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If the ratio of the number of teachers to the number of

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If the ratio of the number of teachers to the number of [#permalink] New post 06 Dec 2012, 03:50
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If the ratio of the number of teachers to the number of students is the same in School District M and School District P, what is the ratio of the number of students in School District M to the number of students in School District P ?

(1) There are 10,000 more students in School District M than there are in School District P.
(2) The ratio of the number of teachers to the number of students in School District M is 1 to 20.
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Re: If the ratio of the number of teachers to the number of [#permalink] New post 06 Dec 2012, 03:52
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If the ratio of the number of teachers to the number of students is the same in School District M and School District P, what is the ratio of the number of students in School District M to the number of students in School District P ?

Given that \frac{T_m}{S_m}=\frac{T_p}{S_p}, where T_m and S_m are the numbers of teachers and students, respectively, in District M, and T_p and S_p are the numbers of teachers and students, respectively, in District P.

We need to find the value of \frac{S_m}{S_p} --> \frac{S_m}{S_p}=\frac{T_m}{T_p}

(1) There are 10,000 more students in School District M than there are in School District P --> S_m=S_p+10,000. Not sufficient.

(2) The ratio of the number of teachers to the number of students in School District M is 1 to 20 --> \frac{T_m}{S_m}=\frac{1}{20}. Not sufficient.

(1)+(2) Still not sufficient, consider S_p=1,000 and S_m=11,000 (answer 11) AND S_p=10,000 and S_m=20,000 (answer 2).

Answer: E.
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Re: If the ratio of the number of teachers to the number of [#permalink] New post 24 Jun 2013, 20:42
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Walkabout wrote:
If the ratio of the number of teachers to the number of students is the same in School District M and School District P, what is the ratio of the number of students in School District M to the number of students in School District P ?

(1) There are 10,000 more students in School District M than there are in School District P.
(2) The ratio of the number of teachers to the number of students in School District M is 1 to 20.


Responding to a pm:

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acc to me my answer is B... 1st statement its insufficient M=10,000+P
2nd statement..1: 20.. so number of students is 20x in both m and p so ratio is 20x:20x... myanswer is B


Teacher:Student ratio in M = 1:20. No of teachers in M = m, No of students in M = 20m
Teacher:Student ratio in P = 1:20. No of teachers in M = p, No of students in M = 20p

Mind you, we dont know the value of m and p. All we know is that the teacher student ratio is 1:20 in both.

Ratio of number of students in M: Number of students in P = 20m : 20p = m:p.
We don't know m:p.

You are assuming that both are 20x. How can you say that the multiplier is the same in both the schools? M could have 20 students and 1 teacher while P could have 40 students are 2 teachers. In that case, ratio of number of students = 1:2
M could have 20 students and 1 teacher while P could have 80 students are 4 teachers. In that case, ratio of number of students = 1:4
and so on...
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Re: If the ratio of the number of teachers to the number of [#permalink] New post 04 May 2014, 10:54
Bunuel wrote:
If the ratio of the number of teachers to the number of students is the same in School District M and School District P, what is the ratio of the number of students in School District M to the number of students in School District P ?

Given that \frac{T_m}{S_m}=\frac{T_p}{S_p}, where T_m and S_m are the numbers of teachers and students, respectively, in District M, and T_p and S_p are the numbers of teachers and students, respectively, in District P.

We need to find the value of \frac{S_m}{S_p} --> \frac{S_m}{S_p}=\frac{T_m}{T_p}

(1) There are 10,000 more students in School District M than there are in School District P --> S_m=S_p+10,000. Not sufficient.

(2) The ratio of the number of teachers to the number of students in School District M is 1 to 20 --> \frac{T_m}{S_m}=\frac{1}{20}. Not sufficient.

(1)+(2) Still not sufficient, consider S_p=1,000 and S_m=11,000 (answer 11) AND S_p=10,000 and S_m=20,000 (answer 2).

Answer: E.


Hi Bunuel,

I'm having a hard time following your reasoning for the scenario where 1&2 are combined. From your answer explanation, it looks like you just accounted for the first statement?
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Re: If the ratio of the number of teachers to the number of [#permalink] New post 04 May 2014, 23:39
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russ9 wrote:
Bunuel wrote:
If the ratio of the number of teachers to the number of students is the same in School District M and School District P, what is the ratio of the number of students in School District M to the number of students in School District P ?

Given that \frac{T_m}{S_m}=\frac{T_p}{S_p}, where T_m and S_m are the numbers of teachers and students, respectively, in District M, and T_p and S_p are the numbers of teachers and students, respectively, in District P.

We need to find the value of \frac{S_m}{S_p} --> \frac{S_m}{S_p}=\frac{T_m}{T_p}

(1) There are 10,000 more students in School District M than there are in School District P --> S_m=S_p+10,000. Not sufficient.

(2) The ratio of the number of teachers to the number of students in School District M is 1 to 20 --> \frac{T_m}{S_m}=\frac{1}{20}. Not sufficient.

(1)+(2) Still not sufficient, consider S_p=1,000 and S_m=11,000 (answer 11) AND S_p=10,000 and S_m=20,000 (answer 2).

Answer: E.


Hi Bunuel,

I'm having a hard time following your reasoning for the scenario where 1&2 are combined. From your answer explanation, it looks like you just accounted for the first statement?


Does the examples used for (1)+(2) violate the second statement in any way? No. The second statement gives the ratio of T_m to S_m, which is of little use. If S_p=1,000 and S_m=11,000 (\frac{S_m}{S_p}=11), then according to the second statement T_m=550 AND if S_p=10,000 and S_m=20,000 (\frac{S_m}{S_p}=2), then according to the second statement T_m=1000.

Does this make sense?
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NEW TO MATH FORUM? PLEASE READ THIS: ALL YOU NEED FOR QUANT!!!

PLEASE READ AND FOLLOW: 11 Rules for Posting!!!

RESOURCES: [GMAT MATH BOOK]; 1. Triangles; 2. Polygons; 3. Coordinate Geometry; 4. Factorials; 5. Circles; 6. Number Theory; 7. Remainders; 8. Overlapping Sets; 9. PDF of Math Book; 10. Remainders; 11. GMAT Prep Software Analysis NEW!!!; 12. SEVEN SAMURAI OF 2012 (BEST DISCUSSIONS) NEW!!!; 12. Tricky questions from previous years. NEW!!!;

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.


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Re: If the ratio of the number of teachers to the number of   [#permalink] 04 May 2014, 23:39
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