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## Official Guide Explanation:Data Sufficiency #79

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: 79
Page: 279
Difficulty: 6 (Moderately Difficult)
Category 1: Algebra > Inequalities > other
Category 2: Arithmetic > Percents > other
Category 3: Word Problems > Other >

Explanation: In either state, the price of the computer, including sales tax, is p + p(((t)/100))--that is, the price without sales tax plus the amount of sales tax, which is given by multiplying the price by the sales tax percentage.

Statement (1) is insufficient. Without knowing the prices of the computers in the two states, the tax rates are irrelevant. If the prices are the same, the computer will cost more in the state with the higher sales tax rate. However, if the price is much lower in the state with the higher tax rate, the overall cost is greater in the state with the lower tax rate.

Statement (2) is also insufficient. It compares the amount of sales tax charged on the price of the computer in each state. Again, if the prices were equal in both states, this would tell us in which state the cost is greater, but without knowing the prices, we can't answer the question.

Taken together, the statements are still insufficient. It's easy to see how the overall cost would be greater in state 1 -- if the prices are equal in both states, the state with the higher tax rate will have the higher overall cost. To see how the overall cost would be greater in state 2, consider the following scenario:

p1 = 75

p2 = 100

t1 = 10%

t2 = 5%

This fulfills the requires of both statements--the tax rate is higher in 1, and the amount of tax charged is \$7.50 in 1, greater than \$5 in 2. However, the overall cost is greater in 2. In 1, the overall cost is \$82.50, while in 2, the overall cost is \$105. Choice (E) is correct.

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