GMAT Question of the Day - Daily to your Mailbox; hard ones only

 It is currently 22 Sep 2018, 00:23

GMAT Club Daily Prep

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

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

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

Author Message
TAGS:

Hide Tags

Math Expert
Joined: 02 Sep 2009
Posts: 49300
If p1 and p2 are the populations and r1 and r2 are the  [#permalink]

Show Tags

18 Sep 2012, 03:26
1
11
00:00

Difficulty:

25% (medium)

Question Stats:

73% (01:03) correct 27% (01:01) wrong based on 883 sessions

HideShow timer Statistics

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

_________________
Math Expert
Joined: 02 Sep 2009
Posts: 49300
Re: If p1 and p2 are the populations and r1 and r2 are the  [#permalink]

Show Tags

18 Sep 2012, 03:26
4
6
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.

_________________
General Discussion
Director
Joined: 22 Mar 2011
Posts: 604
WE: Science (Education)
Re: If p1 and p2 are the populations and r1 and r2 are the  [#permalink]

Show Tags

18 Sep 2012, 05:41
2
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:
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.

_________________

PhD in Applied Mathematics
Love GMAT Quant questions and running.

Senior Manager
Joined: 24 Aug 2009
Posts: 476
Schools: Harvard, Columbia, Stern, Booth, LSB,
Re: If p1 and p2 are the populations and r1 and r2 are the  [#permalink]

Show Tags

18 Sep 2012, 05:56
2
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.
_________________

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

Manager
Joined: 02 Jun 2011
Posts: 89
Re: If p1 and p2 are the populations and r1 and r2 are the  [#permalink]

Show Tags

18 Sep 2012, 10:25
1
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:
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.

Senior Manager
Joined: 13 Aug 2012
Posts: 436
Concentration: Marketing, Finance
GPA: 3.23
Re: If p1 and p2 are the populations and r1 and r2 are the  [#permalink]

Show Tags

20 Sep 2012, 00:24
1
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.

_________________

Impossible is nothing to God.

Math Expert
Joined: 02 Sep 2009
Posts: 49300
Re: If p1 and p2 are the populations and r1 and r2 are the  [#permalink]

Show Tags

21 Sep 2012, 04:03
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.

Kudos points given to everyone with correct solution. Let me know if I missed someone.
_________________
Intern
Joined: 15 Nov 2012
Posts: 3
If p1 and p2 are the populations and r1 and r2 are the  [#permalink]

Show Tags

29 Dec 2012, 12:40
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.
Intern
Joined: 21 Mar 2009
Posts: 19
If p1 and p2 are the populations and r1 and r2 are the  [#permalink]

Show Tags

31 Dec 2012, 12:10
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.
Intern
Joined: 09 Oct 2012
Posts: 7
Location: United States
Concentration: Strategy, Finance
GMAT 1: 590 Q34 V38
GPA: 3.56
WE: Analyst (Consumer Products)
If P1 and P2 are the populations and R1 and R2 are the numbers o  [#permalink]

Show Tags

07 Feb 2013, 10:57
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.
Director
Joined: 23 Jan 2013
Posts: 590
Schools: Cambridge'16
If p1 and p2 are the populations and r1 and r2 are the  [#permalink]

Show Tags

31 Jul 2014, 08:43
1
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
Director
Status: No dream is too large, no dreamer is too small
Joined: 14 Jul 2010
Posts: 542
Re: If p1 and p2 are the populations and r1 and r2 are the  [#permalink]

Show Tags

18 Apr 2015, 08:27
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.
_________________

Collections:-
PSof OG solved by GC members: http://gmatclub.com/forum/collection-ps-with-solution-from-gmatclub-110005.html
DS of OG solved by GC members: http://gmatclub.com/forum/collection-ds-with-solution-from-gmatclub-110004.html
100 GMAT PREP Quantitative collection http://gmatclub.com/forum/gmat-prep-problem-collections-114358.html
Collections of work/rate problems with solutions http://gmatclub.com/forum/collections-of-work-rate-problem-with-solutions-118919.html
Mixture problems in a file with best solutions: http://gmatclub.com/forum/mixture-problems-with-best-and-easy-solutions-all-together-124644.html

Intern
Joined: 20 Oct 2010
Posts: 6
Re: If p1 and p2 are the populations and r1 and r2 are the  [#permalink]

Show Tags

22 Dec 2015, 13:35
Suppose p1>p2 AND r1>r2

Target Test Prep Representative
Affiliations: Target Test Prep
Joined: 04 Mar 2011
Posts: 2835
Re: If p1 and p2 are the populations and r1 and r2 are the  [#permalink]

Show Tags

19 May 2016, 07:38
2
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).

_________________

Jeffery Miller

GMAT Quant Self-Study Course
500+ lessons 3000+ practice problems 800+ HD solutions

Intern
Joined: 21 Mar 2013
Posts: 12
Re: If p1 and p2 are the populations and r1 and r2 are the  [#permalink]

Show Tags

09 Aug 2016, 11:50
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?
Math Expert
Joined: 02 Sep 2009
Posts: 49300
Re: If p1 and p2 are the populations and r1 and r2 are the  [#permalink]

Show Tags

09 Aug 2016, 11:53
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 $$r_1>r_2$$
_________________
Intern
Joined: 21 Mar 2013
Posts: 12
Re: If p1 and p2 are the populations and r1 and r2 are the  [#permalink]

Show Tags

09 Aug 2016, 19:16
ah! silly me. thanks!!

"Read the question carefully" doesn't ever get old.
Intern
Joined: 11 Sep 2012
Posts: 5
Re: If p1 and p2 are the populations and r1 and r2 are the  [#permalink]

Show Tags

10 Aug 2016, 03:11
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.
Manager
Joined: 01 Feb 2018
Posts: 51
Location: India
Concentration: Entrepreneurship, Marketing
GPA: 4
WE: Consulting (Consulting)
Re: If p1 and p2 are the populations and r1 and r2 are the  [#permalink]

Show Tags

23 Mar 2018, 09:01
fameatop 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

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.

can u please use numbers and verify, as i tried using numbers, i could get p1/r1 = p2/r2 as well.

pls revert.
Re: If p1 and p2 are the populations and r1 and r2 are the &nbs [#permalink] 23 Mar 2018, 09:01
Display posts from previous: Sort by

Events & Promotions

 Powered by phpBB © phpBB Group | Emoji artwork provided by EmojiOne Kindly note that the GMAT® test is a registered trademark of the Graduate Management Admission Council®, and this site has neither been reviewed nor endorsed by GMAC®.