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# For all positive integers m, [m]=3m when m is odd

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For all positive integers m, [m]=3m when m is odd [#permalink]

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08 Sep 2010, 06:38
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For all positive integers m, [m]=3m when m is odd and [m]=(1/2)*m when m is even. What is [9]*[6] equivalent to?

A. [81]
B. [54]
C. [37]
D. [27]
E. [18]
[Reveal] Spoiler: OA

Last edited by Bunuel on 23 Jul 2013, 10:37, edited 2 times in total.
Edited the question.
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08 Sep 2010, 07:41
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Guduna wrote:
For all positive integers m, m*= 3m when m is odd and m*=1/2 when m is even. Which of the following is equivalent to 9* x 6*
81
54
36
27
18

Pleas post the questions in their original form.

For all positive integers m, [m]=3m when m is odd and [m]=(1/2)*m when m is even. What is [9]*[6] equivalent to?

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

Notice that [] is just some function such that "[m]=3m when m is odd and [m]=(1/2)*m when m is even".

So, [m]=3m when m is odd, [m]=(1/2)*m when m is even.
As 9 is odd then [9] equals to 3*9=27;
As 6 is even then [6] equals to 1/2*6=3;

So [9]*[6]=27*3=81. Note that numbers in the answer choices are also in boxes, so we have: [m]=81. m could be 27 (in this case as 27 is odd [27]=3*27=81) OR 162 (in this case as 162 is even [162]=162/2=81) --> only [27] is in the answer choices.

Similar question to practice: when-x-is-even-x-2-1-when-x-is-odd-2x-1-then-132059.html
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08 Sep 2010, 08:01
Bunuel

Thank you so much I didn't look at the answers that they were also in squares..

Thanks
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08 Dec 2010, 20:36
got answer D is explained above. Bunuel good point on the even number bracket as well for the function. Did not think of that.
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For all positive integers m, [m]=3m when m is odd and [m]= [#permalink]

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22 Nov 2011, 18:33
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For all positive integers m, [m]=3m when m is odd and [m]=(1/2)*m when m is even. What is [9]*[6] equivalent to?

A. [81]
B. [54]
C. [37]
D. [27]
E. [18]
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Last edited by Bunuel on 07 Apr 2012, 09:28, edited 1 time in total.
Edited the question
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22 Nov 2011, 22:12
galaxyblue wrote:
[m] = 3m when m is odd
[m] = 1/2m when m is even
what is [9]x[6]?

A 81
B 54
C 36
D 27
E 18

9 is odd, 6 is even.

By the way this is set up, it should be 3*9*(1/2*6)

with that said, 27*3 should be A IMO
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23 Nov 2011, 06:46
rooster wrote:

9 is odd, 6 is even.

By the way this is set up, it should be 3*9*(1/2*6)

with that said, 27*3 should be A IMO

That is what I got, but it is not the answer.

I even set it up like: 9 = 3m, therefore m is 3 and 6 = 1/2 m, then m = 12. So 12 x 3 = 36. Still wrong.

So then I did 9x6 = [54] = 3m x 1/2m => 54 = 3/2m => solve for m, m=36
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Re: Formula Question - Gmatprep [#permalink]

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10 Jan 2012, 07:59
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Janealams wrote:
I have exam tomorrow. I will really appreciate if any of you can explain solution to this question. Thanks

Why should we not solve 9 and 6 individually?

when m is 9 (odd) then [m] = 3 * m = [9] = 27 and

m is 6 (even) then [m] =1/2m = [6] = (1/2)*6 = 3

so we get [9] * [6] = 27 *3 = 81

but answers are all in [] so 81 (odd and hence in 3m format) will be equal to [27]

[] used for box symbol used in q
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Re: For all positive integers m, [m]=3m when m is odd [#permalink]

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03 Apr 2012, 02:41
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Pure deception. Got caught in the trap.
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03 Apr 2012, 06:53
Bunuel wrote:
Guduna wrote:
For all positive integers m, m*= 3m when m is odd and m*=1/2 when m is even. Which of the following is equivalent to 9* x 6*
81
54
36
27
18

Pleas post the questions in their original form.

For all positive integers m, [m]=3m when m is odd and [m]=(1/2)*m when m is even. What is [9]*[6] equivalent to?

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

Note that [] is just some function such that "[m]=3m when m is odd and [m]=(1/2)*m when m is even".

