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If p1 and p2 are the populations and r1 and r2 are the

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If p1 and p2 are the populations and r1 and r2 are the [#permalink] New post 18 Sep 2012, 02:26
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If p_1 and p_2 are the populations and r_1 and r_2 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?

(1) p_1>p_2
(2) r_2>r_1

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Re: If p1 and p2 are the populations and r1 and r2 are the [#permalink] New post 18 Sep 2012, 02:26
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If p_1 and p_2 are the populations and r_1 and r_2 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?

Question asks whether \frac{p_1}{r_1}>\frac{p_2}{r_2}. Or, since the numbers are positive, we are asked to determine whether p_1*r_2>p_2*r_1.

(1) p_1>p_2. No info about r_1 and r_2. Not sufficient.
(2) r_2>r_1. No info about p_1 and p_2. Not sufficient.

(1)+(2) Since the multiples on left hand side are greater than the respective multiples on the right hand side then p_1*r_2>p_2*r_1. Sufficient.

Answer: C.
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Re: If p1 and p2 are the populations and r1 and r2 are the [#permalink] New post 18 Sep 2012, 04:41
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The Official Guide for GMAT® Review, 13th Edition - Quantitative Questions Project

If p_1 and p_2 are the populations and r_1 and r_2 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?

(1) p_1>p_2
(2) r_2>r_1

Practice Questions
Question: 43
Page: 278
Difficulty: 600


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The question asks to compare to fractions: \frac{p_1}{r_1} and \frac{p_2}{r_2}, where all 4 numbers are positive integers.

(1) Not sufficient, because we don't have any information about the denominators of the two fractions to be compared.
For example, we can choose p_1=10r_1 and p_2=100r_2 or the other way around.
(2) Again, not sufficient, because now we don't have any information on the numerators.
We can choose again the same values for p_1 and p_2 as above.

(1) and (2) together: We know that the numerator of the first fraction \frac{p_1}{r_1} is greater than the numerator of the second fraction \frac{p_2}{r_2}. In addition, the denominator of the first fraction is smaller than the denominator of the second fraction. Therefore, the first fraction is greater than the second, because \frac{p_1}{r_1}>\frac{p_2}{r_1}>\frac{p_2}{r_2}. Between two positive fractions with the same numerator, the largest fraction is that with the smallest denominator.

Answer C.
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Re: If p1 and p2 are the populations and r1 and r2 are the [#permalink] New post 18 Sep 2012, 04:56
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If p_1 and p_2 are the populations and r_1 and r_2 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?
(1) p_1>p_2
(2) r_2>r_1

The Question can be restated as which one is greater p_1.r_2 or p_2.r_1
1) No info is given regarding the ratio of r_2 & r_1 ---->Insufficient
2) No info is given regarding the ratio of p_2 & p_1 ---->Insufficient
1+2) We can easily say that p_1.r_2 is greater than p_2.r_1-->Sufficient

Answer C

Note:- If the option (2) had been r_2<r_1 rather than r_2>r_1, then the answer would have been E

Hope it helps.
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Re: If p1 and p2 are the populations and r1 and r2 are the [#permalink] New post 18 Sep 2012, 09:25
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Bunuel wrote:
The Official Guide for GMAT® Review, 13th Edition - Quantitative Questions Project

If p_1 and p_2 are the populations and r_1 and r_2 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?

(1) p_1>p_2
(2) r_2>r_1

Practice Questions
Question: 43
Page: 278
Difficulty: 600


GMAT Club is introducing a new project: The Official Guide for GMAT® Review, 13th Edition - Quantitative Questions Project

Each week we'll be posting several questions from The Official Guide for GMAT® Review, 13th Edition and then after couple of days we'll provide Official Answer (OA) to them along with a slution.

We'll be glad if you participate in development of this project:
1. Please provide your solutions to the questions;
2. Please vote for the best solutions by pressing Kudos button;
3. Please vote for the questions themselves by pressing Kudos button;
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Thank you!


Need to find is P1/R1 > P2/R2

Option 1: P1>p2 only by judging neumerator we can not conclude which ratio is greator the other. therefore Option 1 is not sufficient to answer the question.
Option 2: R2>R1 again the same thing only by looking at the denominator we can not say that which ratio is greator. therefor Option 2 is also not sufficient to answer the question.

by combining both the option it is coming that Neumerator for the P1/R1 is greator than P2/R2 and Denominator of P1/R1 is lesser than the Denominator of P2/R2. therefor P1/R1 is greator the P2/R2.

