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Question 20
If a and b are non-negative real numbers such that a+ 2b = 6, then the average of the maximum and minimum possible values of (a+ b) is
Solution
a + 2b = 6
From the above equation, we can say that maximum value b can take is 3 and minimum value b can take is 0.
a + b + b = 6
a + b = 6 - b
a + b is maximum when b is minimum, i.e. b = 0
Maximum value of a + b = 6 - 0 = 6
a + b is minimum when b is maximum, i.e. b = 3
Minimum value of a + b = 6 - 3 = 3
Average = $$\ \frac{\ 6+3}{2}$$ = 4.5
The answer is option D.
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