A school district is organized such that each of its D

Question

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

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

Zarrolou · Answer

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

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

fameatop · Answer

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
No of Department heads- D
 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
Answer E

Skag55 · Answer

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?

Zarrolou · Answer

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

Skag55 · Answer

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!

DmitrySavelyev · Answer

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

Skag55 · Answer

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?

GMAT40 · Answer

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

Bunuel · Answer

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?

DLEmba · Answer

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...

Bunuel · Answer

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.

qlx · Answer

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.

Bunuel · Answer

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?

khumoyuns · Answer

Combining both statements you get the ration of students to teachers. Isn't it what the question is asking? Why the hell we need S*T?

Both statements combined give you that the ratio of students to dep. heads is 8. If this is not the answer, then the question is very poorly worded.

IanStewart · Answer

It's very tempting, reading the question here, to think it's asking for the ratio of S to D. But S is  not  the number of students in this school district. S is only the number of students  per teacher . If there are D departments, and each department has T teachers, there are D*T teachers in total. If each teacher has S students, then there are D*T*S students in total. So the ratio the question is asking for is the ratio of D*T*S to D, or dividing by D, the ratio of T*S to 1, so we'd need the value of T*S to answer the question, and we can't find that from the Statements.

BlueDefender · Answer

What is the ratio of students to department heads in this school district?
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

in both the example the ratio is 8:1

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