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## Official Guide Explanation:

Problem Solving #68

**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.

Click here for an example of the PDF booklets. Click here to purchase a PDF copy.

**Solution and Metadata**

**Question****: 68**

Page: 161

Difficulty: **6** (Moderately Difficult)

Category 1: Algebra > Functions > other

Category 2: Algebra > Linear Equations-One Unk >

**Explanation:** Any time you see a word problem this long, especially with a formula given, trust that it will not ultimately be that complicated. Your main task is sifting through all the information and finding the straightforward math problem hidden inside.

Given the formula for N, we need values of L, d, and s. The question tells us that L = 2 and s = 40. It also tels us that the length of the portion of the highway is (1/2)mile, though d needs to be in feet. Since it's given that 1 mile equals 5,280 feet, (1/2) mile is 2,640 feet, so d = 2,640. Plug in these three values:

N = ((20Ld)/(600 + s^{2}))

= ((20(2)(2,640))/(600 + 40^{2}))

= ((40(2,640))/(600 + 1600))

= ((40(2,640))/2200)

= ((4(264))/22)

= ((2(264))/11) = (528/11)

We don't need to find the exact value of the fraction. If the numerator were 550, the value would be 50. The only answer choice even remotely in the same range is (D), 48.

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