Data Sufficiency

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.

OG answer is E ... can someone show me how to solve using the plug in the numbers technique? Much appreciated thanks!

Hi,
In this question we need to find the ratio: Sm/Sp

I am unable to understand, why statement 2 is not sufficient.

Tm:Sm = 1:20 = Tp:Sp ---> Equation 2

From the above, can we write as follows :

Tm:Tp = 1:20 = Sm:Sp

Can't we then conclude that Sm:Sp = 1:20 (This is the ratio that's require)

I tried a few values:
Assume, Tm = 1, Sm = 20 ; Tp = 20, Sp = 400.

Therefore, the ratio Tm:Sm = 1:20 = Tp:Sp is valid for the above assumption.

Now, from this I can calculate Sm:Sp = 20:400 = 1:20

So why is Statement (2) alone not sufficient? Please explain in detail.

factor26 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.

Each district has the same teacher-student ratio.
Statement 2 implies that, in each district, the number of teachers is 1/20 of the number of students.
The following cases satisfy BOTH statements.

CASE 1:

_________________P_____________M

Students_______2000________12000

Teachers_______100___________600

Here, the student ratio = 2000:12000 = 1:6.

CASE 2:

__________________P_____________M

Students_______10000________20000

Teachers________500__________1000

Here, the student ratio = 10000:20000 = 1:2.

Since different student ratios are possible, the two statements combined are INSUFFICIENT.

The correct answer is E.

Hi Mitch,

Thanks for your explanation
But in general, doesn't the "Cross Multiplication" rules apply, when we have 3 ratios ?

For, example:

a:b = 1:20
c:d = 1:20

Does it mean that we cannot equate as follows :

a:b = c:d ??

Your examples are pretty clear, but from arithmetic point of view, why is cross multiplication valid for 2 ratios and not when combining 3 ratios ?

Please explain.