In a company of 140 employees, there are three departments,

Question

In a company of 140 employees, there are three departments, A, B and C. The average number of sick days taken by employees in department A in 2005 was 10, and the average number of sick days taken by employees B was 12.25. Was the average number of sick days taken by company employees over 11?

(1) The 45 employees in department C took an average of 13 sick days in 2005.
(2) There are 44 employees in department B.

game over · Answer

(1) alone is not sufficient.

for example: 99 employees work in dep. A, 1 in B, 40 in C.
Then the average number of sick days is 99*10 + 1*12.25 + 40*13 = 990+520+12.25 < 11*140=1540.
but: 56*10+44*12.25+40*13 > 1540.

(2) alone is not sufficient:
95*10+44*12.25+1*13=950+539+13<1540
but 1*10+44*12.25+95*13 > 1540.

Both statements together are sufficient (see the example of (1)).

rbcola · Answer

This is tricky. SInce the average of B employees is 12.25, we should assume that there are at least 4 employees in Team B.

The problem basicaly is asking if total sick days for all employees is >1540.

Assuming that employee cannot take 1/4 day then A is sufficient.

beacuse for all combinations of B > 2 and A, the total is greater than 1540.

However, is the employee can take 1/4 day sick leave then A is not sufficient beacause if B = 1. then the total sick days = 1537.5, with A = 94. In which case C is the answer.

These type of problems take up too much time.

game over · Answer

good point rbcola!

kevincan · Answer

You're right- the way you've done it requires a lot of number crunching, and that is not what the exam is about! Can you think of an easier way to get to your correct conclusion?

ps_dahiya · Answer

A

The way I did is this:
Total average will be minimum when the number of employees in the department with minimum average are larger.

St1: If C has 45 employee then for total average to be minimum we can have most employees in dept A. B must have atleast 4. A must have rest i.e (140-4-45 = 91 employees). If we transfer 1 sick day from all 45 employees of C to 90 of A and one sick day form B to remaining of A then we have 139 employees with 11 sick days and one with 11.25 sick days. So average will be greater than 11.: SUFF

St2: We don't know anything about C: INSUFF

In a company of 140 employees, there are three departments,

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