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## Official Guide Explanation:

Data Sufficiency #D30

**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.

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**Solution and Metadata**

**Question****: D30**

Page: 24

Difficulty: **6** (Moderately Difficult)

Category 1: Word Problems > Other >

**Explanation:** This is a trickier question than it first looks like. Consider the minimum and maximum values of the gift certifications. If all of them are $10, the value is $200. If all are $100, the value is $2,000. Changing one gift certification from a $10 to a $100 affects the total by $90. For instance, if instead of 20 $10 gift certificates, they were made up of 19 $10s and 1 $100, the total would be $90 greater than $200 -- $290. On the flip side, if instead of 20 $100 gift certificates, they were made up of 19 $100s and 1 $10, the total would be $90 less than $2,000 -- $1,910. The relevent point is that there are a finite number of possible values, and they are separated by $90 between $200 and $2,000.

Statement (1) is sufficient. Continue to count down from $2,000 by $90s to see what the possibilities are in this range. 19 $100s is $1,910; 18 $100s is $1,820; 17 $100s is $1,730, and 16 $100s is $1,640. The only possibility in the range btween $1,650 and $1,800 is $1,730--17 $100 gift certificates and 3 $10 gift certificates.

Statement (2) is insufficient. The number of $10 gift certificates could be as many as 4 and as few as zero. Choice (A) is correct.

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