Is picking numbers the quickiest approach here?

[mepinoargote]

If p1 and p2 are the populations and r1 and r2 are the number or 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??

(1) p1>p2
(2) r2<r1

Is easy and very quick to conclude (1) and (2) are insufficient, but what´s the quickiest approach to test (1) and (2) together? picking numbers?

p1/r1 < p2/r2 or p1/r1 > p2/r2 ???

In this particular question we know p1, p2, r1 and r2 are > 0 since they are populations and representatives, but what if a question gives you no restrictions, and p1/r1, p2/r2 could be any number (possitive, negative, fraction, decimal, etc.)

how can we test this quicky? is pícking numbers the best strategy?

[niksworth]

It is fairly basic that If p1>p2 and r1>r2, then p1/r1 is not necessarily greater than or less than p2/r2. Hence the answer is E. One need not pick numbers for that.

The danger in picking numbers is that you may choose a wrong set of numbers a get the wrong result.
E.g. if you choose p1 = 100, p2 = 50, r1 = 20 and r2 = 5 then p1/r1 < p2/r2.
However, if p1 = 100, p2 = 50, r1 = 20, r2 = 15 then p1/r1 > p2/r2.

Picking numbers may help if you have a hunch of what the answer might be and you want to confirm it. For e.g. in this question, if you feel that the given information is not sufficient but are not sure, a quick check with numbers like those used above may help to clarify.

I think that, in general, picking numbers help in negation more than in assertion.

[mepinoargote]

actually the official answer is C, i made the same mistake as you and assumed more information was needed.

[niksworth]

actually the official answer is C, i made the same mistake as you and assumed more information was needed.

Then clearly, the OA is wrong. We cannot conclusively say about the ratios unless there is some other information.

2 questions -
1) Is there any explanation provided?
2) What is the source?

[mepinoargote]

type error, sorry, statement (2) is r2>r1. question is from og 12 DS # 38.

[Maciek]

Hi all!

(1) & (2)
the quickest way to check whether both statements are sufficient is:
p1 > p2, for example p1 = 5p2
r2>r1, for example r1 = 0.5r2
p1/r1 = 5p2/(0.5r2) = 10*p2/r2
p1/r1 > p2/r2

Statements 1 and 2 both are sufficient.

check how to analyze a GMATPrep Data Sufficiency Question:
https://www.beatthegmat.com/mba/2010/03/ ... y-question

Hope it helps!
Best,
Maciek