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If p1 and p2 are the populations and r1 and r2 are the [#permalink]
18 Sep 2012, 02:26
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15% (low)
Question Stats:
71% (02:02) correct
29% (01:08) wrong based on 587 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
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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
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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]
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
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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
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
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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.
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
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