Solution

We may find it helpful to translate the given information into an algebraic expression. Since the price of the book is unknown, we can call it x
dollars, and then the total amount that Mary paid is x dollars plus 4% of x dollars, or 1.04x dollars. The problem states that Mary received some change from a $10 bill, so 1.04x dollars must be less than $10. Since the change was less than $3.00, the total amount Mary paid for the book must have been greater than $7.00.

This information can be expressed algebraically by the inequality

\(7.00<1.04x<10.00\)

Solving the inequality for x by dividing by 1.04, and rounding, you get

\(6.73<x<9.62\)

So you see that x, the price of the book, must be between $6.73 and $9.62. With this information, you can quickly examine the first two statements. Choice A is not necessarily true because the price could be as high as $9.61, and Choice B is not necessarily true because the price could be as low as $6.74.

To examine Choice C, we compute the tax for the greatest possible price, which would be 4% of 9.61, or (0.04)(9.61)=0.38. Since this greatest
possible tax is less than $0.45, Choice C must be true.

You can also quickly see that Choice C must be true if you note that 4% of $10.00 would only be $0.40, and since the price must be less than $10.00, the tax must be less than $0.40. The correct answer consists of Choice C.
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The total amount that Mary paid for a book was equal to the price of the book plus a sales tax that was 4 percent of the price of the book. Mary paid for the book with a $10 bill and received the correct change, which was less than $3.00. Which of the following statements must be true? Indicate all such statements.
A The price of the book was less than $9.50.
B The price of the book was greater than $6.90.
C The sales tax was less than $0.45.

---------- Official answer C

A: Book could be $6 - wrong
B: Book could be $9.90 - wrong
C: Tax could be $0.44 or $0.05 - wrong

for this type of questions - if I could find one case in the given range where it's wrong then the whole statement is wrong... correct?
I don't understand the explanation of why C is correct because I found so many cases where C could be wrong.
If C is correct in this case, shouldn't A and B also be correct statements?

Merged similar topic.

Please see the explanation above.

Use , before to post a question on the board, the search tool https://greprepclub.com/forum/search.php

The question, especially if it is an official question, probably has been already discussed.

regards

Let B = the price of the book (without the tax)
So, 0.04B = the tax paid on the book.

So, B + 0.04B = TOTAL amount paid
In other words, 1.04B = TOTAL amount paid

Mary paid for the book with a $10 bill and received the correct change, which was less than $3.00.
So, $10 - 1.04B = the change received

Since the changed received is less than $3.00, we can write: 10 - 1.04B < 3.00

Take: 10 - 1.04B < 3.00
Subtract 10 from both sides: -1.04B < -7.00
Divide both sides by -1.04 to get: B > $6.73

NOTE: This, of course, doesn't mean that the book (B) can be ANY price greater than $6.73
We know this, because Mary received CHANGE after paying $10
So, we know that the TOTAL amount paid must be less than $10
In other words, we can write: 1.04B < $10
Divide both sides by 1.04 to get B < $9.62

Combine our inequalities to get: $6.73 < B < $9.62

A The price of the book was less than $9.50.
Since $6.73 < B < $9.62, we know that the price of the book (B) COULD be $9.60
So, statement A need not be true


B The price of the book was greater than $6.90.
Since $6.73 < B < $9.62, we know that the price of the book (B) COULD be $9.70
So, statement B need not be true


C The sales tax was less than $0.45.
Notice that 4% of $10 = $0.40
Since we know that the book costs LESS THAN $10, the sales tax must be less than $0.40
So, statement C IS true

Cheers,
Brent
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Paraphrase

The total amount that Mary paid for a book was equal to the price of the book plus a sales tax that was 4 percent of the price of the book. Mary paid for the book with a $10 bill and received the correct change, which was less than $3.00. Which of the following statements must be true?

Don,t bogged down with the color sentence, and 4%. The above color sentence is identical. Firstly, give 10$ ,than make change 3$. Eventually, we need to evaluate the 4%.
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obdi

How are we making these assumptions?
A: Book could be $6 - wrong
B: Book could be $9.90 - wrong
C: Tax could be $0.44 or $0.05 - wrong

Have you used this part of the question?
Mary paid for the book with a $10 bill and received the correct change, which was less than $3.00
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