The problem has been transcribed incorrectly.
In the original problem, all of the answer choices including function notation.
The following represents the intent of the problem:

For all positive integers m, @m=3m when m is odd and @m=(1/2)m when m is even. Which of the following is equivalent to @9 x @6?

A - @81
B - @59
C - @36
D - @27
E - @18

Since @m=3m when m is odd, @9 = 3*9 = 27.

Since @m=(1/2)m when m is even, @6 = (1/2)6 = 3.

Thus, @9 * @6 = 27*3 = 81.

Notice the @ symbol in the answer choices.
The correct answer must be the EQUIVALENT of 81.

Answer choice D: @27
Since @m=3m when m is odd, @27 = 3*27 = 81.

The correct answer is D.

Answer choice A is A TRAP.
Always beware of an answer choice that seems TOO EASY or TOO OBVIOUS.

GATGuruNY - spot on my mistake.
I overlooked the symbols.
Thanks for your clarity!

Giovanni

GMATGuruNY wrote:The problem has been transcribed incorrectly.
In the original problem, all of the answer choices including function notation.
The following represents the intent of the problem:

For all positive integers m, @m=3m when m is odd and @m=(1/2)m when m is even. Which of the following is equivalent to @9 x @6?

A - @81
B - @59
C - @36
D - @27
E - @18

Since @m=3m when m is odd, @9 = 3*9 = 27.

Since @m=(1/2)m when m is even, @6 = (1/2)6 = 3.

Thus, @9 * @6 = 27*3 = 81.

Notice the @ symbol in the answer choices.
The correct answer must be the EQUIVALENT of 81.

Answer choice D: @27
Since @m=3m when m is odd, @27 = 3*27 = 81.

The correct answer is D.

Answer choice A is A TRAP.
Always beware of an answer choice that seems TOO EASY or TOO OBVIOUS.