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

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factor26: Senior | Next Rank: 100 Posts; Posts: 99; Joined: Sun Mar 13, 2011 12:42 pm

by factor26 » Wed Dec 07, 2011 5:56 pm

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!

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Source: Beat The GMAT — Data Sufficiency | Wed Dec 07, 2011 5:56 pm

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Anurag@Gurome: GMAT Instructor; Posts: 3835; Joined: Fri Apr 02, 2010 10:00 pmFollowed by: 523 members; Location: Milpitas, CA; Thanked: 1854 times; GMAT Score:770

by Anurag@Gurome » Wed Dec 07, 2011 6:35 pm

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.

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

Let the number of teachers and students in school district M are Tm and Sm respectively.
Also let us assume that the number of teachers and students in school district P are Tp and Sp respectively.
It is given that Tm : Sm = Tp : Sp
We have to find Sm : Sp

(1) Sm = 10000 + Sp
So, Sm : Sp = (10000 + Sp) : Sp, but we do not know Sp; NOT sufficient.

(2) Tm : Sm = 1 : 20 = Tp : Sp
Again this is NOT sufficient.

Combining (1) and (2), Sm : Sp = (10000 + Sp) : Sp and Tm : Sm = 1 : 20 = Tp : Sp, but again we do not get the ratio of Sm to Sp using this information; NOT sufficient.

The correct answer is E.

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vijaykondepudi: Newbie | Next Rank: 10 Posts; Posts: 5; Joined: Fri Jan 01, 2010 2:00 pm

by vijaykondepudi » Wed Dec 19, 2012 7:57 am

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.

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GMATGuruNY: GMAT Instructor; Posts: 15539; Joined: Tue May 25, 2010 12:04 pmFollowed by: 1906 members; Location: New York, NY; Thanked: 13060 times; GMAT Score:790

by GMATGuruNY » Wed Dec 19, 2012 2:41 pm

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.

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vijaykondepudi: Newbie | Next Rank: 10 Posts; Posts: 5; Joined: Fri Jan 01, 2010 2:00 pm

by vijaykondepudi » Wed Dec 19, 2012 6:46 pm

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.

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