A pet store holds cats and dogs. If the difference between the number of cats and the number of dogs is 11. What could be the ratio of Cats to dogs in the pet store? Choose the correct choice from the following answers
A) 1 : 3 B) 1 : 4 C) 1 : 5 D) 44 : 55 E) 4 : 6

Rationale: say theratioof cats to dogs is a / b . then thenumberof cats would be ax and thenumberof dogs bx , for some positive integer x . we are told that ax - bx = 11 - - > x ( a - b ) = 11 . since 11 is a prime number it could be broken into the product of two positive multiples only in one way : x ( a - b ) = 1 * 11 . the above implies that either x = 1 and ( a - b ) = 11 or x = 11 and ( a - b ) = 1 . therefore the correct answer should have the difference between numerator and denominator equal to 1 or 11 . for the original question only option which fits is e , 4 : 5 . cats = 11 * 4 = 44 and dogs = 11 * 5 = 55 . answer : d .
Answer: D