Vincen wrote: ↑

Thu Sep 03, 2020 6:08 am

Michael arranged all his books in a bookcase with 10 books on each shelf and no books left over. After Michael acquired 10 additional books, he arranged all his books in a new bookcase with 12 books on each shelf and no books left over. How many books did Michael have before he acquired the 10 additional books?

(1) Before Michael acquired the 10 additional books, he had fewer than 96 books.
(2) Before Michael acquired the 10 additional books, he had more than 24 books.

Answer: A

Source: Official Guide

The books should always remain in the multiples of 10.

Now it is important to note that after acquiring 10 additional books, the number of books should not only be a multiple of 10, but also of 12.

To solve, calculate the LCM of 10 and 12 \(\Longrightarrow\) 60, 120, 180...

Statement 1: Number of books is less than 96, which is sufficient to answer since we have only one LCM available less than 96 (i.e. 60)
Therefore he had 50 books earlier; after acquiring 10 more, he had 60. Sufficient \(\Large{\color{green}\checkmark}\)

Statement 2: Number of books is more than 24, which is not sufficient since we can have 120 or 180 or 240... so on. Not Sufficient \(\Large{\color{red}\chi}\)

Therefore, A