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## If the ratio of the number of teachers to the number. . .

This topic has 1 expert reply and 0 member replies

### Top Member

Vincen Legendary Member
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#### If the ratio of the number of teachers to the number. . .

Fri Sep 22, 2017 9:51 am
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.

The OA is E.

What are the formulas I should set to solve this DS question?

### GMAT/MBA Expert

Jay@ManhattanReview GMAT Instructor
Joined
22 Aug 2016
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Sun Sep 24, 2017 9:45 pm
Vincen 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.

The OA is E.

What are the formulas I should set to solve this DS question?
Say the number of teachers in School M is x, the number of teachers in School P is y, the number of students in School M is m, and the number of students in School P is n.

Thus, x / m = y / n

=> m/n = x/y. We have to find out the value of m/n.

Statement 1: There are 10,000 more students in School District M than there are in School District P.

=> m = 10000 + n ---(1)

Clearly insufficient.

Statement 2: The ratio of the number of teachers to the number of students in School District M is 1 to 20.

x/m = 1/20 ---(2)

Clearly insufficient.

Statement 1 & 2:

Since in equation (2), we have a variable x that cannot be omitted with the help of equation (1), we cannot get the value of m/n. Insufficient.

The correct answer: E

Hope this helps!

Download free ebook: Manhattan Review GMAT Quantitative Question Bank Guide

-Jay
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Manhattan Review GMAT Prep

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