x i.e. 18.35*0.09>x*0.09>13.76*0.09

i.e. 1.65>0.09x>0.41 --> so option C is incorrect since our upper bound value is greater than 1.50$

Answers A and B

if we let the Marked price be x, we can set up a equation based on the constraints given:

20>x+9x/100>15 (the Total sale price will always be less than 20$ since John received a certain amount as change, and the Total sale price should be greater than 15 , since the exact change was less than 5$)

Thus, 20>1.09x>15 --> 20/1.09>x>15/1.09 --> 18.35>x>13.76

Now let us look at the answer choices:

A. The marked price of the book was more than $13.50 - the option looks correct since lower bound value of x (MP) > 13.76

B. The marked price of the book was less than $18.50 - the option looks correct since upper bound value of x (MP) <18.35

C. The sales tax on the book was less than $1.50. - Sales tax is 9% of x i.e. 18.35*0.09>x*0.09>13.76*0.09

i.e. 1.65>0.09x>0.41 --> so option C is incorrect since our upper bound value is greater than 1.50$

Answers A and B

gmatclubot

John bought one book and paid the price marked inside the bo [#permalink]

09 Aug 2023, 18:36
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