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

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For all positive integers m, [m]=3m when m is odd and [m]= [#permalink]  22 Nov 2011, 17:33
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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]
[Reveal] Spoiler: OA

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Last edited by Bunuel on 07 Apr 2012, 08:28, edited 1 time in total.
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Re: Special Characters [#permalink]  22 Nov 2011, 21:12
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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Re: Special Characters [#permalink]  23 Nov 2011, 05:46
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: Special Characters [#permalink]  07 Apr 2012, 08:23
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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Re: Special Characters [#permalink]  07 Apr 2012, 08:27
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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

Question should read:
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.

Answer: D.
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Re: For all positive integers m, [m]=3m when m is odd and [m]= [#permalink]  16 Jun 2014, 02:07
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Re: For all positive integers m, [m]=3m when m is odd and [m]= [#permalink]  19 Jun 2014, 03:51
[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)

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

Answer = D
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Re: For all positive integers m, [m]=3m when m is odd and [m]=   [#permalink] 19 Jun 2014, 03:51
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