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

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Guduna
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For all positive integers m, [m]=3m when m is odd and [m]=(1/2)*m when [#permalink] New post   Updated on: 05 Oct 2022, 10:00
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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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D

Originally posted by Guduna on 08 Sep 2010, 06:38.
Last edited by Bunuel on 05 Oct 2022, 10:00, edited 4 times in total.
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Re: For all positive integers m, [m]=3m when m is odd and [m]=(1/2)*m when [#permalink] New post   08 Sep 2010, 07:41
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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]

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.

Answer: D.

Similar question to practice: https://gmatclub.com/forum/when-x-is-eve ... 32059.html
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Re: For all positive integers m, [m]=3m when m is odd and [m]=(1/2)*m when [#permalink] New post   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)


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

Answer = D
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Re: For all positive integers m, [m]=3m when m is odd and [m]=(1/2)*m when [#permalink] New post   08 Sep 2010, 08:01
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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] New post   10 Jan 2012, 07:59
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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 and [m]=(1/2)*m when [#permalink] New post   03 Apr 2012, 02:41
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Pure deception. Got caught in the trap. :shock:
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Re: For all positive integers m, [m]=3m when m is odd and [m]=(1/2)*m when [#permalink] New post   03 Apr 2012, 06:53
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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 [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.



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] New post   13 Jun 2014, 19:13
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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 [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.

Answer: D.

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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Re: For all positive integers m, [m]=3m when m is odd and [m]=(1/2)*m when [#permalink] New post   14 Jun 2014, 01:50
Expert Reply
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.

Answer: D.

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]=(1/2)*m when [#permalink] New post   10 Dec 2014, 12:35
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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 [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.

Answer: D.

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 and [m]=(1/2)*m when [#permalink] New post   16 Jan 2017, 18:04
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Guduna wrote:
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]


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 [9]*[6].

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

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

Thus, [9]*[6] = 27 x 3 = 81.

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

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

Answer: D
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Re: For all positive integers m, [m]=3m when m is odd and [m]=(1/2)*m when [#permalink] New post   19 Apr 2018, 15:53
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Guduna wrote:
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]


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
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Re: For all positive integers m, [m]=3m when m is odd and [m]=(1/2)*m when [#permalink] New post   20 Feb 2020, 13:10
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.

Answer: D.

Similar question to practice: https://gmatclub.com/forum/when-x-is-eve ... 32059.html


Hi Bunuel

I am getting confused between options [54] and [27] because even though [27] is satisfying the given condition [m]=3m when m is odd ----> [27] = 3*27 =81, but it doesn't satisfy [m]=(1/2)*m
 i.e 1/2*27 won't be an integer, but [54] can satisfy for even & not odd.

Can you please help?
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Re: For all positive integers m, [m]=3m when m is odd and [m]=(1/2)*m when [#permalink] New post   21 Feb 2020, 00:32
Expert Reply
Anurag06 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.

Answer: D.

Similar question to practice: https://gmatclub.com/forum/when-x-is-eve ... 32059.html


Hi Bunuel

I am getting confused between options [54] and [27] because even though [27] is satisfying the given condition [m]=3m when m is odd ----> [27] = 3*27 =81, but it doesn't satisfy [m]=(1/2)*m
 i.e 1/2*27 won't be an integer, but [54] can satisfy for even & not odd.

Can you please help?


I think you misunderstood the question.

[9]*[6] = 27*3 = 81.

Which of the options also give 81?

D. [27] = 3*27 = 81.
81 = 81.

B. [54] = 1/2*54 = 27.
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] New post   24 Apr 2020, 21:44
Bunuel, you are THE MASTER, i really got confused trying to understand the problem.

thank for your explanation, i have it clear now.
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Re: For all positive integers m, [m]=3m when m is odd and [m]=(1/2)*m when [#permalink] New post   26 May 2020, 11:53
The math itself is pretty simple. After calculation, you will get 27 x 3 = 81.
-9 is odd, so apply 3m = 27
-6 is even, so apply m/2 = 3

The trap is that the answers are in boxes. So the potential answers could be [162] (in which case you would apply m/2) or [81] (in which case you would apply 3m). Since the only answer choice available is [81] in this case, D is your answer.
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Re: For all positive integers m, [m]=3m when m is odd and [m]=(1/2)*m when [#permalink] New post   09 Jun 2021, 05:29
Top Contributor
Solution:

This is an elegant question from Function and Custom Characters and here [] represents the function such that

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

Now, [9] = 3*9 = 27 as 9 is an odd number and

[6] = 1/2 * 6 = 3 as 6 is even

=> [9]*[6] = 27 *3 =81

If you check the options now,you would find

A-[81] = 3 * 81 and NOT equal to 81 -Eliminate-
B-[54] = 1/2 *54 and NOT equal to 81 -Eliminate-
C-[37] = 3*37 and NOT equal to 81 -Eliminate-
D-[27]= 3 *27 = 81 and hence this is our appropriate choice.(option d)

Happy Studying :student_woman: !

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Re: For all positive integers m, [m]=3m when m is odd and [m]=(1/2)*m when [#permalink] New post   20 Aug 2021, 00:22
[9]*[6] = 3*3 * 12/2
= 9*6
= 54
m is even
[m]= 54/2
= 27

Hence the correct option id D i.e 27.
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Re: For all positive integers m, [m]=3m when m is odd and [m]=(1/2)*m when [#permalink] New post   19 May 2022, 21:36
For these type of questions you always have to remember this quote...
Quote:
GMAT can't be this easy...
:D :D :D
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Re: For all positive integers m, [m]=3m when m is odd and [m]=(1/2)*m when [#permalink] New post   26 Jul 2022, 04:28
EASILY UNDERSTANDABLE APPROACH:

First, multiply = 9x6=54 (EVEN number)

Now, look at the condition given, as the product above is even, divide by 2, i.e. 54/2=27

Therefore, the answer is 27.
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Re: For all positive integers m, [m]=3m when m is odd and [m]=(1/2)*m when [#permalink]
26 Jul 2022, 04:28
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