So, [m]=3m when m is odd, [m]=(1/2)*m when m is even.
As 9 is odd then [9] equals to 3*9=27;
As 6 is even then [6] equals to 1/2*6=3;

So [9]*[6]=27*3=81. Note that numbers in the answer choices are also in boxes, so we have: [m]=81. m could be 27 (in this case as 27 is odd [27]=3*27=81) OR 162 (in this case as 162 is even [162]=162/2=81) --> only [27] is in the answer choices.

i had selected A, but then realised my mistake....Buneal the god....wounderful explanation....
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07 Apr 2012, 09:23
galaxyblue wrote:
rooster wrote:

9 is odd, 6 is even.

By the way this is set up, it should be 3*9*(1/2*6)

with that said, 27*3 should be A IMO

That is what I got, but it is not the answer.

I even set it up like: 9 = 3m, therefore m is 3 and 6 = 1/2 m, then m = 12. So 12 x 3 = 36. Still wrong.

So then I did 9x6 = [54] = 3m x 1/2m => 54 = 3/2m => solve for m, m=36

Going by the answer, they might have calculated this way [9][6] = [54] = 54/2 =27, but I would still go for option A.
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07 Apr 2012, 09:27
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Expert's post
galaxyblue wrote:
[m] = 3m when m is odd
[m] = 1/2m when m is even
what is [9]x[6]?

A 81
B 54
C 36
D 27
E 18

For all positive integers m, [m]=3m when m is odd and [m]=(1/2)*m when m is even. What is [9]*[6] equivalent to?

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

Note that [] is just some function such that "[m]=3m when m is odd and [m]=(1/2)*m when m is even".

So, [m]=3m when m is odd, [m]=(1/2)*m when m is even.
As 9 is odd then [9] equals to 3*9=27;
As 6 is even then [6] equals to 1/2*6=3;

So [9]*[6]=27*3=81. Note that numbers in the answer choices are also in boxes, so we have: [m]=81. m could be 27 (in this case as 27 is odd [27]=3*27=81) OR 162 (in this case as 162 is even [162]=162/2=81) --> only [27] is in the answer choices.

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Re: For all positive integers m, [m]=3m when m is odd [#permalink]

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21 Jun 2013, 03:47
Bumping for review and further discussion*. Get a kudos point for an alternative solution!

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13 Apr 2014, 02:32
AJ21 wrote:
For all positive integers m, m = 3m when m is odd and m = 1/2m when m is even. Which of the following is equivalent to 9 x 6

a.81
b.54
c.36
d.27
e.18

Hi,

9 x 6 = 3*9*6/2 = 27*3 = 81

So, from the given options the answer is A.

But as the official answer you have given is D, The options should have _ line under them.
If options are:

a.81
b.54
c.36
d.27
e.18

The answer would be D because 27= 3*27 = 81

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13 Jun 2014, 19:13
Bunuel wrote:
Guduna wrote:
For all positive integers m, m*= 3m when m is odd and m*=1/2 when m is even. Which of the following is equivalent to 9* x 6*
81
54
36
27
18

Pleas post the questions in their original form.

For all positive integers m, [m]=3m when m is odd and [m]=(1/2)*m when m is even. What is [9]*[6] equivalent to?

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

Notice that [] is just some function such that "[m]=3m when m is odd and [m]=(1/2)*m when m is even".

So, [m]=3m when m is odd, [m]=(1/2)*m when m is even.
As 9 is odd then [9] equals to 3*9=27;
As 6 is even then [6] equals to 1/2*6=3;

So [9]*[6]=27*3=81. Note that numbers in the answer choices are also in boxes, so we have: [m]=81. m could be 27 (in this case as 27 is odd [27]=3*27=81) OR 162 (in this case as 162 is even [162]=162/2=81) --> only [27] is in the answer choices.

Similar question to practice: when-x-is-even-x-2-1-when-x-is-odd-2x-1-then-132059.html

Hi Bunuel,

I'm a little confused by this question as a whole. I can easily follow your steps but the way I did/interpreted the problem is as follows:

[9] X [6] =>

[9]=3m
m=3

[6]=1/2m
m=12

Therefore: 12*3 = 36 since since both of the [m] functions were multiplied, the answer is also in a [36] (function form). Why is that wrong?

