Official Guide Explanation:
Data Sufficiency #82




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Solution and Metadata

Question: 82
Page: 158
Difficulty: 5 (Moderate)
Category 1: Arithmetic > Properties of Integers > Factors and Multiples
Category 2: Algebra > Inequalities > other
Category 3: Word Problems > Other >

Explanation: This question is testing the concept of multiples. If Michael had 10 books on each shelf with no books left over, his number of books (call it b) is a multiple of 10. If he acquired 10 more books, then had exactly 12 on each shelf, the result (b + 10) is divisible by 12. If b is a multiple of 10, then b + 10 is a multiple of 10 as well. Thus, b + 10 must be both a multiple of 10 and a multiple of 12. The least common multiple of 10 and 12 is 60, meaning that the possible values for b + 10 are multiples of 60: 60, 120, 180, etc. The possible values for b, then, are 50, 110, 170, etc.

Statement (1) is sufficient. If b<96, the only possible value for b is 50.

Statement (2) is insufficient. If b>24, any of the listed possibilities are acceptable. Choice (A) is correct.

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