Source: Official Guide for the GMAT 13th Ed. Data Sufficiency; #43 Official Guide for the GMAT 2015 14th Ed. Data Sufficiency; #43

7

# If p and p are the populations

If p and p are the populations and r and r are the numbers of representatives of District 1 and District 2, respectively, the ratio of the population to the number of representatives is greater for which of the two districts?

### 3 Explanations

1

Felipe Levi Gurgel

The question is asked where is the ratio of the population to the number of representatives is greater?

with the 2 information ( P1 > P2 and R2>R1) i could see that you could deduce the ratio of the population P1 > than the number of representatives

Dec 9, 2016 • Comment

Sam Kinsman, Magoosh Tutor

Hi Felipe, that's right - the question is asking us which district has a greater ratio of population to number of representatives.

As Cydney explains below, if we consider both statements, we find that the ratio of population to number of representatives is greater for District 1 than for District 2.

1

Kalifa Howard

I still don't understand how the answer is C.

Jan 22, 2016 • Comment

Cydney Seigerman, Magoosh Tutor

In this question, we need to compare the ratio of population to number of representatives in the two groups: p1/r1 vs p2/r2. To do that, we need information about both the population size and number of representatives. Since neither of the two statements give us information on both of these values, neither one is sufficient alone. Combined, however, the two statements tell us information about both values: p1>p2 and r2>r1.

With that in mind, let's return to the ratios I mentioned before:

p1/r1 (1)
p2/r2 (2)

For two given fractions, if the denominator is the same, the fraction with the larger numerator will be greater. In this case, p1>p2, so if the denominators were equal, we could say that (1) > (2).

At the same time, if the numerator is the same for two given fractions, the fraction with the smaller denominator will be greater. Here, since r2>r1, if the numerators were equal, we could say that (1) > (2).

As we can see, in both cases, we have (1) > (2). So, combining the two statements, the observation (1) > (2) remains the same. Therefore, we can conclude that (1) > (2), using the two statements together.

For more about how to compare fractions with different numerators and denominators, I definitely recommend checking out the table that Mike includes in the blog post on this specific practice problem. (http://magoosh.com/gmat/2012/comparing-ratios-on-the-gmat/).

Hope this helps :) Mike McGarry, Magoosh Tutor