Jane Odd is the owner of Oddly Odd Book Store. Jane Odd loves odd things, but her book seller only sells books in even numbers. If there are an even number of books in the book store (b = an even number), and Jane divides the books into groups of 18 books, which results in an odd number of groupings (b/18 = an odd number). Now, if Jane doubles the number of books in the store, how can she divide the books up to keep an odd number of groupings (b^2/X = an odd number)?	Pick one:
A) b^2/12	B) b^2/18	C) b^2/9	D) b^2/6	E) b^2/2
Divisible by 2 (Parity Mathematics) states: an even number is an integer of the form n = 2k, where k is an integer; an odd number is an integer of the form n = 2k + 1.   Since a is an even number, a = 2k, a^2 = 4k^2 = (2)(2)(k)^2, and a/18 is an odd number 2k/18.   18 = (2)(9). Now (2k)/((2)(9)) = k/9. So, we are looking for a (2)(2) factor in the denominator.   Factors are:   12 = (2)(2)(3)   18 = (2)(9)   9 = (3)(3)   6 = (2)(3)   2 = (2)   So, 12 has more than 1 (2).   b^2/12nswer: b^2/12
<result>A</result>
Jane Odd is the owner of Oddly Odd Book Store. Jane Odd loves odd things, but her book seller only sells books in even numbers. If there are an even number of books in the book store (b = an even number), and Jane divides the books into groups of 18 books, which results in an odd number of groupings (b/18 = an odd number). Now, if Jane doubles the number of books in the store, how can she divide the books up to keep an odd number of groupings (b^2/X = an odd number)?