Question

If abcd = 81, what is the minimum value of a + b + c + d ?

• A. 18
• B. 9
• C. 12
• D. 36

Answer 1

Answer: (C)

12

If xyz is constant, then the sum of x, y, z (i.e., x + y + z) takes minimum value when each of x, y, z takes equal value.
$\therefore$ Minimum value of a + b + c + d for given constant product abcd will be when a = b = c = d
$\therefore$ a = b = c = d
As $abcd=81=3^4$
$\therefore$ Minimum value of a + b + c + d = 3 + 3 + 3 + 3 = 12