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## Official Guide Explanation:Problem Solving #127

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: 127
Page: 170
Difficulty: 6 (Moderately Difficult)
Category 1: Word Problems > Rate Problems > other
Category 2: Algebra > Equations >

Explanation: There are a couple of ways to go about this. First, the traditional way. If the packages are mailed separately, the first package costs x + 2y cents to ship, and the second costs x + 4y cents, for a total of 2x + 6y cents. If they are combined, they cost x + 7y cents to ship. The difference is (2x + 6y) - (x + 7y) = x - y. Since x is greater than y, the difference is positive, which means that shipping them separately costs more. Thus, choice (A) is correct: it's cheaper to ship them combined, and the savings is x - y cents.

Alternatively, consider the difference between the methods without doing the math. In both cases, at least one pound will be charged at the rate of x cents per pound, and at least six pounds will be charged at the rate of y cents per pound. The only difference is the charge for the remaining pound. Since y is less than x, the cheaper method is the one that results in that last pound costing y cents instead of x cents (combining them), and the difference in cost is the difference between x and y.

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