Thanks
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14 Jun 2014, 01:50
russ9 wrote:
Bunuel wrote:
Guduna wrote:
For all positive integers m, m*= 3m when m is odd and m*=1/2 when m is even. Which of the following is equivalent to 9* x 6*
81
54
36
27
18

Pleas post the questions in their original form.

For all positive integers m, [m]=3m when m is odd and [m]=(1/2)*m when m is even. What is [9]*[6] equivalent to?

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

Notice that [] is just some function such that "[m]=3m when m is odd and [m]=(1/2)*m when m is even".

So, [m]=3m when m is odd, [m]=(1/2)*m when m is even.
As 9 is odd then [9] equals to 3*9=27;
As 6 is even then [6] equals to 1/2*6=3;

So [9]*[6]=27*3=81. Note that numbers in the answer choices are also in boxes, so we have: [m]=81. m could be 27 (in this case as 27 is odd [27]=3*27=81) OR 162 (in this case as 162 is even [162]=162/2=81) --> only [27] is in the answer choices.

Similar question to practice: when-x-is-even-x-2-1-when-x-is-odd-2x-1-then-132059.html

Hi Bunuel,

I'm a little confused by this question as a whole. I can easily follow your steps but the way I did/interpreted the problem is as follows:

[9] X [6] =>

[9]=3m
m=3

[6]=1/2m
m=12

Therefore: 12*3 = 36 since since both of the [m] functions were multiplied, the answer is also in a [36] (function form). Why is that wrong?

Thanks

[9] doe not equal to 3m.
[m] = 3m when m is odd. 9 is odd , hence [9] = 3*9 = 27.

The same way, [6] does not equal to 1/2*m.
[m]=(1/2)*m when m is even. 6 is even, hence [6] = 1/2*6 = 3.

Hope it's clear.
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Re: For all positive integers m, [m]=3m when m is odd and [m]= [#permalink]

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19 Jun 2014, 04:51
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[9] = 9 * 3 = 27

$$[6] = \frac{6}{2} = 3$$

[9] * [6] = 27 * 3 = 81 ............. (1)

From all the given options, we require to calculate to get answer 81

A. [81] = 81 * 3 = 243 .... IGNORE

$$B. [54] = \frac{54}{2} = 27 ......... IGNORE$$

C. [37] = 37 * 3 = 111 ..... IGNORE

D. [27] = 27 * 3 = 81 ........... Matches with (1)

$$E. [18] = \frac{18}{2} = 9 ........... IGNORE$$

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Re: For all positive integers m, [m]=3m when m is odd [#permalink]

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10 Dec 2014, 12:35
Bunuel wrote:
Guduna wrote:
For all positive integers m, m*= 3m when m is odd and m*=1/2 when m is even. Which of the following is equivalent to 9* x 6*
81
54
36
27
18

Pleas post the questions in their original form.

For all positive integers m, [m]=3m when m is odd and [m]=(1/2)*m when m is even. What is [9]*[6] equivalent to?

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

Notice that [] is just some function such that "[m]=3m when m is odd and [m]=(1/2)*m when m is even".

So, [m]=3m when m is odd, [m]=(1/2)*m when m is even.
As 9 is odd then [9] equals to 3*9=27;
As 6 is even then [6] equals to 1/2*6=3;

So [9]*[6]=27*3=81. Note that numbers in the answer choices are also in boxes, so we have: [m]=81. m could be 27 (in this case as 27 is odd [27]=3*27=81) OR 162 (in this case as 162 is even [162]=162/2=81) --> only [27] is in the answer choices.

Similar question to practice: when-x-is-even-x-2-1-when-x-is-odd-2x-1-then-132059.html

Easy math but very tricky. Excelent explanation by Bunuel.
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Re: For all positive integers m, [m]=3m when m is odd [#permalink]

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24 Mar 2015, 05:11
Dang, I cross-checked this answer and I was thinking, the GMAT would surely test harder questions on this exam and as it was the second question, it would not be this easy..

Well, I got stung, lesson learned, pay as much attention to answer choices as to the question itself...
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Re: For all positive integers m, [m]=3m when m is odd and [m]= [#permalink]

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22 Apr 2016, 17:28
Excellent Question...!!
Here is my approach
Here [9] = 27
[6]=3 => multiplying them we get 81 = 27*3 so [27]
SMASH that D
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Re: For all positive integers m, [m]=3m when m is odd and [m]=   [#permalink] 22 Apr 2016, 17:28

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