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# A school district is organized such that each of its D

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A school district is organized such that each of its D  [#permalink]

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20 Jun 2013, 21:57
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A school district is organized such that each of its D department heads has exactly T teachers reporting to her, and that each teacher has exactly S students. What is the ratio of students to department heads in this school district?

(1) T/D=2/1
(2) S/T=4/1

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Re: A school district is organized such that each of its D  [#permalink]

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20 Jun 2013, 22:05
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A school district is organized such that each of its D department heads has exactly T teachers reporting to her, and that each teacher has exactly S students. What is the ratio of students to department heads in this school district?

Number of students= $$D*T*S$$

$$Ratio = \frac{D*T*S}{D}=T*S$$

We are asked what is the number of teacher * number of students per teacher.

(1) T/D=2/1

(2) S/T=4/1

Both statement give us ratios, not the actual number.
Example T=40 D=20 S=160 or T=20 D=10 and S=80. All ratios still are respected but T*S changes.
E
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Re: A school district is organized such that each of its D  [#permalink]

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20 Jun 2013, 22:09
A school district is organized such that each of its D department heads has exactly T teachers reporting to her, and that each teacher has exactly S students. What is the ratio of students to department heads in this school district?
(1) T/D=2/1
(2) S/T=4/1

No of students - DST
Required ratio - ST i.e. the question is basically asking the value of ST

Statement 1- => T=2D . Not sufficient
Statement 2- => S=4T .
so the final value will be $$4T^2$$
But still we don't know the value of T.
Not sufficient

Statement 1& 2- =>
so the final value will be $$4(2D)^2$$
But still we don't know the value of D.
Not sufficient
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Re: A school district is organized such that each of its D  [#permalink]

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23 Jun 2013, 05:17
Zarrolou wrote:
A school district is organized such that each of its D department heads has exactly T teachers reporting to her, and that each teacher has exactly S students. What is the ratio of students to department heads in this school district?

Number of students= $$D*T*S$$

$$Ratio = \frac{D*T*S}{D}=T*S$$

We are asked what is the number of teacher * number of students per teacher.

(1) T/D=2/1

(2) S/T=4/1

Both statement give us ratios, not the actual number.
Example T=40 D=20 S=160 or T=20 D=10 and S=80. All ratios still are respected but T*S changes.
E

So...the question asks: What is the ratio of students to department heads in this school district?
But you say: Both statement give us ratios, not the actual number.

I'm confused. Since the question asks for a ratio, we provide a ratio. No?
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Re: A school district is organized such that each of its D  [#permalink]

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23 Jun 2013, 05:22
Skag55 wrote:
Zarrolou wrote:
A school district is organized such that each of its D department heads has exactly T teachers reporting to her, and that each teacher has exactly S students. What is the ratio of students to department heads in this school district?

Number of students= $$D*T*S$$

$$Ratio = \frac{D*T*S}{D}=T*S$$

We are asked what is the number of teacher * number of students per teacher.

(1) T/D=2/1

(2) S/T=4/1

Both statement give us ratios, not the actual number.
Example T=40 D=20 S=160 or T=20 D=10 and S=80. All ratios still are respected but T*S changes.
E

So...the question asks: What is the ratio of students to department heads in this school district?
But you say: Both statement give us ratios, not the actual number.

I'm confused. Since the question asks for a ratio, we provide a ratio. No?

We have to rewrite the main question as $$Ratio = \frac{D*T*S}{D}$$ or $$T*S$$

As you see now, what we have to find is an "absolute" number, no more a ratio. The real question is "what is the number of teachers*number of students?"

As you see we need values, not ratios to anwer the question, take a look at some examples from my above post to get what I am saying
Example T=40 D=20 S=160 or T=20 D=10 and S=80. All ratios still are respected but T*S changes.

Hope it' s clear
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Re: A school district is organized such that each of its D  [#permalink]

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23 Jun 2013, 05:26
Zarrolou wrote:
Skag55 wrote:
Zarrolou wrote:
A school district is organized such that each of its D department heads has exactly T teachers reporting to her, and that each teacher has exactly S students. What is the ratio of students to department heads in this school district?

