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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

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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

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]

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Source: — Data Sufficiency |
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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

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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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