Reni wrote:

araspai wrote:

1. A pet store holds cats and dogs. If the difference between the number of cats and the number of dogs is 13. What could be the ratio of Cats to dogs in the pet store?

a. 1:3 b. 1:4 c. 1:5 d. 2:5 e. 4:5

I got this same exercise but with diff options:

a)4:1

b)3:1

c)4:3

d)5:2

e)5:3

The answer is C.

Bunnuel, could you please help and explain it to us?

Thank you!

A pet store holds cats and dogs. If the difference between the number of cats and the number of dogs is 13. What could be the ratio of Cats to dogs in the pet store?A. 1:3

B. 1:4

C. 1:5

D. 2:5

E. 4:5

Say the

ratio of cats to dogs is a/b. Then the

number of cats would be ax and the

number of dogs bx, for some positive integer x.

We are told that ax - bx = 13 --> x(a - b) = 13. Since 13 is a prime number it could be broken into the product of two positive multiples only in one way: x(a - b) = 1*13.

The above implies that either x = 1 and

a - b = 13 or x = 13 and

a - b = 1.

Therefore the correct answer should have the difference between numerator and denominator equal to 1 or 13.

For the original question only option which fits is E, 4:5. Cats = 13*4 = 52 and dogs = 13*5 = 65.

Answer: E.

For your question the answer would be C, 4:3, for the same reason..

But how can you deduce this from above : Therefore the correct answer should have the difference between numerator and denominator equal to 1 or 13.