For all positive integers \(m, [m] = 3m\) when \(m\) is odd and \([m] = \dfrac12 m\) when \(m\) is even. What is

[Gmat_mission]

For all positive integers \(m, [m] = 3m\) when \(m\) is odd and \([m] = \dfrac12 m\) when \(m\) is even. What is \([9]\cdot [6]\) equivalent to?

A. \([81]\)
B. \([54]\)
C. \([37]\)
D. \([27]\)
E. \([18]\)

Answer: D

Source: GMAT Prep

[deloitte247]

Let [m] = f(m)
f(m) = 3m when m is odd and,
f(m) = (1/2) * m when m is even

Target question => Evaluate [9]*[6]
[9] = f(a) = 3*9 since 9 is 0dd
f(a) = 27
[9] = 27 and,
[6] = f(6) = 1/2 * 6, since 6 is even;
f(6) = 3
[6] = 3

[9] * [6] = 27 * 3 = 81
Expressing ([9] * [6]) as m
[m] = f(m) = 81
If m is odd then m = 81/3 = 27 and [27] = 81
If m is even then m = 81 / 1/2 = 81 * 2/1 = 162 and [162] = 81
But the [27] is the only answer on the option
So, [9] * [6] is equivalent to [27]

Answer = D

[Brent@GMATPrepNow]

For all positive integers \(m, [m] = 3m\) when \(m\) is odd and \([m] = \dfrac12 m\) when \(m\) is even. What is \([9]\cdot [6]\) equivalent to?

A. \([81]\)
B. \([54]\)
C. \([37]\)
D. \([27]\)
E. \([18]\)

Answer: D

Source: GMAT Prep

9 is odd, so [9] = (3)(9) = 27
6 is even, so [6] = 6/2 = 3
So, [9] x [6] = 27 x 3 = 81

BEFORE you select answer choice A, notice that 81 has brackets around it.
Since 81 is odd, [81] = (3)(81) = 243
So, answer choice A is NOT correct.

So, which of the 5 answer choices equals 81?

Since 27 is odd, [27] = (3)(27) = 81

So, the correct answer is D

Cheers,
Brent