Option 'C" is Answer.
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Re: If p1 and p2 are the populations and r1 and r2 are the [#permalink] New post 19 Sep 2012, 23:24
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Is P1/R1 > P2/R2, or vise versa? let's manipulate the inequality to a simpler form.
P1R2 > P2R1 means P1/R1 is the greater ratio?

(1) P1 > P2, we can't answer the question because we need to know R1,R2. INSUFFICIENT
(2) r2 > R1, we can't answer the question because we need to know P1, P2. INSUFFICIENT.

Together, let's multiple the inequalities.
p1r2 > p2r1', so we now know that P1/r1 is the greater ratio.

answer: C
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Re: If p1 and p2 are the populations and r1 and r2 are the [#permalink] New post 21 Sep 2012, 03:03
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If p_1 and p_2 are the populations and r_1 and r_2 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?

Question asks whether \frac{p_1}{r_1}>\frac{p_2}{r_2}. Or, since the numbers are positive, we are asked to determine whether p_1*r_2>p_2*r_1.

(1) p_1>p_2. No info about r_1 and r_2. Not sufficient.
(2) r_2>r_1. No info about p_1 and p_2. Not sufficient.

(1)+(2) Since the multiples on left hand side are greater than the respective multiples on the right hand side then p_1*r_2>p_2*r_1. Sufficient.

Answer: C.

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If p1 and p2 are the populations and r1 and r2 are the [#permalink] New post 29 Dec 2012, 11:40
I took this approach
1. reads P1>P2 and
rewrote 2. as R1<R2

Each statement by itself is not sufficient.
Combining-
then P1/R1 (greater numerator/lower denominator ) > P2/R2 (lower numerator/greater denominator) will be true.

Hence C.
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If p1 and p2 are the populations and r1 and r2 are the [#permalink] New post 31 Dec 2012, 11:10
metallicafan wrote:
Which way is better to solve this question? Using algebra or testing with some values or numbers? Why? I used numbers, but OG used algebra.

If P1 and P2 are the populations and R1 and R2 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?
(1) P1 > P2
(2) R2 > R1



Testing with Numbers if one can quickly come up with a yes and another no is always helpful on GMAT. But key is to find a contrast. Also it will help if a pattern emerges in a few steps. Usually GMAT doesn't something that holds for x upto say 20 terms and fails on 23rd.
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If P1 and P2 are the populations and R1 and R2 are the numbers o [#permalink] New post 07 Feb 2013, 09:57
ksrajgmat wrote:
Can some one please explain the solution to this problem.


I used substitution for this problem.

St 1 gives us that P1 > P2, for ease of math I subbed P1 = 100 P2 = 50
--> This is NS to solve the problem since we don't know how many Reps there are for each district & therefore cannot find the ratio.
--> Eliminate A & D

St 2 gives us that R2 > R1, for ease of math I subbed R1 = 10 R2 = 20
--> This is NS also, since we don't know the population
--> Eliminate B

Combining the 2 statements we see that P1 > P2 and R2 > R1 -- at this point, even without substitution you should intuitively know that a lower population with a higher pop count will give you the biggest ratio (aka the higher percentage), but just to make sure I will use the same numbers I substituted above.

So, R1/P1 = 10/100 = 1/10 (or 10%...whichever form is easiest for you to work) and R2/P2 = 20/50 = 2/5 (or 40%)...Sufficient....so C

As a reminder, with DS you don't actually have to solve the problem - you just need to be able to recognize whether you have enough information to solve it.
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Re: If p1 and p2 are the populations and r1 and r2 are the [#permalink] New post 25 Mar 2014, 00:06
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If p1 and p2 are the populations and r1 and r2 are the [#permalink] New post 31 Jul 2014, 07:43
Simple logic can help:

ratio is a fraction and for the less denominator and more numerator we get higher fraction

St.1 gives P1>P2, numerator is higher in the first pair
St.2 gives R2>R1, denominator is less in the first pair

so the first pair has higher ratio, C
If p1 and p2 are the populations and r1 and r2 are the   [#permalink] 31 Jul 2014, 07:43
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