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

 It is currently 20 Oct 2019, 20:51 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

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

Manager  Joined: 02 Dec 2012
Posts: 173
If the ratio of the number of teachers to the number of  [#permalink]

Show Tags

9
1
69 00:00

Difficulty:   65% (hard)

Question Stats: 65% (02:18) correct 35% (02:14) wrong based on 1727 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.
Math Expert V
Joined: 02 Sep 2009
Posts: 58435
Re: If the ratio of the number of teachers to the number of  [#permalink]

Show Tags

12
12
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).

_________________
General Discussion
Veritas Prep GMAT Instructor V
Joined: 16 Oct 2010
Posts: 9704
Location: Pune, India
Re: If the ratio of the number of teachers to the number of  [#permalink]

Show Tags

15
4
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

Learn more about how Veritas Prep can help you achieve a great GMAT score by checking out their GMAT Prep Options >
Manager  Joined: 15 Aug 2013
Posts: 228
Re: If the ratio of the number of teachers to the number of  [#permalink]

Show Tags

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).

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 V
Joined: 02 Sep 2009
Posts: 58435
Re: If the ratio of the number of teachers to the number of  [#permalink]

Show Tags

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: 39
Re: If the ratio of the number of teachers to the number of  [#permalink]

Show Tags

3
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
Senior Manager  B
Joined: 10 Mar 2013
Posts: 465
Location: Germany
Concentration: Finance, Entrepreneurship
Schools: WHU MBA"20 (A)
GMAT 1: 580 Q46 V24 GPA: 3.88
WE: Information Technology (Consulting)
Re: If the ratio of the number of teachers to the number of  [#permalink]

Show Tags

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

Show Tags

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 =  / 
Which mean ratio of P =  / 

As [T1]/ [S1] = [T2] / [S2]
So [T1] / [T2] = [S1] / [S2] =  /  =  / 
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.
Veritas Prep GMAT Instructor V
Joined: 16 Oct 2010
Posts: 9704
Location: Pune, India
Re: If the ratio of the number of teachers to the number of  [#permalink]

Show Tags

1
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 =  / 
Which mean ratio of P =  / 

As [T1]/ [S1] = [T2] / [S2]
So [T1] / [T2] = [S1] / [S2] =  /  =  / 
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
Veritas Prep GMAT Instructor

Learn more about how Veritas Prep can help you achieve a great GMAT score by checking out their GMAT Prep Options >
Director  G
Joined: 02 Sep 2016
Posts: 649
Re: If the ratio of the number of teachers to the number of  [#permalink]

Show Tags

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  B
Joined: 26 Mar 2017
Posts: 106
Re: If the ratio of the number of teachers to the number of  [#permalink]

Show Tags

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,

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!
Current Student B
Joined: 25 Feb 2017
Posts: 34
Location: Korea, Republic of
Schools: LBS '19 (A)
GMAT 1: 720 Q50 V38 GPA: 3.67
Re: If the ratio of the number of teachers to the number of  [#permalink]

Show Tags

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.
Director  P
Joined: 29 Jun 2017
Posts: 933
Re: If the ratio of the number of teachers to the number of  [#permalink]

Show Tags

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.
IIMA, IIMC School Moderator V
Joined: 04 Sep 2016
Posts: 1366
Location: India
WE: Engineering (Other)
Re: If the ratio of the number of teachers to the number of  [#permalink]

Show Tags

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.

Feeling stressed, you are not alone!!
Intern  B
Joined: 31 Mar 2019
Posts: 39
Re: If the ratio of the number of teachers to the number of  [#permalink]

Show Tags

Hi All ,

I am totally messed up with the second statement ,
According to my understanding of the ratio of number of teachers to the number of student for M is 1:20 then Tm/Sm =Tp/Sp=1/20 which denotes that Sm/Sp = 1/20 ,

Answer should be B

Posted from my mobile device Re: If the ratio of the number of teachers to the number of   [#permalink] 10 Jul 2019, 19:46
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

 Powered by phpBB © phpBB Group | Emoji artwork provided by EmojiOne  