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

It is currently 18 Jul 2018, 11:43

Close

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
Your Progress

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

Not interested in getting valuable practice questions and articles delivered to your email? No problem, unsubscribe here.

Close

Request Expert Reply

Confirm Cancel

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

  new topic post reply Question banks Downloads My Bookmarks Reviews Important topics  
Author Message
TAGS:

Hide Tags

9 KUDOS received
Manager
Manager
avatar
Joined: 02 Dec 2012
Posts: 178
If the ratio of the number of teachers to the number of [#permalink]

Show Tags

New post 06 Dec 2012, 04:50
9
46
00:00
A
B
C
D
E

Difficulty:

  65% (hard)

Question Stats:

64% (01:49) correct 36% (01:42) wrong based on 1801 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.
Most Helpful Expert Reply
Expert Post
14 KUDOS received
GMAT Club Legend
GMAT Club Legend
User avatar
P
Joined: 16 Oct 2010
Posts: 8127
Location: Pune, India
Re: If the ratio of the number of teachers to the number of [#permalink]

Show Tags

New post 24 Jun 2013, 21:42
14
3
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:

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
Private Tutor for GMAT
Contact: bansal.karishma@gmail.com

General Discussion
Expert Post
10 KUDOS received
Math Expert
User avatar
V
Joined: 02 Sep 2009
Posts: 47084
Re: If the ratio of the number of teachers to the number of [#permalink]

Show Tags

New post 06 Dec 2012, 04:52
10
6
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.
_________________

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?
Extra-hard Quant Tests with Brilliant Analytics

1 KUDOS received
Senior Manager
Senior Manager
avatar
Joined: 15 Aug 2013
Posts: 271
Re: If the ratio of the number of teachers to the number of [#permalink]

Show Tags

New post 04 May 2014, 11:54
1
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?
Expert Post
Math Expert
User avatar
V
Joined: 02 Sep 2009
Posts: 47084
Re: If the ratio of the number of teachers to the number of [#permalink]

Show Tags

New post 05 May 2014, 00:39
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?
_________________

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?
Extra-hard Quant Tests with Brilliant Analytics

2 KUDOS received
Intern
Intern
User avatar
Joined: 21 Apr 2014
Posts: 39
Re: If the ratio of the number of teachers to the number of [#permalink]

Show Tags

New post 04 Feb 2015, 03:56
2
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
Director
User avatar
Joined: 10 Mar 2013
Posts: 562
Location: Germany
Concentration: Finance, Entrepreneurship
GMAT 1: 580 Q46 V24
GPA: 3.88
WE: Information Technology (Consulting)
GMAT ToolKit User
Re: If the ratio of the number of teachers to the number of [#permalink]

Show Tags

New post 02 Nov 2015, 08:25
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.


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.

Share some Kudos, if my posts help you. Thank you !

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

Intern
Intern
User avatar
Joined: 26 Sep 2016
Posts: 7
Re: If the ratio of the number of teachers to the number of [#permalink]

Show Tags

New post 26 Sep 2016, 11:26
I am new to preparation so I am confused a bit.

Ratio of M = [T1] / [S1]
Ratio of P = [T2] / [S2]

As said in question [T1] / [S1] = [T2] / [S2]
Considering statement 2
Ratio of M = [1] / [20]
Which mean ratio of P = [1] / [20]

As [T1]/ [S1] = [T2] / [S2]
So [T1] / [T2] = [S1] / [S2] = [20] / [20] = [1] / [1]
So ratio of Students of M to Students of P is 1:1.

Isn't question has just asked the ratio which can be found by statement 2 i.e 1:1? Where I am wrong? Thanks in advance for guidance.
Expert Post
1 KUDOS received
GMAT Club Legend
GMAT Club Legend
User avatar
P
Joined: 16 Oct 2010
Posts: 8127
Location: Pune, India
Re: If the ratio of the number of teachers to the number of [#permalink]

Show Tags

New post 26 Sep 2016, 21:54
1
Twitter wrote:
I am new to preparation so I am confused a bit.

Ratio of M = [T1] / [S1]
Ratio of P = [T2] / [S2]

As said in question [T1] / [S1] = [T2] / [S2]
Considering statement 2
Ratio of M = [1] / [20]
Which mean ratio of P = [1] / [20]

As [T1]/ [S1] = [T2] / [S2]
So [T1] / [T2] = [S1] / [S2] = [20] / [20] = [1] / [1]
So ratio of Students of M to Students of P is 1:1.

