Median

[torpedo]

What is the median number of employees assigned per project for the projects at Company Z?

(1) 25 percent of the projects at Company Z have 4 or more employees assigned to each project.
(2) 35 percent of the projects at Company Z have 2 or fewer employees assigned to each project.

(A) Statement (1) ALONE is sufficient, but statement (2) alone is not sufficient.
(B) Statement (2) ALONE is sufficient, but statement (1) alone is not sufficient.
(C) BOTH statements TOGETHER are sufficient, but NEITHER statement ALONE is sufficient.
(D) EACH statement ALONE is sufficient.
(E) Statements (1) and (2) TOGETHER are NOT sufficient.

[solmon]

I would say E. We still don't know how many employees were assigned to a project as Statement 1 gives %25 and Statement 2 gives %35. There could be other projects that may contain different amount of employees.

[torpedo]

Even I go with (E). But the Official Answer is given as (C). This question is from GMAT Math Set 21.

[solmon]

I don't see what I am missing here. Does anyone has a different opinion?

[atishree]

I think the answer should be C, (1) says 25% of the projects at company Z have 4 or more employees , Insufficient alone. (2) says 35% of the projects at company Z have 2 or less, Insufficient alone. Combining both, we get 100 - (25 + 35) = 100 - 60 = 40% stands for projects at company Z that have 3 employees. So 3 is median number of employees assigned per project at company Z.

(concept: the maximum distribution over the total distribution represents the measure of central tendency over the total)

[solmon]

Got it. This is a tricky question. Thanks for the explanation.

[torpedo]

Thanks for the solution and concept atishree.

[Rockfeller]

I think the answer should be C, (1) says 25% of the projects at company Z have 4 or more employees , Insufficient alone. (2) says 35% of the projects at company Z have 2 or less, Insufficient alone. Combining both, we get 100 - (25 + 35) = 100 - 60 = 40% stands for projects at company Z that have 3 employees. So 3 is median number of employees assigned per project at company Z.

(concept: the maximum distribution over the total distribution represents the measure of central tendency over the total)

But why do you think that the rest 40% is assigned 3 employees. why not 1, why not 5?

[TomRod]

25% have 4, 5, 6, 7, . . . employees assigned (4 or MORE employees assigned)
35% have 2 or 1 employees assigned (2 or less)

The rest can't have less than three or more than three. Hence, they must have 3.

-Tom

[atishree]

But why do you think that the rest 40% is assigned 3 employees. why not 1, why not 5?

1 is included in 2 or less(25%) & 5 is included in 4 or more(35%) , the only quantity left uncounted in the entire distribution is 3. I hope this explains.