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## Official Guide Explanation:Problem Solving #59

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: 59
Page: 160
Difficulty: 5 (Moderate)
Category 1: Word Problems > Other >
Category 2: Algebra > Linear Equations-One Unk >

Explanation: First, set up an equation for the amount of money that Harry is paid. Use h for hours. For the first 30 hours, he earns x per hour, for a total of:

30x

For additional hours, he earns 1.5x per hour. If he works a total of h hours, the number of additional hours he works is h - 30, so the additional income is:

(h - 30)(1.5x)

That's a total of 30x + (h - 30)(1.5x)

Using the same principle, if we call James's hours j, James's income is:

40x + (j - 40)(2x)

We know that James worked 41 hours, or j = 41, so James's income is:

40x + 1(2x) = 42x

Since Harry's income is equal to James's income, we can solve for h:

30x + (h - 30)(1.5x) = 42x

(h - 30)(1.5x) = 12x

(h - 30) = ((12x)/(1.5x))

h - 30 = 8x

h = 38, choice (D).

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