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If the ratio of the number of teachers to the number of [#permalink]
21 May 2011, 10:12

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Difficulty:

55% (hard)

Question Stats:

61% (02:18) correct
39% (01:17) wrong based on 149 sessions

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]
31 Mar 2014, 10:40

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]
31 Mar 2014, 10:53

1

This post received KUDOS

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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