Number of students= $$D*T*S$$

$$Ratio = \frac{D*T*S}{D}=T*S$$

We are asked what is the number of teacher * number of students per teacher.

(1) T/D=2/1

(2) S/T=4/1

Both statement give us ratios, not the actual number.
Example T=40 D=20 S=160 or T=20 D=10 and S=80. All ratios still are respected but T*S changes.
E

So...the question asks: What is the ratio of students to department heads in this school district?
But you say: Both statement give us ratios, not the actual number.

I'm confused. Since the question asks for a ratio, we provide a ratio. No?

We have to rewrite the main question as $$Ratio = \frac{D*T*S}{D}$$ or $$T*S$$

As you see now, what we have to find is an "absolute" number, no more a ratio. The real question is "what is the number of teachers*number of students?"

As you see we need values, not ratios to anwer the question, take a look at some examples from my above post to get what I am saying
Example T=40 D=20 S=160 or T=20 D=10 and S=80. All ratios still are respected but T*S changes.

Hope it' s clear

Sure, I got that the ration doesn't actually give us any values, I just got lost between the question and the interpretation.
So what I conclude is that it "asks" for a ratio, but it "means" that we need a number. I guess
Thanks for the clarification though!
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Re: A school district is organized such that each of its D  [#permalink]

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18 Sep 2013, 04:40
atalpanditgmat wrote:
A school district is organized such that each of its D department heads has exactly T teachers reporting to her, and that each teacher has exactly S students. What is the ratio of students to department heads in this school district?

(1) T/D=2/1
(2) S/T=4/1

Guys,
I still don't understand. I came to the answer in the following way
D/T = 1/2 and T/S = 1/4 therefore D/T/S = 1/2/8. So the ratio of the students to the department heads is 8/1. Where is the mistake?

Regards
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Re: A school district is organized such that each of its D  [#permalink]

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18 Sep 2013, 06:00
DmitrySavelyev wrote:
atalpanditgmat wrote:
A school district is organized such that each of its D department heads has exactly T teachers reporting to her, and that each teacher has exactly S students. What is the ratio of students to department heads in this school district?

(1) T/D=2/1
(2) S/T=4/1

Guys,
I still don't understand. I came to the answer in the following way
D/T = 1/2 and T/S = 1/4 therefore D/T/S = 1/2/8. So the ratio of the students to the department heads is 8/1. Where is the mistake?

Regards

Further to this, the ratio (which the question asks for) will always be D/S will always be 1/8, whether it's T=40 D=20 S=160 or T=20 D=10 and S=80, the ratio is 1/8. Despite having written that I understand the solution, I don't understand why since we're asked for a ratio, we can't just provide one?
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Re: A school district is organized such that each of its D  [#permalink]

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22 Sep 2013, 05:50
Hi Bunnel,

Why should it be DST as mentioned by Zarrolou?

If we take st 1 and t 2 together we should be able to get the D:S:T ratio as 1:2:8
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A school district is organized such that each of its D  [#permalink]

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23 Sep 2013, 00:15
1
GMAT40 wrote:
A school district is organized such that each of its D department heads has exactly T teachers reporting to her, and that each teacher has exactly S students. What is the ratio of students to department heads in this school district?

(1) T/D=2/1
(2) S/T=4/1

Hi Bunnel,

Why should it be DST as mentioned by Zarrolou?

If we take st 1 and t 2 together we should be able to get the D:S:T ratio as 1:2:8

Consider an example: each of its 2 department heads has exactly 3 teachers reporting to her, and that each teacher has exactly 4 students. How many students are there?

There are 2*3=6 teachers, and since each teacher has exactly 4 students, then there are 6*4=24 students.

Does this make sense?
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Re: A school district is organized such that each of its D  [#permalink]

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24 Apr 2014, 03:54
I'm sorry but I still don't follow how the answer is not C...

No matter how I try to change the numbers I always end up with 8:1 for S:D.

If, D=1, then there would be 2 Teachers, and if T=2, then there would be 8 Students. Therefore S:D = 8:1

If, D=4, then there would be 8 Teachers, and if T=8, then there would be 32 Students. Therefore S:D is again 8:1...
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Re: A school district is organized such that each of its D  [#permalink]

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24 Apr 2014, 05:20
1
BobbyDE wrote:
I'm sorry but I still don't follow how the answer is not C...

