There are an odd number of bananas in every bunch of bananas (b = number of bananas per bunch, and B = number bunches of bananas), and every bag of apples has an even number of apples (a = number apples per bag, and A = number bags of apples). The store refuses to sell individual items. The store only sells bunches and bags. Which equation shows how the fruits can be combined to ensure an equal number of bananas and apples? Select the correct option.
A) (2B + 1)(2b + 1) = (A)(a) B) (2Bb + 1) = (Aa + 1) C) (1/2)(4B + 2)(2b + 1) = (A)(2a + 1) D) (B)(2b + 1) = (A)(2a) E) (B + 1)(b) = (2A + 1)(2a + 1)
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.   So, (A)(2a) will give an even number of apples,   and (B)(2b + 1), from Parity Mathematics Rule: The sum of two odd numbers is even, will give an even number of bananas.   (B)(2b + 1) = (A)(2a)   Answer: (B)(2b + 1) = (A)(2a)
<result>D</result>
There are an odd number of bananas in every bunch of bananas (b = number of bananas per bunch, and B = number bunches of bananas), and every bag of apples has an even number of apples (a = number apples per bag, and A = number bags of apples). The store refuses to sell individual items. The store only sells bunches and bags. Which equation shows how the fruits can be combined to ensure an equal number of bananas and apples?