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

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If the ratio of the number of teachers to the number of [#permalink]

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21 May 2011, 11:12
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Difficulty:

55% (hard)

Question Stats:

64% (02:18) correct 36% (01:22) wrong based on 220 sessions

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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.

OPEN DISCUSSION OF THIS QUESTION IS HERE: if-the-ratio-of-the-number-of-teachers-to-the-number-of-143680.html
[Reveal] Spoiler: OA

Last edited by Bunuel on 31 Mar 2014, 11:55, edited 2 times in total.
Edited the question.
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Re: og12: School District M and School District P [#permalink]

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21 May 2011, 11:49
is OA E?

kindly explain why E?
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Re: og12: School District M and School District P [#permalink]

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24 May 2011, 00:17
1
KUDOS
a. Teachers : Students = Tm:Sm. and Tp:Sp. Sm:Sp = ? (asked)

now, Sm-Sp = 1000 means Sm: (1000-Sm) = not known, Hence not sufficient.

b Tm:Sm = Tp:Sp = 1:20 gives nothing for Sm:Sp. Not sufficient.

a+b Tm:Sm = 1/20 Tp:(1000-Sm) = 1/20 gives not relative information between Tp Tm and Sm.Hence Not sufficient.

Thus E.
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Re: og12: School District M and School District P [#permalink]

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24 May 2011, 19:30
3
KUDOS
T1/S1 = T2/S2

S1/S2 = ?

(1)

S1 = S2 + 1000

Not sufficient

(2)

T1/S1 = 1/20

Not sufficient

(1) + (2) Not sufficient

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Re: og12: School District M and School District P [#permalink]

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24 May 2011, 19:51
2
KUDOS
sm/sp =?

1. Not sufficient

as we dont know sp.

sm = 10000 + sp
=> sm/sp = 10000/sp +1

2. Not sufficient

tm/sm = 1/20 = tp/sp

not enough to find out sm/sp.

Together,

still not sufficient.

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Re: og12: School District M and School District P [#permalink]

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28 May 2011, 09:45
OA is E - this was a DS in the Original Guide 12th edition.
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Re: If the ratio of the number of teachers to the number of [#permalink]

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31 Mar 2014, 11:40
gtr022001 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.

Official Guide 12 Question

 Question: 58 Page: 277 Difficulty: 600

Find All Official Guide Questions

Video Explanations:

Hi ,
If Tm:Sm = Tp:Sp = 1/20
so Applying Alternendo
Tm:Tp= Sm:Sp = 1/20
So isnt 2 Sufficient?
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Re: If the ratio of the number of teachers to the number of [#permalink]

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31 Mar 2014, 11:53
1
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Expert's post
abid1986 wrote:
gtr022001 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.

Official Guide 12 Question

 Question: 58 Page: 277 Difficulty: 600

Find All Official Guide Questions

Video Explanations:

Hi ,
If Tm:Sm = Tp:Sp = 1/20
so Applying Alternendo
Tm:Tp= Sm:Sp = 1/20
So isnt 2 Sufficient?

Yes, from $$\frac{T_m}{S_m}=\frac{T_p}{S_p}$$ we can get that $$\frac{S_m}{S_p}=\frac{T_m}{T_p}$$ but it does NOT mean that the ratio will remain the same, so it does not mean that since $$\frac{T_m}{S_m}=\frac{1}{20}$$, then $$\frac{S_m}{S_p}=\frac{T_m}{T_p}$$ will also be 1/20. Play with some numbers to prove that.

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 ?

Given that $$\frac{T_m}{S_m}=\frac{T_p}{S_p}$$, where $$T_m$$ and $$S_m$$ are the numbers of teachers and students, respectively, in District M, and $$T_p$$ and $$S_p$$ are the numbers of teachers and students, respectively, in District P.

We need to find the value of $$\frac{S_m}{S_p}$$ --> $$\frac{S_m}{S_p}=\frac{T_m}{T_p}$$

(1) There are 10,000 more students in School District M than there are in School District P --> $$S_m=S_p+10,000$$. Not sufficient.

(2) The ratio of the number of teachers to the number of students in School District M is 1 to 20 --> $$\frac{T_m}{S_m}=\frac{1}{20}$$. Not sufficient.

(1)+(2) Still not sufficient, consider $$S_p=1,000$$ and $$S_m=11,000$$ (answer 11) AND $$S_p=10,000$$ and $$S_m=20,000$$ (answer 2).

All OG13 questions are here: the-official-guide-quantitative-question-directory-143450.html

OPEN DISCUSSION OF THIS QUESTION IS HERE: if-the-ratio-of-the-number-of-teachers-to-the-number-of-143680.html
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Re: If the ratio of the number of teachers to the number of   [#permalink] 31 Mar 2014, 11:53
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