### Bookshelf

Total GMAT MathJeff's complete Quant guide, on sale now! |

Total GMAT VerbalEverything you need to ace GMAT Verbal! |

New: GMAT 111Improve every aspect of your GMAT prep! |

**1,800 Practice Math Questions**

GMAT Official Guide

OG Math | OG Verbal

Guides To the Official Guide

Free: OG12 explanations!

**GMAT Question of the Day**

Beginner's Guide to the GMAT

GMAT Hacks Affiliate Program

### Categories

- General Study Tips
- Goals and Planning
- CAT Strategy
- The Mental Game
- GMAT Math Strategy
- GMAT Math Topics
- Mental Math
- Data Sufficiency
- Critical Reasoning
- Reading Comprehension
- Sentence Correction
- Analytical Writing Assessment
- Business School Admissions
- GMAT Prep Resources
- Practice Questions
- Total GMAT Math
- Total GMAT Verbal

## Official Guide Explanation:

Data Sufficiency #109

**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****: 109**

Page: 282

Difficulty: **7** (Very Difficult)

Category 1: Geometry > Triangles > Multiple figures

Category 2: Geometry > Triangles > other

**Explanation:** An important first step is to draw a diagram to represent the description. Regardless of the shape of the triangle you draw, XYC will represent one corner of ABC, and RSC will be an even smaller corner of the triangle inside XYC. The important thing to recognize is that these three triangles are "similar." All three have the same angle (the angle at point C) between two sides that have the same ratio to each other. Since XC is half of AC and YC is half of BC, the ratio of XC to YC is the same as the ratio of AC to BC. The same reasoning goes for RC to SC.

Statement (1) is sufficient. ABX is exactly half the area of ABC -- it has two of the same sides as ABC, and the shorter side (AX) is half the length of the length of the corresponding side in ABC. Thus, if the area of ABX is half the area of ABC, so the area of ABC is 64. Thus, (1/2)bh = 64, or bh = 128. In RSC, each of the sides is one - quarter the length of the corresponding side in ABC. (This is where the "similar" triangles come in -- all of the measurements, not just RS and SC, are one - quarter of the corresponding measurement in ABC.) So we're looking for:

((1/4)b)((1/4)h)

or

(1/16)bh

We know bh, so we can find this value.

Statement (2) is insufficient. It provides one useful piece of information towards finding the area of ABC, but to find the area of a triangle, we need both base and height ("altitude"), not just one. Choice (A) is correct.

Click here for the full list of GMAT OG12 explanations.

You should follow me on Twitter. While you're at it, take a moment to
subscribe to
GMAT Hacks via RSS or Email. |

Total GMAT Math
The comprehensive guide to the GMAT Quant section. It's "far and away the best study material
available," including over 300 realistic practice questions and more than 500 exercises! |