MBA20 wrote:
In Company X, the median annual salary is $50,000. What percent of the employees earned less than $80,000 and more than $50,000?
(1) The employees who earned less than $80,000 and more than $50,000 is equal to the number of the employees who earned no less than $80,000.
(2) 30% of the total salary was earned by the employees who earned less than $80,000 and more than $50,000.
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.
50k is the median so equal number of employees are to its left and to its right.
.................................... 50k ...................................
Note that many people could be at exact 50k value. We need the number of people beyond 50k (and less than 80k)
.................................... 50k
...................80k...............
(1) The employees who earned less than $80,000 and more than $50,000 is equal to the number of the employees who earned no less than $80,000.
This option is saying that there are equal number of people "between 50k and 80k" and "80k and above". So it might seem that 1/4th of all people are between 50k and 80k, but it doesn't tell us what percentage of people are at 50k. Hence this is not sufficient.
e.g.
Case 1: .................................... 50k (avg of middle two values)
51k...................79k 80k...............
25% people are between 50k and 80k exclusive.
Case 2: .................................... 50k 50k 50k 50k
51k..................79k 80k...............
Less than 25% people are between 50k and 80k exclusive.
(2) 30% of the total salary was earned by the employees who earned less than $80,000 and more than $50,000.
This option tells us a bit about the "total salary". 30% of the total money was taken home by "between 50k and 80k" people. But it gives us no information about the number of people who got that salary. Not sufficient.
Using both statements, we cannot say what percentage the number of people between 50k and 80k represent.
Not sufficient. Answer (E)