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## Official Guide Explanation:Problem Solving #13

Background

This is just one of hundreds of free explanations I've created to the quantitative questions in The Official Guide for GMAT Review (12th ed.). Click the links on the question number, difficulty level, and categories to find explanations for other problems.

These are the same explanations that are featured in my "Guides to the Official Guide" PDF booklets. However, because of the limitations of HTML and cross-browser compatibility, some mathematical concepts, such as fractions and roots, do not display as clearly online.

Question: 13
Page: 154
Difficulty: 4 (Moderately Easy)
Category 1: Arithmetic > Percents > other

Explanation: It's worth translating this into an equation--it's a popular type of GMAT question. If the price of an item is x, tax of 7 percent on the amount in excess of \$1,000 is equal to:

tax = 0.07(x - 1000)

We know the tax is \$87.50, so we can plug that into the equation and solve for x, the value of the item:

87.50 = 0.07(x - 1000)

87.50 = 0.07x - 70

0.07x = 157.50

7x = 15,750

x = 2,250

This last step isn't very friendly since you dont have a calculator. One way to break it down is to separate 15,750 into parts that you know are divisible by 7:

15,750 = 14,000 + 1,750

15,750 = 14,000 + 1,400 + 350

15,750 = 7(2,000) + 7(200) + 7(50)

15,750 = 7(2,250)

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