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## Official Guide Explanation:

Problem Solving #150

**Background**

This is just one of hundreds of free explanations I've created to the quantitative questions in The Official Guide for GMAT Quantitative Review (2nd 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****: 150**

Page: 82

Difficulty: **6** (Moderately Difficult)

Category 1: Geometry > Polygons (Convex) >

**Explanation:** Because the diagram is not drawn to scale, we don't know anything about the angles. If QPT and PTS are both very large angles, the length of PT could be very short. But if QPT and PTS are very small, acute angles, PT could be very long. We can use a version of the rules you should know regarding the length of the third side of a triangle. The third side of a triangle cannot be longer than the sum of the other two sides.

The same is true here--PT cannot be longer than the sum of the other four sides. If you tried to draw a figure with a length of PT like that, it would be impossible to connect the other four sides together. The sum of the other four sides is 14, so PT cannot be 15. The other side lengths are acceptable. As we've seen, PT can be very small relative to the other side lengths, so 5 would be easy to construct. 10 is under the limit of 14, so 5 and 10 are both possible. Choice (C) is correct.

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