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

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Gmat_mission: Legendary Member; Posts: 1622; Joined: Thu Mar 01, 2018 7:22 amFollowed by: 2 members

by Gmat_mission » Sun Jan 31, 2021 2:50 pm

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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

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Source: Beat The GMAT — Problem Solving | Sun Jan 31, 2021 2:50 pm

deloitte247: Legendary Member; Posts: 2214; Joined: Fri Mar 02, 2018 2:22 pmFollowed by: 5 members

Re: For all positive integers $m, [m] = 3m$ when $m$ is odd and $[m] = \dfrac12 m$ when $m$ is even. What is

by deloitte247 » Tue Feb 02, 2021 11:24 pm

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

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Brent@GMATPrepNow: GMAT Instructor; Posts: 16207; Joined: Mon Dec 08, 2008 6:26 pmFollowed by: 1268 members; Location: Vancouver, BC; Thanked: 5254 times; GMAT Score:770

Re: For all positive integers $m, [m] = 3m$ when $m$ is odd and $[m] = \dfrac12 m$ when $m$ is even. What is

by Brent@GMATPrepNow » Wed Feb 03, 2021 9:58 am

Gmat_mission wrote: ↑
Sun Jan 31, 2021 2:50 pm
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

Brent Hanneson - Creator of GMATPrepNow.com

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