company

[advita]

At a certain company, each employee has either an office or a cubicle. If each office or cubicle is occupied by exactly one employee, what percent of the employees have offices?

(1) The employees outnumber the cubicles 3 to 2.
(2) There are 50 offices.


ok..its esay..>>>but what exactly statment 1 says..!!

[naremnaresh]

statement 1 says that 2 * employee count = 3 * number of cubicles.
number of cubicles = 2/3 * employee count.
since office+ cubicles = emplyee count
office = employee count * (1 - 2/3)
office/employee count = 1/3 = 33.33% is answer

statement 1. is enough
with statement 2. alone we cannot determine the percentage since we don't know the number of employees.

[kapur.arnav]

At a certain company, each employee has either an office or a cubicle. If each office or cubicle is occupied by exactly one employee, what percent of the employees have offices?

(1) The employees outnumber the cubicles 3 to 2.
(2) There are 50 offices.


ok..its esay..>>>but what exactly statment 1 says..!!

experts.. please explain!!

[anshumishra]

c- no. of cubicles
o- no. of offices
e = c+o -> no. of employees

We want to know, o/e = ?

Statement 2 : clearly Insufficient

Statement 1 :
e/c = 3/2 => c+o/c = 3/2
=> o/c = 1/2
=> o/e = o/(o+c) = 1/(1+2) = 1/3
Sufficient.

Hence A.

[prachich1987]

c- no. of cubicles
o- no. of offices
e = c+o -> no. of employees

We want to know, o/e = ?

Statement 2 : clearly Insufficient

Statement 1 :
e/c = 3/2 => c+o/c = 3/2
=> o/c = 1/2
=> o/e = o/(o+c) = 1/(1+2) = 1/3
Sufficient.

Hence A.

My doubt may sound silly
But is it necessary that there is no office/cubicle which is empty
In the question they say"each employee has either an office or a cubicle"
Is the converse has to be true.

WHAT IS THE OA?

[anshumishra]

c- no. of cubicles
o- no. of offices
e = c+o -> no. of employees

We want to know, o/e = ?

Statement 2 : clearly Insufficient

Statement 1 :
e/c = 3/2 => c+o/c = 3/2
=> o/c = 1/2
=> o/e = o/(o+c) = 1/(1+2) = 1/3
Sufficient.

Hence A.

My doubt may sound silly
But is it necessary that there is no office/cubicle which is empty
In the question they say"each employee has either an office or a cubicle"
Is the converse has to be true.

WHAT IS THE OA?

The question says : If each office or cubicle is occupied by exactly one employee, what percent of the employees have offices?

So, that means even if there are some offices vacant, we don't need to take those in account.
Hence in my solution
o-> no. of offices occupied by employees.

I don't know the OA.

Thanks

[prachich1987]

c- no. of cubicles
o- no. of offices
e = c+o -> no. of employees

We want to know, o/e = ?

Statement 2 : clearly Insufficient

Statement 1 :
e/c = 3/2 => c+o/c = 3/2
=> o/c = 1/2
=> o/e = o/(o+c) = 1/(1+2) = 1/3
Sufficient.

Hence A.

My doubt may sound silly
But is it necessary that there is no office/cubicle which is empty
In the question they say"each employee has either an office or a cubicle"
Is the converse has to be true.

WHAT IS THE OA?

The question says : If each office or cubicle is occupied by exactly one employee, what percent of the employees have offices?

So, that means even if there are some offices vacant, we don't need to take those in account.
Hence in my solution
o-> no. of offices occupied by employees.

I don't know the OA.

Thanks

According to me if we assume that, then & then only we can answer, otherwise we can't
One of the step is below
o+c=e---according to which, office+cubicle=no.of employees
But its not necessary.
We can definitely say that 'o+c' is not lesser than 'e' as we know that only one employee can occupy a cubicle.
But may be o+c>e

I would be grateful if experts can reply

[anshumishra]

c- no. of cubicles
o- no. of offices
e = c+o -> no. of employees

We want to know, o/e = ?

Statement 2 : clearly Insufficient

Statement 1 :
e/c = 3/2 => c+o/c = 3/2
=> o/c = 1/2
=> o/e = o/(o+c) = 1/(1+2) = 1/3
Sufficient.

Hence A.

My doubt may sound silly
But is it necessary that there is no office/cubicle which is empty
In the question they say"each employee has either an office or a cubicle"
Is the converse has to be true.

WHAT IS THE OA?

The question says : If each office or cubicle is occupied by exactly one employee, what percent of the employees have offices?

So, that means even if there are some offices vacant, we don't need to take those in account.
Hence in my solution
o-> no. of offices occupied by employees.

