If a and b are non-negative numbers such that a + 2b = 6, what is the

Question

If a and b are non-negative numbers such that a + 2b = 6, what is the average (arithmetic mean) of the maximum and minimum possible values of a + b?

A. 3 
 B. 3.5 
 C. 4 
 D. 4.5 
 E. 5

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tgsankar10 · Answer

a    is maximum when    b=0   ,    a=6

b  is maximum when  a=0 ,  b=3

Max  a+b=6 , min  a+b=3

Average of  	ext{6 & 3}=4.5

Answer: D

Ayeka · Answer

Given: a+2b= 6 
To find: Average of Min and Max value of a+b
 Max value, b=0 & a=6 
 a+b=6 
Min value, b=3 & a=0 
 a+b=3

Average= (6+3)/2= 9/2= 4.5

D

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Krunaal · Answer

We are given neither a nor b can be negative, and a + 2b = 6 ......................(1)

To find min. and max. of a + b we need to substitute one value as least as we can go on number line maintaining the restraints given in qs.

The least value we can consider here is 0

When a = 0, b = 3 ..................(from 1)
a + b = 3; this is minimum

When b = 0, a = 6 ..................(from 1)
a + b = 6 ; this is maximum

Average => (6 + 3)/2 = 4.5

Answer D.

dumi2005 · Answer

Given a + 2b = 6, we can isolate a to get a = 6 - 2b.
Substitute this into the target expression (a + b):
(6 - 2b) + b = 6 - b

Next, determine the bounds for b:
Since a must be non-negative (a >= 0), then 6 - 2b >= 0, which simplifies to b <= 3.
Since b is also non-negative, the allowed range for b is 0 <= b <= 3.

Calculate the Maximum and Minimum:
Maximum: To maximize the expression 6 - b, use the lowest possible value for b (0).
6 - 0 = 6
Minimum: To minimize the expression 6 - b, use the highest possible value for b (3).
6 - 3 = 3
Calculate the Average:
(6 + 3) / 2 = 4.5

Correct Answer: D

If a and b are non-negative numbers such that a + 2b = 6, what is the

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If a and b are non-negative numbers such that a + 2b = 6, what is the

Prep Toolkit

615 to 715 in 15 Days (Ria's Strategies)

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