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Quantitative Aptitude

Maximum Value of AB, If A + B = Constant

If a+b+c=13, ...

Question

If a + b + c = 13, what is the maximum value of (a - 3)(b - 2)(c + 1) ?

A

26

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B

27

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C

30

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D

19

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Solution

The correct option is B 27
If x + y + z is constant, the product xyz takes maximum value when each of x, y, z takes equal value.
$∵ a + b + c = 13$
$∴ (a - 3) + (b - 2) + (c + 1) = 13 - 3 - 2 + 1 = 9$
For the maximum value of (a - 3) = (b - 2) = (c + 1)
$= (a - 3) = (b - 2) = (c + 1) = \frac{9}{3} = 3$
So, $(a - 3) (b - 2) (c + 1) = 3 \times 3 \times 3 = 27$

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Similar questions

If a+b+c = 13, then what is the maximum value of

(a - 3)( b - 2)(c + 1)

a + 3 b + 2 c = 12

, then the maximum value of

6 b c (1 + a) + a (3 b + 2 c)

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{∣ ∣ ∣ 2 \to a - 3 \to b ∣ ∣ ∣}^{2} + {∣ ∣ ∣ 2 \to b - 3 \to c ∣ ∣ ∣}^{2} + {∣ ∣ 2 \to c - 3 \to a ∣ ∣}^{2}

3^{a} + 3^{b} = 756, 7^{a} + 2^{c} = 375, 5^{a} + 3 = 128

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, what is the value of b?

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