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) ?
A
32
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B
8
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C
16
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D
81
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Solution
The correct option is C 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