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Cats/Dogs Ratio in Magoosh?

Did anybody else encounter this question? It asked which of two towns had a greater number of cats, where Town A had a 4:11 cat/dog ratio, and Town B had a 3:8 cat/dog ratio. Magoosh said the answer is D, but that can't possibly be correct. (Video lessons said if there are no variables present, D cannot be the answer.) Further, if A had a scale factor of 8, and B had a scale factor of 11, then the ratios would be 32:88 and 33:88 respectively, meaning B has more cats. Am I misunderstanding something about how proportions work?

Author
Brandon Price

Posted Jun 25, 2018

1 Explanation

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Gravatar David Recine, Magoosh Tutor

I can help, Brandon. :) The link to the question is here: https://gre.magoosh.com/questions/200/ . (Magoosh GRE login required to view the question.)

As for (D) being impossible if there are no variables, this is true. But the definition of "variables" is broad. For the purposes of QC, "variables" are any gaps in information; any unknown information that is needed to solve the problem. Here, there is in fact missing information that could be expressed as variables. However, before we get to that, let's first look at your thoughts on scale factor.

First, scale factor only works for objects that are directly proportional to each other, and there should only be a single scale factor between two ratios. If, for example, Town A had a ratio of 4:12 cats to dogs, and Town B's cats:dogs was 3:9, the ratios would be proportional to each other; both 4:12 and 3:9 can be simplified to 1:3. The scale factor itself comes from creating a ratio of just one element that appears in both rations (either cats or dogs, in this case); since the two elements are proportional, you can use either one to get the ratio of one to another. The scale factor here is 4. 4 cats from Town A to 1 cat in the town B ratio would be 4/1 or 4. You get the same result if you calculate the scale factor based on dogs int he two town ratios. 12/3= 4.

But even if the numbers were adjusted as I showed you above, you still wouldn't have enough info to know the actual number of cats or dogs. Whether we're dealing with 4:12 and 3:9 (my scalable hypothetical above), or 4:11 and 3:8 (the actual problem), we don't know how many times we're multiplying the number of cats and dogs by. The 4:11, for instance, could represent 20 cats and 55 dogs (multiplying 4 and 11 by 5), or 4,000 cats and 11,000 dogs (multiplying 4 and 11 by 1,000), or simply 4 cats and 11 dogs (multiplying 4 and 11 by 1).

And that's where the variables comes in! To solve for this problem we really need the following equations:

4x/11x (Town A cats/dogs); 3y/11y (Town B cats/dogs). Then we need to solve for x and y. In this case, though, x and y would not be related to each other in the solution, since we're not treating the two town ratios as having an interconnected scale factor of any sort. (And in fact, even if a scale factor seemed possible, we'd need a reason to use one-- a reason that if the number of cats in Town A changes, the number of cats in town B would also change.)

We can't solve 4 x and y, because we have the variables, but no information that puts a limit or parameter on the variables, or gives us an equation to solve for in relation to the variables. Thus, the answer is D.

Jun 26, 2018 • Comment

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