Official Guide Explanation:
Data Sufficiency #D30




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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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