lheiannie07 wrote:In a set of three variables, the average of the first two variables is greater than 2, the average of the last two variables is great than or equal to 3 , the average of the first and third variable is 4.Which of the following could be the average of the three variables?

A)1
B)1.5
C)2
D)3
E)3.5

How can i easily solve this problem? Can some experts help?

OA E

Average = (a + b + c)/3

(1) (a + b)/2 > 2
(2) (b + c)/2 >= 3
(3) (a + c)/2 = 4

Multiply all of the above by 2 on each side.

(1) (a + b) > 4
(2) (b + c) >= 6
(3) (a + c) = 8

Sum (1), (2) and (3) --> this must be greater than 18

(a + b) + (b + c) + (a + c) > 18
2(a + b + c) > 18
(a + b + c) > 9
(a + b + c)/3 > 3

E. 3.5 is the only answer which is greater than 3.

Answer is E

lheiannie07 wrote:In a set of three variables, the average of the first two variables is greater than 2, the average of the last two variables is great than or equal to 3 , the average of the first and third variable is 4.Which of the following could be the average of the three variables?

A)1
B)1.5
C)2
D)3
E)3.5

We can let the three variables be a, b and c. So we have:

(a + b)/2 > 2

a + b > 4

and

(b + c)/2 ≥ 3

b + c ≥ 6

and

(a + c)/2 = 4

a + c = 8.

If we add up these three inequalities/equations, we have:

2a + 2b + 2c > 18

a + b + c > 9

(a + b + c)/3 > 3

The only number is greater than 3 is 3.5, thus it's the answer.

Answer: E