Question

For all positive integers w and y, where w$>$ y, let the operation $\otimes$ be defined by w $\otimes$y$=\frac{2^{w+y}}{2^{w-y}}$. For how many positive integers w is w$\otimes 1$ equal to $4$?

• A. None
• B. One
• C. Two
• D. Four
• E. More than four

Answer 1

The correct option is E More than four

$w⨂1=\frac{2^{w+1}}{2^{w-1}}=\frac{2^w.2}{2^w.\frac{1}{2}}=4$

Hence for all integers w greater than 1 $w⨂1=4$ is true.

Correct answer is E.