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).

Answer: E.

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the-official-guide-quantitative-question-directory-143450.htmlOPEN DISCUSSION OF THIS QUESTION IS HERE: if-the-ratio-of-the-number-of-teachers-to-the-number-of-143680.html
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