I don't know the OA.

Thanks

According to me if we assume that, then & then only we can answer, otherwise we can't
One of the step is below
o+c=e---according to which, office+cubicle=no.of employees
But its not necessary.
We can definitely say that 'o+c' is not lesser than 'e' as we know that only one employee can occupy a cubicle.
But may be o+c>e

I would be grateful if experts can reply

Let me use an example to make it clear :

Lets assume there are 15 offices, 10 cubicles
And assume that 8 offices and 6 cubes are occupied by employees (means total 14 employees)

Then the % of employees which have offices = 8/14.

[See, you never need to bother about the 15 offices, 1o cubicles]

Using this example to my equation:
c=6
o=8
e=c+o = 14

We need to calculate : o/e = 8/14

Hope it is clear now.

[prachich1987]

c- no. of cubicles
o- no. of offices
e = c+o -> no. of employees

We want to know, o/e = ?

Statement 2 : clearly Insufficient

Statement 1 :
e/c = 3/2 => c+o/c = 3/2
=> o/c = 1/2
=> o/e = o/(o+c) = 1/(1+2) = 1/3
Sufficient.

Hence A.

My doubt may sound silly
But is it necessary that there is no office/cubicle which is empty
In the question they say"each employee has either an office or a cubicle"
Is the converse has to be true.

WHAT IS THE OA?

The question says : If each office or cubicle is occupied by exactly one employee, what percent of the employees have offices?

So, that means even if there are some offices vacant, we don't need to take those in account.
Hence in my solution
o-> no. of offices occupied by employees.

I don't know the OA.

Thanks

According to me if we assume that, then & then only we can answer, otherwise we can't
One of the step is below
o+c=e---according to which, office+cubicle=no.of employees
But its not necessary.
We can definitely say that 'o+c' is not lesser than 'e' as we know that only one employee can occupy a cubicle.
But may be o+c>e

I would be grateful if experts can reply

Let me use an example to make it clear :

Lets assume there are 15 offices, 10 cubicles
And assume that 8 offices and 6 cubes are occupied by employees (means total 14 employees)

Then the % of employees which have offices = 8/14.

[See, you never need to bother about the 15 offices, 1o cubicles]

Using this example to my equation:
c=6
o=8
e=c+o = 14

We need to calculate : o/e = 8/14

Hope it is clear now.

Thanks!It's clear now
sorry for creating confusion

[fskilnik@GMATH]

At a certain company, each employee has either an office or a cubicle. If each office or cubicle is occupied by exactly one employee, what percent of the employees have offices?

(1) The employees outnumber the cubicles 3 to 2.
(2) There are 50 offices.

Hi there,

Beautiful problem, beautiful discussion, beautiful (and correct) arguments, anshumishra´s in particular on the "empty offices" possibility.

Let me give you another alternative, pretty quick, for the solution but, before that, let me say something:

If the question stem were:

At a certain company, each employee has either an office or a cubicle. If each office AND each cubicle is occupied by exactly one employee

many students would be messed-up, but mathematically speaking, we would guarantee that no place was left unoccupied, no people would be without place to sit, and it would have one person per place (bijection).

Why?

I. "Each employee has either an office or a cubicle" means that no employee is left without place to sit.
II. "If each office AND each cubicle is occupied..." means that no office AND no cubicle was left without one person there.

All that understood, I really believe that the person who wrote the problem simply WRONGLY chose OR in the place of AND, that´s why you all got discussing. The fact is, "by luck" the question itself was not related to that, as anshumishra wisely explained. (The example was the "smoking gun" for sure, LOL.)

Well, now the problem itself, the way I see it!

First: let us call the number of employees as "E".

We know that alfa*E is the fraction of E that sits in an office and (1-alfa)*E is the fraction of E that sits in a cubicle, where 0<= alfa <= 1 is a real constant that makes the place for the fraction we are looking for!

(You see: we are not dealing with the first problem discussed, as anshumishra noticed. In both cases, this way of modelling the problem suits because all employees "sit", that is all that matter!)

Focus is on ALPHA, ok?!

(1) E over cubicles = 3:2 means "for every 3 employees, 2 sit in cubicles" (on average, I know) therefore "for every 3 employees, 1 sit in office" (again), therefore offices (occupied by employees)/cubicles is 1:2 and offices (occupied by employees)/E = 1/3 and that means alfa = 1/3.

(2) we know that alpha*E = 50 (suppose all offices are occupied, for instance), therefore:

If E = 100, then alpha = 1/2
If E = 200, then alpha = 1/4

I hope you like it all.

Regards,
Fabio.