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

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21 May 2011, 11:12

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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.

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

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31 Mar 2014, 11:40

gtr022001 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.

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

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31 Mar 2014, 11:53

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Expert's post

abid1986 wrote:

gtr022001 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.

Hi , If Tm:Sm = Tp:Sp = 1/20 so Applying Alternendo Tm:Tp= Sm:Sp = 1/20 So isnt 2 Sufficient?

Yes, from \(\frac{T_m}{S_m}=\frac{T_p}{S_p}\) we can get that \(\frac{S_m}{S_p}=\frac{T_m}{T_p}\) but it does NOT mean that the ratio will remain the same, so it does not mean that since \(\frac{T_m}{S_m}=\frac{1}{20}\), then \(\frac{S_m}{S_p}=\frac{T_m}{T_p}\) will also be 1/20. Play with some numbers to prove that.

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).

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