Isn't question has just asked the ratio which can be found by statement 2 i.e 1:1? Where I am wrong? Thanks in advance for guidance.


I have answered this question (why stmnt 2 alone is not sufficient) here:
if-the-ratio-of-the-number-of-teachers-to-the-number-of-143680.html#p1239274
_________________

Karishma
Private Tutor for GMAT
Contact: bansal.karishma@gmail.com

Director
Director
avatar
G
Joined: 02 Sep 2016
Posts: 742
Premium Member
Re: If the ratio of the number of teachers to the number of [#permalink]

Show Tags

New post 27 Dec 2016, 00:48
Hello karishma
Is it necessary to plug in values in DS questions ? In which cases we should do it because in this question I did not check my answer by plugging in values.

Here is my method:

We know T/S=T'/S'
(T= teachers in school M; S= students in school M) (T'= Teachers in school P; S'=students in school P)

To find: S/S'=?

First statement: (S'+10000)/S'
(S=S'+10000)

So T/(S'+10000) = T'/S'
We have more than one unknown variables. Therefore not sufficient.
BCE

Statement 2: T/S=1/20
Even if we plug this ratio in the above equation, we would have more than one variable.

Thus, insufficient.

T/(S'+10000)= 1/20

(S'+10000)/(S'+10000)= T'/S'

T'/S'= 1/20

Couldn't go beyond this. More than one variable to solve and thus I chose E.

Please let me know if this makes sense.:)
_________________

Help me make my explanation better by providing a logical feedback.

If you liked the post, HIT KUDOS !!

Don't quit.............Do it.

Manager
Manager
avatar
B
Joined: 26 Mar 2017
Posts: 145
Re: If the ratio of the number of teachers to the number of [#permalink]

Show Tags

New post 09 Apr 2017, 08:53
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,

and the ratios could still be 1/20 since we have no restrictions for the number of teachers... right ?

Thank you very much.
_________________

I hate long and complicated explanations!

Intern
Intern
avatar
B
Joined: 25 Feb 2017
Posts: 40
Location: Korea, Republic of
Schools: LBS '19 (A)
GMAT 1: 720 Q50 V38
GPA: 3.67
Reviews Badge
Re: If the ratio of the number of teachers to the number of [#permalink]

Show Tags

New post 29 Apr 2017, 21:22
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.

My 2 cents.

First, identify what is given and what is our goal.
Given : Mt / Ms = Pt / Ps
Goal : Find Ms / Ps

1) Ms = 10,000 + Ps --> insufficient, as we don't have any value for Ms or Ps
2) Mt / Ms = 1/20 --> insufficient, as we know nothing about Ps

For checking whether C is the answer,
we need to be careful of premise 2.
Premise 2 is giving us the "ratio", not the value...so we only have the relationship, but no value.
Therefore, as we have no value for Ms, C won't work.
Thus, E.
Senior Manager
Senior Manager
avatar
S
Joined: 29 Jun 2017
Posts: 343
Re: If the ratio of the number of teachers to the number of [#permalink]

Show Tags

New post 11 Nov 2017, 07:50
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.


from both conditions, we have
m number of teacher in M
20m is number of student in M
p is number of teacher in P
20p is number of student in P

if 20m=20p+1000
we can have some value of m, p which satisfy this equation and the ratio of 20m/20p+1000 is variable
p=1
m=1020
p=10
m=1200

it is clear that the ratio is different.
Study Buddy Forum Moderator
User avatar
D
Joined: 04 Sep 2016
Posts: 1094
Location: India
WE: Engineering (Other)
Premium Member CAT Tests
Re: If the ratio of the number of teachers to the number of [#permalink]

Show Tags

New post 29 Dec 2017, 06:11
Bunuel, niks18, amanvermagmat

Quote:
(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).



Can I also say we have three different variables : \(S_p\), \(T_m\), \(S_m\)and only two linear equations hence both statements combined are insufficient?
_________________

It's the journey that brings us happiness not the destination.

Re: If the ratio of the number of teachers to the number of   [#permalink] 29 Dec 2017, 06:11
Display posts from previous: Sort by

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

  new topic post reply Question banks Downloads My Bookmarks Reviews Important topics  

Events & Promotions

PREV
NEXT


GMAT Club MBA Forum Home| About| Terms and Conditions and Privacy Policy| GMAT Club Rules| Contact| Sitemap

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®.