A pet store holds cats and dogs. If the difference between

e?
we have c cats and d dogs... d=c+13... so our ratio is c/d=c/(c+13)... if we plug every answer (not very elegant, i admit it), we see that the only way to get an integer for c is 4/5

yes E. 4:5 is the correct answer.
the difference between the number of cats and dogs must be divisible by difference between the numbers that represent both animals in ratio. Since 13 is a prime number , it is only divisible by 1 and 13 .Therefore, the correct choice is the one where the difference between the numbers is 1.

Regards,
Ara

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!

I understood till this point : The above implies that either x = 1 and a - b = 13 or x = 13 and a - b = 1.
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.
Please explain.

The answer options does not have 1 and has 13 and hence the difference is 13. The question says "could" be and hence 13 is the answer

Regards
Siva

Hi EricImasogie,

That's a clever way to interpret this question and it showcases how paying attention to the answer choices (and using them to your advantage) can lead to quicker solutions to a given question (than just doing long-winded calculations).

GMAT assassins aren't born, they're made,
Rich

This question tests your understanding of the ratio scale vs actual values. If you recognise it, it takes you a few secs to get to your answer.
This concept has been discussed in detail here:
https://www.gmatclub.com/forum/veritas-prep-resource-links-no-longer-available-399979.html#/2011/03 ... of-ratios/

We all are aware that to convert ratio scale values to actual values, we multiply the ratio by the multiplier. We have also often used the sum of values concept for the "total" of actual values.
This question tests the same concept with the difference between values.
If the actual difference between values is 13, what could be the difference in values on the ratio scale? To get 13, the multiplier could have been 1 or 13. In case it was 1, then the difference between the values on ratio scale would be 13. If instead, the multiplier is 13, the difference between the values on the ratio scale would be 1.
Only option (E) satisfies this condition (difference between values on ratio scale is 1)

If you realise, the question is indirectly talking about multiples of 13. Then you will be able to see only option E adjusts for the difference.

Cats : Dogs
13*4 : 13*5

52 : 65

65 - 52 = 13

If its any other option, difference will become much greater than 13. Hence E is the answer

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