Official Guide Explanation:
Problem Solving #13




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Solution and Metadata

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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