Michael arranged all his books in a bookcase with 10 books on each she

OFFICIAL GMAT EXPLANATION

Arithmetic Properties of numbers

If x is the number of books Michael had before he acquired the 10 additional books, then x is a multiple of 10. After Michael acquired the 10 additional books, he had x + 10 books and x + 10 is a multiple of 12.

(1) If x < 96, where x is a multiple of 10, then x = 10, 20, 30, 40, 50, 60, 70, 80, or 90 and x + 10 = 20, 30, 40, 50, 60, 70, 80, 90, or 100. Since x + 10 is a multiple of 12, then x + 10 = 60 and x = 50; SUFFICIENT.

(2) If x > 24, where x is a multiple of 10, then x must be one of the numbers 30, 40, 50, 60, 70, 80, 90, 100, 110, …, and x + 10 must be one of the numbers 40, 50, 60, 70, 80, 90, 100, 110, 120, …. Since there is more than one multiple of 12 among these numbers (for example, 60 and 120), the value of x + 10, and therefore the value of x, cannot be determined; NOT sufficient.

Statement 1 alone is sufficient.

Does anyone know any other official DS question (based on applied word problems) that requires/uses the concept of LCM to be solved? Word problems provide an excellent opportunity to understand LCM!

If we take statement 2 into account then does that mean that the number of shelfs in the bookcase are not fixed?
For example
if we say there are 110 books initially and then we have 10 more to make it 120 - then number of shelfs become 120/12 = 10
if we say there are 170 books initially and then we have 10 more to make it 180- then number of shelfs become 180/12 = 15

so we have to assume that the number of shelfs are not fixed?

Can someone clarify

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