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Suppose you have three variable resistors each of range 15 ohms to 30 ohms. Which of the following values of equivalent resistance cannot be obtained using these 3 variable resistors?

$\begin {array} {1 1} (A)\;10\Omega & \quad (B)\;45\Omega \\ (C)\;61\Omega & \quad (D)\;100\Omega \end {array}$

The range of equivalent resistances possible to generate using these is
$\large\frac{15}{3}$$ohms$ to $30 \times 3\: ohms.$ Since variable resistors have a continuous range,
equivalent resistors have a continuous range. Hence, one can obtain all values
between $5\: ohms\: to\: 90\: ohms.$
Ans : (D)
edited Mar 14, 2014