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

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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) $$r_2>r_1$$

Practice Questions
Question: 43
Page: 278
Difficulty: 600
[Reveal] Spoiler: OA

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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.

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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

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]

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18 Sep 2012, 04:41
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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

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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.

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Re: If p1 and p2 are the populations and r1 and r2 are the [#permalink]

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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.

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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.

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Re: If p1 and p2 are the populations and r1 and r2 are the [#permalink]

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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.

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31 Jul 2014, 07:43
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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
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Re: If p1 and p2 are the populations and r1 and r2 are the [#permalink]

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19 May 2016, 06:38
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Bunuel wrote:
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) $$r_2>r_1$$

Solution:

We are given the following:

p_1 = population of District 1

p_2 = population of District 2

r_1 = the numbers of representatives of District 1

r_2 = numbers of representatives of District 2

We need to determine whether the ratio of the population to the number of representatives is greater in District 1 or District 2. We can translate the question into an inequality.

Is p_1/r_1 > p_2/r_2 ?

After cross multiplying we obtain:

Is (p_1)(r_2) > (r_1)(p_2) ?

Note that we could write the initial equation as p_1/r_1 < p_2/r_2 as well, because the question is only asking which one is greater. Whichever way we write the equation would be acceptable.

Statement One Alone:

p_1 > p_2

Although p_1 > p_2, we do not have enough information to determine whether (p_1)(r_2) is greater than (r_1)(p_2). Let’s consider two cases.

Case # 1

p_1 = 300

p_2 = 200

r_1 = 2

r_2 = 1

We see that (p_1)(r_2) > (r_1)(p_2) = 300 > 400 is not true.

Case # 2

p_1 = 300

p_2 = 200

r_1 = 2

r_2 = 2

We see that (p_1)(r_2) > (r_1)(p_2) = 600 > 400 is true.

Statement one alone is not sufficient to answer the question. We can eliminate answer choices A and D.

Statement Two Alone:

r_2 > r_1

Although r_2 > r_1, we do not have enough to determine whether (p_1)(r_2) is greater than (r_1)(p_2). Let’s consider two cases.

Case # 1

p_1 = 100

p_2 = 200

r_1 = 2

r_2 = 3

We see that (p_1)(r_2) > (r_1)(p_2) = 300 > 400 is not true.

Case # 2

p_1 = 200

p_2 = 200

r_1 = 2

r_2 = 3

We see that (p_1)(r_2) > (r_1)(p_2) = 600 > 400 is true.

Statement two alone is not sufficient to answer the question. We can eliminate answer choice B.

Statements One and Two Together:

Using the information from statements one and two we know the following:

p_1 > p_2 and r_2 > r_1. Thus, (p_1)(r_2) must be greater than (r_1)(p_2).

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21 Sep 2012, 03:03
SOLUTION

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.

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29 Dec 2012, 11:40
I took this approach
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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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]

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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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18 Apr 2015, 07:27
1. p1 = 20, p2 = 18 NS
2. r2 = 9, r1 = 8 NS

Plug in the values we get answer c. But Bunnuel is surely best.
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Re: If p1 and p2 are the populations and r1 and r2 are the [#permalink]

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22 Dec 2015, 12:35
Suppose p1>p2 AND r1>r2

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Re: If p1 and p2 are the populations and r1 and r2 are the [#permalink]

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09 Aug 2016, 10:50
Bunuel wrote:
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

We are interested in a ratio of either P1/R1 or P2/R2. The statements provide P1 > P2 and R1 > R2.

What if P1 = 6 and P2 = 3? P1 > P2.
What if R1 = 12 and R2 = 6? R1 > R2.

But it still doesn't mean P1/R1 > P2/R2. They can also be the equal. So to me the answer should be (E).

Where am I wrong in my assumption?
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Re: If p1 and p2 are the populations and r1 and r2 are the [#permalink]

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09 Aug 2016, 10:53
Witchcrafts wrote:
Bunuel wrote:
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

We are interested in a ratio of either P1/R1 or P2/R2. The statements provide P1 > P2 and R1 > R2.

What if P1 = 6 and P2 = 3? P1 > P2.
What if R1 = 12 and R2 = 6? R1 > R2.

But it still doesn't mean P1/R1 > P2/R2. They can also be the equal. So to me the answer should be (E).

Where am I wrong in my assumption?

(2) says $$r_2>r_1$$ not $$r_1>r_2$$
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09 Aug 2016, 18:16
ah! silly me. thanks!!

"Read the question carefully" doesn't ever get old.
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Re: If p1 and p2 are the populations and r1 and r2 are the [#permalink]

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10 Aug 2016, 02:11
The question asks if P1/R1 > P2/R2 or opposite.
(1) p1>p2 => INSUFFICIENT
(2) r2>r1 => INSUFFICIENT

(1) and (2):
(1) p1 > p2
(2)1/r1>1/r2 (because r2>r1)
Multiply (1) and (2) as above, we have p1/r1 > p2/r2 => SUFFICIENT => C is the right answer

However, if the (2) is r1>r2 instead of r2>r1, we will have E as the answer. Because in that case we have p1/r2>p2/r1 and we have no way to identify if p1/r1 is larger than p2/r2 or not.
Re: If p1 and p2 are the populations and r1 and r2 are the   [#permalink] 10 Aug 2016, 02:11
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