Author 
Message 
TAGS:

Hide Tags

Math Expert
Joined: 02 Sep 2009
Posts: 44423

If p1 and p2 are the populations and r1 and r2 are the [#permalink]
Show Tags
18 Sep 2012, 03:26
Question Stats:
74% (01:01) correct 26% (01:01) wrong based on 789 sessions
HideShow timer Statistics



Math Expert
Joined: 02 Sep 2009
Posts: 44423

Re: If p1 and p2 are the populations and r1 and r2 are the [#permalink]
Show Tags
18 Sep 2012, 03:26
SOLUTIONIf \(p_1\) 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.
_________________
New to the Math Forum? Please read this: Ultimate GMAT Quantitative Megathread  All You Need for Quant  PLEASE READ AND FOLLOW: 12 Rules for Posting!!! Resources: GMAT Math Book  Triangles  Polygons  Coordinate Geometry  Factorials  Circles  Number Theory  Remainders; 8. Overlapping Sets  PDF of Math Book; 10. Remainders  GMAT Prep Software Analysis  SEVEN SAMURAI OF 2012 (BEST DISCUSSIONS)  Tricky questions from previous years.
Collection of Questions: PS: 1. Tough and Tricky questions; 2. Hard questions; 3. Hard questions part 2; 4. Standard deviation; 5. Tough Problem Solving Questions With Solutions; 6. Probability and Combinations Questions With Solutions; 7 Tough and tricky exponents and roots questions; 8 12 Easy Pieces (or not?); 9 Bakers' Dozen; 10 Algebra set. ,11 Mixed Questions, 12 Fresh Meat DS: 1. DS tough questions; 2. DS tough questions part 2; 3. DS tough questions part 3; 4. DS Standard deviation; 5. Inequalities; 6. 700+ GMAT Data Sufficiency Questions With Explanations; 7 Tough and tricky exponents and roots questions; 8 The Discreet Charm of the DS; 9 Devil's Dozen!!!; 10 Number Properties set., 11 New DS set.
What are GMAT Club Tests? Extrahard Quant Tests with Brilliant Analytics



Director
Joined: 22 Mar 2011
Posts: 608
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
This post received KUDOS
Bunuel wrote: The Official Guide for GMAT® Review, 13th Edition  Quantitative Questions ProjectIf \(p_1\) 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 ProjectEach 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.



Senior Manager
Joined: 24 Aug 2009
Posts: 488
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
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 EHope 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: 115

Re: If p1 and p2 are the populations and r1 and r2 are the [#permalink]
Show Tags
18 Sep 2012, 10:25
1
This post received KUDOS
Bunuel wrote: The Official Guide for GMAT® Review, 13th Edition  Quantitative Questions ProjectIf \(p_1\) 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 ProjectEach 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. Option 'C" is Answer.



Senior Manager
Joined: 13 Aug 2012
Posts: 453
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
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. answer: C
_________________
Impossible is nothing to God.



Math Expert
Joined: 02 Sep 2009
Posts: 44423

Re: If p1 and p2 are the populations and r1 and r2 are the [#permalink]
Show Tags
21 Sep 2012, 04:03
SOLUTIONIf \(p_1\) 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.
_________________
New to the Math Forum? Please read this: Ultimate GMAT Quantitative Megathread  All You Need for Quant  PLEASE READ AND FOLLOW: 12 Rules for Posting!!! Resources: GMAT Math Book  Triangles  Polygons  Coordinate Geometry  Factorials  Circles  Number Theory  Remainders; 8. Overlapping Sets  PDF of Math Book; 10. Remainders  GMAT Prep Software Analysis  SEVEN SAMURAI OF 2012 (BEST DISCUSSIONS)  Tricky questions from previous years.
Collection of Questions: PS: 1. Tough and Tricky questions; 2. Hard questions; 3. Hard questions part 2; 4. Standard deviation; 5. Tough Problem Solving Questions With Solutions; 6. Probability and Combinations Questions With Solutions; 7 Tough and tricky exponents and roots questions; 8 12 Easy Pieces (or not?); 9 Bakers' Dozen; 10 Algebra set. ,11 Mixed Questions, 12 Fresh Meat DS: 1. DS tough questions; 2. DS tough questions part 2; 3. DS tough questions part 3; 4. DS Standard deviation; 5. Inequalities; 6. 700+ GMAT Data Sufficiency Questions With Explanations; 7 Tough and tricky exponents and roots questions; 8 The Discreet Charm of the DS; 9 Devil's Dozen!!!; 10 Number Properties set., 11 New DS set.
What are GMAT Club Tests? Extrahard Quant Tests with Brilliant Analytics



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 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.



Intern
Joined: 21 Mar 2009
Posts: 20

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
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: 600

If p1 and p2 are the populations and r1 and r2 are the [#permalink]
Show Tags
31 Jul 2014, 08:43
1
This post received KUDOS
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: 574

Re: If p1 and p2 are the populations and r1 and r2 are the [#permalink]
Show Tags
18 Apr 2015, 08:27



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
Would the answer be E?



Target Test Prep Representative
Status: Head GMAT Instructor
Affiliations: Target Test Prep
Joined: 04 Mar 2011
Posts: 2166

Re: If p1 and p2 are the populations and r1 and r2 are the [#permalink]
Show Tags
19 May 2016, 07:38
1
This post received KUDOS
Expert's post
1
This post was BOOKMARKED
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). The answer is C.
_________________
Jeffery Miller
Head of GMAT Instruction
GMAT Quant SelfStudy 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: 44423

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 \(r_1>r_2\)
_________________
New to the Math Forum? Please read this: Ultimate GMAT Quantitative Megathread  All You Need for Quant  PLEASE READ AND FOLLOW: 12 Rules for Posting!!! Resources: GMAT Math Book  Triangles  Polygons  Coordinate Geometry  Factorials  Circles  Number Theory  Remainders; 8. Overlapping Sets  PDF of Math Book; 10. Remainders  GMAT Prep Software Analysis  SEVEN SAMURAI OF 2012 (BEST DISCUSSIONS)  Tricky questions from previous years.
Collection of Questions: PS: 1. Tough and Tricky questions; 2. Hard questions; 3. Hard questions part 2; 4. Standard deviation; 5. Tough Problem Solving Questions With Solutions; 6. Probability and Combinations Questions With Solutions; 7 Tough and tricky exponents and roots questions; 8 12 Easy Pieces (or not?); 9 Bakers' Dozen; 10 Algebra set. ,11 Mixed Questions, 12 Fresh Meat DS: 1. DS tough questions; 2. DS tough questions part 2; 3. DS tough questions part 3; 4. DS Standard deviation; 5. Inequalities; 6. 700+ GMAT Data Sufficiency Questions With Explanations; 7 Tough and tricky exponents and roots questions; 8 The Discreet Charm of the DS; 9 Devil's Dozen!!!; 10 Number Properties set., 11 New DS set.
What are GMAT Club Tests? Extrahard Quant Tests with Brilliant Analytics



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.



Intern
Joined: 01 Feb 2018
Posts: 15
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
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. 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
[#permalink]
23 Mar 2018, 09:01






