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Question

# 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.

A
Statement (1) alone is sufficient, but statement (2) alone is not sufficient.
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B
Statement (2) alone is sufficient, but statement (1) alone is not sufficient.
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C
Both statements together are sufficient, but neither statement alone is sufficient.
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D
Each statement alone is sufficient.
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E
Statements (1) and (2) together are not sufficient.
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Solution

## The correct option is D Statements (1) and (2) together are not sufficient.It is given that $\frac{Tm}{Sm}= \frac{Tp}{Sp}$ where Tm and Sm are the numbers of teachers and students, respectively, in District m, and Tp and Sp are the numbers of teachers and students, respectively, in District p, we have to find the value of $\frac{Sm}{Sp}$. Given that Sm=Sp+10000, then $\frac{Sm}{Sp}= \frac{Sp+1000}{Sp}$, but the value of Sp is unknown; NOT sufficient. Given that $\frac{Tm}{Sm}= \frac{1}{20}$ and $\frac{Tm}{Sm}= \frac{Tp}{Sp}$, then $\frac{Tp}{Sp}= \frac{1}{20}$. So, Sp=20Tp and Sm=20Tm. It follows that $\frac{Sm}{Sp}= \frac{20Tm}{20Tp}$, but the values of Tm and Tp are unknown; NOT sufficient. Taking (1) and (2) together, for variable values of Sp and Sm we get variable ratios of $\frac{Sm}{Sp}$. Therefore, the value of $\frac{Sm}{Sp}$cannot be determined. The correct answer is E; both statements together are still not sufficient.

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