In a set of three variables, the average of the first two variables is

Question

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

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

rohit8865 · Answer

quiet difficult to get avg below 4 i can get a set {0.7 , 3.4 , 7.3} having avg = 3.8 i will go with E +1 for alternative approach

stonecold · Answer

Ahh.
Thats not a precise solution  rohit8865 
Did you try adding the in-equations/equations ?
Can we ever get a mean below 3?

Never.
To put it simply => For mean to be 3.5 => Sum must be 10.5
As x+z=8=> y must be 2.5

Here is what i did in this question =>

Let the 3 variables be x,y,z

As per the question =>
x+y>4
y+z≥6
x+z=8

Lets just add them up.

Adding them =>
2(x+y+z)>18 ((notice the sign))

x+y+z>9

Hence x+y+z/3 >3

So mean must be greater than 3.

Only option that obeys that is E.

SMASH that E.

Alternatively we could just use the equation solving technique

using x+z=8 in x+y>4
y-z>-4
y+z>6
Adding them => 2y>2
y>1

Hence y>1

So the least average would be when y>1
At y=1 => Mean = x+y+z/3 =>9/3=3 which is not possible as y>1

Hence mean >3

Again => Smash that E.

rohit8865 · Answer

thanks however my guess was also > 3 because getting a avg < 3 is impossible just correct the above 2 typo...

JeffTargetTestPrep · Answer

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

hellosanthosh2k2 · Answer

Let first variable a, second - b, third = c

given: a + b > 4 , b+c >= 6, a + c = 8

average: (a + b + c)/3 = (8 + b)/3

a + b > 4 ----(1)
b + (8-a) >= 6
a - b <=2 ---(2)

Let a - b = 2 from (2)
then subsituting a = 2 + b in ---(1), 2 + b + b > 4 => 2b > 2 => b > 1
Let a - b < 2 from (2)
Adding (1) + (2)
a + b - (a - b) > 4 - 2 => 2b > 2 => b > 1

so either case b > 1,
so average , (8 + (>1))/3 => should be greater than 3, only one option stands (E)

PSKhore · Answer

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

Adding all 3 equations,

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

(a+b+c) > 9

Average should be greater than 9/3 = 3

The only option is 3.5

In a set of three variables, the average of the first two variables is

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In a set of three variables, the average of the first two variables is

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