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The expression \(x[n]y\) is defined for positive values of \(x\) and \(y\) and for positive integer values of \(n\) as follows:
\(x[1]y = x^y,\)
If \(n\) is odd, \(x[n+1]y = (x[n]y)^x,\)
If \(n\) is even, \(x[n+1]y = (x[n]y)^y.\)
If \(y = \dfrac12\) and \(x[4]y = 2,\) then \(x =\)
A. \(\dfrac14\)
B. \(\dfrac12\)
C. \(1\)
D. \(2\)
E. \(4\)
Answer: D
Source: Manhattan GMAT
\(x[1]y = x^y,\)
If \(n\) is odd, \(x[n+1]y = (x[n]y)^x,\)
If \(n\) is even, \(x[n+1]y = (x[n]y)^y.\)
If \(y = \dfrac12\) and \(x[4]y = 2,\) then \(x =\)
A. \(\dfrac14\)
B. \(\dfrac12\)
C. \(1\)
D. \(2\)
E. \(4\)
Answer: D
Source: Manhattan GMAT
