Source: Official Guide Revised GRE 1st Ed. Part 8; Section 5; #15

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The total amount that Mary paid for

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. The price of the book was less than $9.50., The price of the book was greater than $6.90., The sales tax was less than $0.45.

7 Explanations

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P P

I can figure out the upper limit but why is the lower limit $7?

Oct 11, 2018 • Comment

Sam Kinsman

Hi there,

Happy to help!

Think of it like this: what was the lowest possible cost of the book? In other words, what is the lowest possible value for (price of book + tax)?

Well, the person paid with $10, and got less than $3 change.

If the person had received EXACTLY $3 change, then the price (plus tax) would have been:

$10 - $3 = $7

But we know that the change was less than $3. Therefore the price (plus tax) must have been more than $7.

Does that make sense?

Oct 13, 2018 • Reply

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Shahram Ghahramani

This is a inequality problem! First, determine 4% of 10$ which is equal to 1.04 then:
7$<1.04x<10 then solve for x (price of book) !
6.73

Mar 7, 2018 • Comment

David Recine

That's exactly correct, Shahram. Nicely done. :)

Mar 8, 2018 • Reply

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Ishaan Tomar

Option A says that price of the book was less than 9.50. It doesn't say (as chris) the price has to be less than 9.50, so I think A should work. But obviosly its wrong. So how do we tackle this?

Aug 23, 2017 • Comment

Sam Kinsman

Hi Ishaan,

The question says "Which of the following statements must be true?" Option A says "the price of the book was LESS than $9.50." So if we can show that the price of the book could be $9.50, then we would prove that answer choice A is wrong (i.e. answer choice A does not have to be true).

As Chris showed, if the price of the book is $9.50, then the tax would be $0.38, and the total price would be $9.88. So Mary pays with $10, and gets 12 cents change. That fits what the question described (her change was less than $3.00). So the price of the book can be $9.50, and A is not correct.

I hope this helps!

Aug 26, 2017 • Reply

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PRASHANT VERMA

Hey
i just went a much simple way that was forming the equation as the question says and then forming the range of price of book and tax:-
price of book 7< 1.04x <10
i just got stuck up at dividing 7 by 1.04 without using a calculator(i could have used but i tried all my effort to do it without a calculator but couldn't do it)??

Apr 13, 2017 • Comment

Cydney Seigerman, Magoosh Tutor

Hi Pawan :)

It looks like your inequality matches the information in the prompt:

7 < 1.04x

where x is the price of the book.

And if we plug in either $9.50 (to test A) or $6.90 (to test B), we can see that the book could be either of these prices and the inequality would hold true. Therefore, we can conclude that A and B do not necessarily have to be true.

On the other hand, we cannot use the inequality directly to test (C), which discusses the sales tax of the book and not the price of the book itself. For (C), the approach Chris goes over in the lesson video directly tests the sales tax, using the maximum possible value of the book as a starting point.

Apr 16, 2017 • Reply

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Inmobi

I didn't really understand how option a and b are wrong, can you please explain?

Jun 7, 2016 • Comment

Cydney Seigerman, Magoosh Tutor

Hi Inmobi :)

I'm happy to help! Let's look at (A) and (B) to see why they're not correct :)

A. The price of the book was less than $9.50

If the book cost $9.50, then the sales tax would be 4% of this price or $0.38 (9.5*0.04). The total price of the book plus tax would be $9.88, in which case if Mary paid with a $10 bill, she would receive $0.18 back as change. This amount is less than $3, meeting the requirements of the question. In other words, the price of the book could be $9.50 and therefore does not have to be less than $9.50.

B. The price of the book was greater than $6.90.

To see if this statement must be true, let's consider when the price is equal to $6.90. In that case, the tax would be 4% of $6.90 or 27.6 cents. Let's round the cents up to 28 cents. So, the total cost of the book plus tax would be

$6.90 + $0.28 = $7.28

And if Mary paid with a $10 bill, she would receive $2.72 as change, which is less than $3. Therefore, the book could cost $6.90 and (B) is therefore not correct.

I hope this clears things up :)

Jun 10, 2016 • Reply

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Qingxiang Jia

I am confused about the last option, which says the sales tax should be less than $0.45. But if we assume the maximum price is very close to $10 (which gives the maximum tax), the tax should be very close to $0.40, which is a tighter bound than the option C. So I concluded that option C is wrong too.

Aug 30, 2015 • Comment

Sam Kinsman

Hi Qingxiang, if the price of the book were $10, the sales tax would be $0.40. If the price of the book is lower than $10, the sales tax will be lower as well.
Mary paid with a $10 bill and got change, so the total cost of the book must be less than $10. Therefore, we know that the sales tax has to be lower than $0.40 - so we know option C is correct.

Oct 9, 2015 • Reply

chang feli

but option C is less than 0.45, then between 0.4 and 0.45, the condition is not valid. right?

Oct 25, 2018 • Reply

Adam

Hey Chang, we know for sure that the tax paid was less than $0.40. This means that it is most assuredly less than $0.45, no matter what. The sales tax is less than $0.45, and that is all that option C mentions. Thus, option C is true. It does not say anything about between $0.40 and $0.45, and since we know the tax is less than that, we don't have to think about that range at all.

Oct 29, 2018 • Reply

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Chris Lele