Find all School-related info fast with the new School-Specific MBA Forum

 It is currently 01 Jul 2016, 18:06

### 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

# Events & Promotions

###### Events & Promotions in June
Open Detailed Calendar

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

Author Message
TAGS:

### Hide Tags

Manager
Joined: 02 Dec 2012
Posts: 178
Followers: 3

Kudos [?]: 1684 [2] , given: 0

If the ratio of the number of teachers to the number of [#permalink]

### Show Tags

06 Dec 2012, 04:50
2
KUDOS
19
This post was
BOOKMARKED
00:00

Difficulty:

75% (hard)

Question Stats:

57% (02:52) correct 43% (02:01) wrong based on 741 sessions

### HideShow timer Statistics

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.
[Reveal] Spoiler: OA
Math Expert
Joined: 02 Sep 2009
Posts: 33600
Followers: 5956

Kudos [?]: 74027 [2] , given: 9906

Re: If the ratio of the number of teachers to the number of [#permalink]

### Show Tags

06 Dec 2012, 04:52
2
KUDOS
Expert's post
6
This post was
BOOKMARKED
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).

_________________
Veritas Prep GMAT Instructor
Joined: 16 Oct 2010
Posts: 6686
Location: Pune, India
Followers: 1838

Kudos [?]: 11181 [4] , given: 219

Re: If the ratio of the number of teachers to the number of [#permalink]

### Show Tags

24 Jun 2013, 21:42
4
KUDOS
Expert's post
1
This post was
BOOKMARKED
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:

Quote:
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...
_________________

Karishma
Veritas Prep | GMAT Instructor
My Blog

Get started with Veritas Prep GMAT On Demand for \$199

Veritas Prep Reviews

Senior Manager
Joined: 15 Aug 2013
Posts: 328
Followers: 0

Kudos [?]: 38 [0], given: 23

Re: If the ratio of the number of teachers to the number of [#permalink]

### Show Tags

04 May 2014, 11:54
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).

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?
Math Expert
Joined: 02 Sep 2009
Posts: 33600
Followers: 5956

Kudos [?]: 74027 [0], given: 9906

Re: If the ratio of the number of teachers to the number of [#permalink]

### Show Tags

05 May 2014, 00:39
Expert's post
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).

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?
_________________
Intern
Joined: 21 Apr 2014
Posts: 40
Followers: 1

Kudos [?]: 16 [1] , given: 0

Re: If the ratio of the number of teachers to the number of [#permalink]

### Show Tags

04 Feb 2015, 03:56
1
KUDOS
So the first step is to figure out what the original statement is saying and what it is looking for.
It says that the ratio of teachers so students is the same for school one and school two, so: T(M)/S(M)=T(P)/S(P)
and it wants to know the exact value of S(M)/S(P)

(1) essentially tells us S(M)=S(P)+10,000 but that doesn't tell us anything about the ratios, because S(M) could be 1 or 20,000
(2) tells us that T(M)/S(M)=1/20, thus T(P)/S(P)=1/20, however this tells us nothing about S(M)/S(P), because there could be one teacher in school m and 20 students and 100 teachers in school p and 2,000 students or vice versa.

Both together seems promising, because we know both ratios and that S(M)=S(P)+10,000 however there are still a variety of scenarios that fit that, so the answer is E
_________________

Eliza
GMAT Tutor
bestgmatprepcourse.com

Director
Joined: 10 Mar 2013
Posts: 605
Location: Germany
Concentration: Finance, Entrepreneurship
GMAT 1: 580 Q46 V24
GPA: 3.88
WE: Information Technology (Consulting)
Followers: 8

Kudos [?]: 157 [0], given: 200

Re: If the ratio of the number of teachers to the number of [#permalink]

### Show Tags

02 Nov 2015, 08:25
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.

Solved this one by testing different values.

Statement (1)
$$\frac{Tm}{Sm}=\frac{3000}{12000} \frac{Tp}{Sp}=\frac{500}{2000}$$ --> $$\frac{Sm}{Sp}=\frac{12000}{2000}$$=6

$$\frac{Tm}{Sm}=\frac{10000}{20000} \frac{Tp}{Sp}=\frac{5000}{10000}$$ --> $$\frac{Sm}{Sp}=\frac{20000}{10000}$$=2

So we get 2 different ratios here - Not Sufficient

Statement (2) don't give us enough information - see example above

(1) + (2) calculation example above give us different outcomes for the ratios Answer (E)
_________________

When you’re up, your friends know who you are. When you’re down, you know who your friends are.

800Score ONLY QUANT CAT1 51, CAT2 50, CAT3 50
GMAT PREP 670
MGMAT CAT 630
KAPLAN CAT 660

Re: If the ratio of the number of teachers to the number of   [#permalink] 02 Nov 2015, 08:25
Similar topics Replies Last post
Similar
Topics:
6 What was the ratio of the number of cars to the number of tr 7 30 Jan 2014, 23:42
What is the ratio of the number of burgers to the number of 1 20 Jun 2011, 21:05
11 If the ratio of the number of teachers to the number of 7 21 May 2011, 11:12
2 What is the ratio of number of cups of flour to number of 3 23 Mar 2011, 04:47
20 The ratio of the number of women to the number of men to the 13 28 Apr 2008, 13:24
Display posts from previous: Sort by