No matter how I try to change the numbers I always end up with 8:1 for S:D.

If, D=1, then there would be 2 Teachers, and if T=2, then there would be 8 Students. Therefore S:D = 8:1

If, D=4, then there would be 8 Teachers, and if T=8, then there would be 32 Students. Therefore S:D is again 8:1...

The point is that T is NOT the total number of teachers. T is the number of teachers reporting to each of the D departments. Hence the total number of teachers is DT.

Similarly, S is NOT the total number of students. S is the number of students each of T teacher has. Hence the total number of students is S*DT.

We need to find the ratio of students to department heads --> SDT/D = ST.

Check here too: a-school-district-is-organized-such-that-each-of-its-d-154681.html#p1270040

Hope it helps.
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A school district is organized such that each of its D  [#permalink]

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Updated on: 30 Jun 2014, 01:29
Bunuel wrote:
GMAT40 wrote:
Hi Bunnel,

Why should it be DST as mentioned by Zarrolou?

If we take st 1 and t 2 together we should be able to get the D:S:T ratio as 1:2:8

Consider an example: each of its 2 department heads has exactly 3 teachers reporting to her, and that each teacher has exactly 4 students. How many students are there?

There are 2*3=6 teachers, and since each teacher has exactly 4 students, then there are 6*4=24 students.

Does this make sense?

If there are 6 teachers and 2 department heads as obtained above then the ratio of T/D = 3/1 which is not possible as given in statement 1, T/D= 2/1

SO T/D can be : 2x/1x ( Statement 1 )

and S/T = 4y/1y ( Statement 2 )

when x = 1 then T = 2 and D =1
So putting y = 2 ( to equate teachers ) we get S= 8 ,T= 2 hence S/D= 8/1

when x = 2 then T = 4 and D=2 putting y = 4 we get S= 16, T=4 hence S/D= 16/2 = 8/1

So it seems the ration of S/D is always 8/1 ,

I also feel answer should be C

We need the ratio and also in the examples provided by Zarrolou the ratio of S/D comes to be 8/1

a-school-district-is-organized-such-that-each-of-its-d-154681.html#p1238106

Let me know if I have missed something. Thanks.

Originally posted by qlx on 28 Jun 2014, 04:59.
Last edited by qlx on 30 Jun 2014, 01:29, edited 1 time in total.
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Re: A school district is organized such that each of its D  [#permalink]

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28 Jun 2014, 06:16
qlx wrote:
Bunuel wrote:
GMAT40 wrote:
Hi Bunnel,

Why should it be DST as mentioned by Zarrolou?

If we take st 1 and t 2 together we should be able to get the D:S:T ratio as 1:2:8

Consider an example: each of its 2 department heads has exactly 3 teachers reporting to her, and that each teacher has exactly 4 students. How many students are there?

There are 2*3=6 teachers, and since each teacher has exactly 4 students, then there are 6*4=24 students.

Does this make sense?

If there are 6 teachers and 2 department heads as obtained above then the ratio of T/D = 3/1 which is not possible as given in statement 1, T/D= 2/1

SO T/D can be : 2x/1x ( Statement 1 )

and S/T = 4y/1y ( Statement 2 )

when x = 1 then T = 2
So putting y = 2 ( to equate teachers ) we get S= 8 hence S/D= 8/1

when x = 2 then T = 4 putting y = 4 we get S= 16 hence S/D= 16/2 = 8/1

So it seems the ration of S/D is always 8/1 ,

I also feel answer should be C

We need the ratio and also in the examples provided by Zarrolou the ratio of S/D comes to be 8/1

a-school-district-is-organized-such-that-each-of-its-d-154681.html#p1238106

Let me know if I have missed something. Thanks.

First of all example (numbers) in my post is to explain the stem and has nothing to do with the statements.

Next, when we combine the statements we get that T:D:S = 2:1:8. We need to find the value of ST. How are you going to do that knowing only that T:S = 2:8?
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Re: A school district is organized such that each of its D  [#permalink]

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