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Intern  Joined: 05 Sep 2010
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For all positive integers m, [m]=3m when m is odd and [m]=(1/2)*m when  [#permalink]

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9
108 00:00

Difficulty:   35% (medium)

Question Stats: 63% (01:10) correct 37% (01:09) wrong based on 1122 sessions

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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 * equivalent to?

A. 
B. 
C. 
D. 
E. 

Originally posted by Guduna on 08 Sep 2010, 06:38.
Last edited by Bunuel on 02 Jun 2019, 23:07, edited 3 times in total.
Edited the question.
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Re: For all positive integers m, [m]=3m when m is odd and [m]=(1/2)*m when  [#permalink]

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53
41
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 * equivalent to?

A. 
B. 
C. 
D. 
E. 

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  equals to 3*9=27;
As 6 is even then  equals to 1/2*6=3;

So *=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 =3*27=81) OR 162 (in this case as 162 is even =162/2=81) --> only  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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Re: For all positive integers m, [m]=3m when m is odd and [m]=(1/2)*m when  [#permalink]

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12
1
 = 9 * 3 = 27

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

 *  = 27 * 3 = 81 ............. (1)

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

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

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

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

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

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

##### General Discussion
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Re: For all positive integers m, [m]=3m when m is odd and [m]=(1/2)*m when  [#permalink]

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Re: For all positive integers m, [m]=3m when m is odd and [m]=(1/2)*m when  [#permalink]

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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 =  = 27 and

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

so we get  *  = 27 *3 = 81

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

[] used for box symbol used in q
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Re: For all positive integers m, [m]=3m when m is odd and [m]=(1/2)*m when  [#permalink]

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2
Bunuel

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

Thanks
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Re: For all positive integers m, [m]=3m when m is odd and [m]=(1/2)*m when  [#permalink]

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1
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 =  = 3m x 1/2m => 54 = 3/2m => solve for m, m=36
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Re: For all positive integers m, [m]=3m when m is odd and [m]=(1/2)*m when  [#permalink]

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1
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 * equivalent to?

A. 
B. 
C. 
D. 
E. 

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  equals to 3*9=27;
As 6 is even then  equals to 1/2*6=3;

So *=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 =3*27=81) OR 162 (in this case as 162 is even =162/2=81) --> only  is in the answer choices.

i had selected A, but then realised my mistake....Buneal the god....wounderful explanation....
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Re: For all positive integers m, [m]=3m when m is odd and [m]=(1/2)*m when  [#permalink]

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

A. 
B. 
C. 
D. 
E. 

We are given that [m] = 3m when m is odd, and [m] = (1/2)*m when m is even, and we must determine the value of *.

Since 9 is odd,  = 3 x 9 = 27.

Since 6 is even,  = (1/2) x 6 = 3.

Thus, * = 27 x 3 = 81.

Now we must determine which “bracketed” answer choice is equal to 81.

Since 27 is odd, we see that  = 27 x 3 = 81.

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Re: For all positive integers m, [m]=3m when m is odd and [m]=(1/2)*m when  [#permalink]

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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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Re: For all positive integers m, [m]=3m when m is odd and [m]=(1/2)*m when  [#permalink]

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1
galaxyblue wrote:
[m] = 3m when m is odd
[m] = 1/2m when m is even
what is x?

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: For all positive integers m, [m]=3m when m is odd and [m]=(1/2)*m when  [#permalink]

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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 =  = 3m x 1/2m => 54 = 3/2m => solve for m, m=36

Going by the answer, they might have calculated this way  =  = 54/2 =27, but I would still go for option A.
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Re: For all positive integers m, [m]=3m when m is odd and [m]=(1/2)*m when  [#permalink]

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Bumping for review and further discussion*. Get a kudos point for an alternative solution!

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Re: For all positive integers m, [m]=3m when m is odd and [m]=(1/2)*m when  [#permalink]

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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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Re: For all positive integers m, [m]=3m when m is odd and [m]=(1/2)*m when  [#permalink]

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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 * equivalent to?

A. 
B. 
C. 
D. 
E. 

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  equals to 3*9=27;
As 6 is even then  equals to 1/2*6=3;

So *=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 =3*27=81) OR 162 (in this case as 162 is even =162/2=81) --> only  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:

 X  =>

=3m
m=3

=1/2m
m=12

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

Thanks
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Re: For all positive integers m, [m]=3m when m is odd and [m]=(1/2)*m when  [#permalink]

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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 * equivalent to?

A. 
B. 
C. 
D. 
E. 

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  equals to 3*9=27;
As 6 is even then  equals to 1/2*6=3;

So *=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 =3*27=81) OR 162 (in this case as 162 is even =162/2=81) --> only  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:

 X  =>

=3m
m=3

=1/2m
m=12

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

Thanks

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

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

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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 * equivalent to?

A. 
B. 
C. 
D. 
E. 

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  equals to 3*9=27;
As 6 is even then  equals to 1/2*6=3;

So *=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 =3*27=81) OR 162 (in this case as 162 is even =162/2=81) --> only  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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GMAT 1: 690 Q48 V36 Re: For all positive integers m, [m]=3m when m is odd and [m]=(1/2)*m when  [#permalink]

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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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GRE 1: Q169 V154 Re: For all positive integers m, [m]=3m when m is odd and [m]=(1/2)*m when  [#permalink]

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Excellent Question...!!
Here is my approach
Here  = 27
=3 => multiplying them we get 81 = 27*3 so 
SMASH that D
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I have tried to understand this but not sure if I have got it correct.Pls guide me if I am wrong.So [m]=3m when m is odd ,therefore=3*9 =27 and =1/2*6=3 as m is even ;27*3=81 but answer choices are showing us[] so basically we have to pick an answer choice where the[]=81.Two ways we can get is 3*27 and 1/2*162= .Since we do not have answer option 162,so we go with . But still again in the highlighted parts it is not inside the box[] Re: For all positive integers m, [m]=3m when m is odd and [m]=(1/2)*m when   [#permalink] 14 Jul 2016, 07:29

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