An auto dealership has multiple departments. Each of the departments

Question

An auto dealership has multiple departments. Each of the departments has a manager, each department has multiple employees who work with the manager, and each department has the same number of of people in it. If there are only department managers and other department employees working at the dealership, and if there are fewer than 25 employees at the dealership, how many employees does the dealership have?

(1) The ratio of managers to non manager employees is 1:7.

(2) There are 21 non manager employees at the dealership.

(1) The ratio of managers to non manager employees is 1:7.

(2) There are 21 non manager employees at the dealership.

chetan2u · Answer

Hi all,

lets check the INFO from Q.. 
 1) Each department has a manager M, and some employees E..
2) since the number of people in it, and manager is 1, E will also be same for all..
3) Number of people <25
4) However, we do not know the NUMBER of DEPT and number of PEOPLE per DEPT, to work out all employees

Now lets check the statements:-

(1) The ratio of managers to non manager employees is 1:7.  
let teh ratio be x.. so M=x and E=7x..
total=8X, but 8X<25, so x can be 8,16,24..
Insuff as different possible answers

(2) There are 21 non manager employees at the dealership. 
21 non manager means E=21..
so M can be 3, if departments are 3 in which case E=7 per dept
M can be 7, if departments are 7 in which case E=3 per dept..
here we may have two cases BUT we can ELIMINATE one because of restriction of people<25..
1) When M=3, total E= 3*7=21.. people= 3+21=24, which is <25..ok
2) When M=7, total E= 3*7=21.. people= 7+21=28, which is >25..not ok
so we have ans as 24..
Sufficient 
B

etdenlinger · Answer

For (B), can't we have a 21 non-managers and 1 manager. For a total of 22 employees?

etdenlinger · Answer

For (B), can't we have a 21 non-managers and 1 manager for a total of 22 employees?

MartyTargetTestPrep · Answer

"An auto dealership has  multiple  departments. Each of the departments has a manager,"

chetan2u · Answer

Hi,
In the Q we are given

. Each of the departments has a manager,  each department has multiple employees who work with the manager, and each department has the same number of of people in it.
 so we have two ways.. 
1)  7 departments-  each has 3 employees and 1 manager
total 7*4=28 >25 NOT possible
2)  3 departments-  each has 21/3=7 employees and 1 manager..
total = 8* 3=24 <25 Ok

third could have been all 21 in one department and 1 manager, as you propose..
total 22 .. 
But because of following words we have to eliminate this choice..
 An auto dealership has multiple departments 
so there have to be more than 1 department

Hope it helps

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An auto dealership has multiple departments. Each of the departments

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An auto dealership has multiple departments. Each of the departments

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