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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 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]

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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]

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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]

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New post 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).

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]

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

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

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

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

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New post 26 Sep 2016, 21:54
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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
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Re: If the ratio of the number of teachers to the number of [#permalink]

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

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

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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.
Re: If the ratio of the number of teachers to the number of   [#permalink] 29 Apr 2017, 21:22
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