Explanation for answer

Here is the solution to your questions. Hope I am clear. Let me know if you don't uderstand the explanation.

1st Ques:
Let us assume the salary of Mary, Jim and Kate as M , J and K.

As per the question:

M-J = 2(M-K)

M-J = 2M-2K

2K-J = M

The average of salaries of Mary, Jim and Kate will be :

J + K + M / 3

J + K + 2K-J / 3

3K/3 = K

So, The average of 3 salaries is kate's salary.

Statement 2 Alone is sufficient.



2nd Ques :
What is a median ?
The middle value in a set of numbers arranged in increasing order. If there is an even number of values, then median is the average of the middle two values

So, if you arrange all the number of amounts in ascending order, you will get the median by the average of middle two values.

48,48,70,70,70,80,80,80,80,84,84,84,84,84,84,84,96,96,96,96

The middle two values are 84, so the median is 84.

3rd Ques :
Let x be the amount by which the height increases every year.

So the ht after 6 yrs = 4+6x.
Ht after 4 yrs = 4+4x.

AS per the statement, At the end of 6th year, the tree was 1/5 taller thanit was at the end of 4th year.

4+6x = 4+4x + 1/5(4+4x)

2x = 4/5 + 4/5x

(2-4/5)x = 4/5

6/5x = 4/5

x = 4/6 = 2/3.

Thanks mba.dude for your help on the explanation.

Another way to go about the problem is to ask why did they say that Mary's salary is the highest? Information like that must be useful in some way...

Well, what that means is that Jim's salary is the lowest among the three, and therefore Kate's is in the middle -- in fact Kate's salary is exactly in the middle between Jim's and Mary's. We know this because the difference between Jim's and Mary's is twice the difference between Kate's and Mary's.

So that means that Kate's salary equals the average of the three salaries. (2) is therefore sufficient while (1) is not.