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Question

If a, b, c and d are four positive numbers such that a + b + c + d = 4, then what is the maximum value of (a + 1)(b + 1) (c + 1)(d + 1) ?


Your Answer
A
32
Your Answer
B
8
Correct Answer
C
16
Your Answer
D
81

Solution

The correct option is A 16
If a + b + c + d is constant, then the product abcd is maximum when a = b = c = d.
(a+1)=(b+1)=(c+1)=(d+1)
Given that a+b+c+d=4
(a + 1) + (b + 1) + (c + 1) + (d + 1) = 8
4(a+1)=8
(a+1)=(b+1)=(c+1)=(d+1)=2
Maximum value =2×2×2×2=16

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