If the ratio of the number of teachers to the number of students is the same in School District $M$ and School

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M7MBA: Moderator; Posts: 2058; Joined: Sun Oct 29, 2017 4:24 amFollowed by: 5 members; Thanked: 1 times

by M7MBA » Fri May 08, 2020 8:31 am

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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.

[spoiler]OA=E[/spoiler]

Source: Official Guide

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Source: Beat The GMAT — Data Sufficiency | Fri May 08, 2020 8:31 am

deloitte247: Legendary Member; Posts: 2214; Joined: Fri Mar 02, 2018 2:22 pmFollowed by: 5 members

Re: If the ratio of the number of teachers to the number of students is the same in School District $M$ and School

by deloitte247 » Sun May 10, 2020 12:14 am

Let the number of teachers in school District M = a
Let the number of students in School District M = b
Let the number of teachers in school District P = x
Let the number of students in school District P= y
a:b x:y => a/b = x/y

Target question => What is the ratio of the number of students in School District M to the number of students in School District P?
i.e from b:y =>b/y and from a/b =>x/y
ay = xb => a/b a/x = b/y

Statement 1 => There are 10,000 more in School District M than there are in School District P
i.e b = y + 10,000. The value of b and y is not given, statement 1 is NOT SUFFICIENT

Statement 2 => The ratio of the number of teachers to the number of students in School District M is 1 to 20
a:b = 1:20 => a/b = 1/20. There is no information about x and y, Statement 2 is NOT SUFFICIENT

Combining both statements together =>
From statement 1 => b = y + 10,000
From statement 2 => a:b = 1:20
If y = 1000, then b = 11,000 ; and b:y = 11,000:1000 = 11
If y = 2000, then b = 12,000 ; and b:y = 12,000:2000 = 6

The available information is not enough to arrive at a definite answer. Hence, both statements together ARE NOT SUFFICIENT

Answer = E

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