Thank you for using the timer - this advanced tool can estimate your performance and suggest more practice questions. We have subscribed you to Daily Prep Questions via email.

Customized for You

we will pick new questions that match your level based on your Timer History

Track Your Progress

every week, we’ll send you an estimated GMAT score based on your performance

Practice Pays

we will pick new questions that match your level based on your Timer History

Not interested in getting valuable practice questions and articles delivered to your email? No problem, unsubscribe here.

It appears that you are browsing the GMAT Club forum unregistered!

Signing up is free, quick, and confidential.
Join other 350,000 members and get the full benefits of GMAT Club

Registration gives you:

Tests

Take 11 tests and quizzes from GMAT Club and leading GMAT prep companies such as Manhattan GMAT,
Knewton, and others. All are free for GMAT Club members.

Applicant Stats

View detailed applicant stats such as GPA, GMAT score, work experience, location, application
status, and more

Books/Downloads

Download thousands of study notes,
question collections, GMAT Club’s
Grammar and Math books.
All are free!

Thank you for using the timer!
We noticed you are actually not timing your practice. Click the START button first next time you use the timer.
There are many benefits to timing your practice, including:

If p1 and p2 are the populations and r1 and r2 are the [#permalink]
18 Sep 2012, 02:26

1

This post received KUDOS

Expert's post

6

This post was BOOKMARKED

00:00

A

B

C

D

E

Difficulty:

25% (medium)

Question Stats:

71% (01:00) correct
29% (01:08) wrong based on 486 sessions

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

Re: If p1 and p2 are the populations and r1 and r2 are the [#permalink]
18 Sep 2012, 02:26

2

This post received KUDOS

Expert's post

3

This post was BOOKMARKED

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.

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

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; 4. Please share your views on difficulty level of the questions, so that we have most precise evaluation.

Thank you!

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. _________________

PhD in Applied Mathematics Love GMAT Quant questions and running.

Re: If p1 and p2 are the populations and r1 and r2 are the [#permalink]
18 Sep 2012, 04:56

2

This post received KUDOS

1

This post was BOOKMARKED

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. _________________

If you like my Question/Explanation or the contribution, Kindly appreciate by pressing KUDOS. Kudos always maximizes GMATCLUB worth-Game Theory

If you have any question regarding my post, kindly pm me or else I won't be able to reply

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

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; 4. Please share your views on difficulty level of the questions, so that we have most precise evaluation.

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.

Re: If p1 and p2 are the populations and r1 and r2 are the [#permalink]
19 Sep 2012, 23:24

1

This post received KUDOS

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.

Re: If p1 and p2 are the populations and r1 and r2 are the [#permalink]
21 Sep 2012, 03:03

Expert's post

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.

Answer: C.

Kudos points given to everyone with correct solution. Let me know if I missed someone. _________________

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

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

If P1 and P2 are the populations and R1 and R2 are the numbers o [#permalink]
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.

Re: If p1 and p2 are the populations and r1 and r2 are the [#permalink]
25 Mar 2014, 00:06

Hello from the GMAT Club BumpBot!

Thanks to another GMAT Club member, I have just discovered this valuable topic, yet it had no discussion for over a year. I am now bumping it up - doing my job. I think you may find it valuable (esp those replies with Kudos).

Want to see all other topics I dig out? Follow me (click follow button on profile). You will receive a summary of all topics I bump in your profile area as well as via email. _________________

Hey, everyone. After a hectic orientation and a weeklong course, Managing Groups and Teams, I have finally settled into the core curriculum for Fall 1, and have thus found...

MBA Acceptance Rate by Country Most top American business schools brag about how internationally diverse they are. Although American business schools try to make sure they have students from...

After I was accepted to Oxford I had an amazing opportunity to visit and meet a few fellow admitted students. We sat through a mock lecture, toured the business...