Data Sufficiency

1) Each employee on a certain task force is either a manager or director. What percentage of the employees on task force are directors ?

1) The average salary (mean) of managers is $5000 less than the the average salary of the task force.
2) The average salary (mean) of directors is $15000 greater than the the average salary of the task force

I chose E and I was wrong.

2) Points A,B,C, and D are in a number line not necessarily in that order. Distance between A and B is 18 and between C &D is 8.What is the distance between B & D ?

1) Distance between A and C is same as the distance between B and C
2) A is to the left of D on the number line.

I chose C and I was wrong.

I will post the OA s after some discussions

Problem 1 has been solved here before. OA C

https://www.beatthegmat.com/what-percent ... 16143.html
https://www.beatthegmat.com/avg-salary-a ... 23038.html
https://www.manhattangmat.com/forums/eac ... -t772.html

2nd one is also solved but I will give it a shot here.

1) Since AC is equal to BC and A and B are distinct points, C is to the middle of A nd B.
This means BD=17 or BD =1. Both these positions of D are to the right of A.

2) Not enough to suggest anything.

1 AND 2:
A is to the left of D. No new Info in 2 as this has already been established in stmt 1.

Answer is E.

Thanks for the solutions and links Vineesh.Algebraic approach seems to take more time in the case of first problem .

Each employee on a certain task force is either a manager or a director. What percent of the employees on the task force are directors?

1) The average salary of the managers on the task force is 5,000 less than the average salary of all employees on the task force.

2) The average salary of the directors on the task force is 15,000 greater than the average salary of all employees on the task force.

When combining the statements, we can plug in for the average salary of all the employees and use alligation.

Let:
A = average salary of all the employees.
M = average salary of the managers.
D = average salary of the directors.

Let A = 10,000.
M = 10,000 - 5000 = 5000.
D = 10,000 + 15,000 = 25,000.

Using alligation:

The proportion needed of each starting average is the positive difference between the other two averages.

Proportion needed of M = 25,000-10,000 = 15,000.
Proportion needed of D = 10,000-5,000 = 5000.
M : D = 15,000 : 5000 = 3:1.
Since 3+1=4, D = 1/4 = 25%.

The correct answer is C.

Can you please explain the logic behind this proportion rule?

Thanks in advance!