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

Question

For all positive integers m, = 3m when m is odd and = (1/2)*m when m is even. What is * equivalent to? A. B. C. D. E. GMAT Prep.JPG

Bunuel · Accepted Answer

For all positive integers m, =3m when m is odd and =(1/2)*m when m is even. What is * equivalent to? A. B. C. D. E. Notice that is just some function such that " =3m when m is odd and =(1/2)*m when m is even". So, =3m when m is odd, =(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: =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. Answer: D. Similar question to practice: https://gmatclub.com/forum/when-x-is-eve ... 32059.html

PareshGmat · Answer

= 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

Answer = D

Guduna · Answer

Bunuel

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

Thanks

kp1811 · Answer

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

m is 6 (even) then   =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

stevie1111 · Answer

Pure deception. Got caught in the trap. :shock:

harshavmrg · Answer

i had selected A, but then realised my mistake....Buneal the god....wounderful explanation....

russ9 · Answer

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   functions were multiplied, the answer is also in a   (function form). Why is that wrong?

Thanks

Bunuel · Answer

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

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

Hope it's clear.

marcosgensollen · Answer

Easy math but very tricky. Excelent explanation by Bunuel.

ScottTargetTestPrep · Answer

We are given that   = 3m when m is odd, and   = (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.

Answer: D

BrentGMATPrepNow · Answer

9 is odd, so   = (3)(9) = 27
6 is even, so   = 6/2 = 3
So,   x   = 27 x 3 =  81

BEFORE you select answer choice A  , notice that 81 has brackets around it. 
Since 81 is odd,   = (3)(81) =  243 
So, answer choice A is NOT correct.

So, which of the 5 answer choices equals  81 ?

Since 27 is odd,   = (3)(27) =  81

So, the correct answer is D

Cheers,
Brent

Anurag06 · Answer

Hi Bunuel

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

Can you please help?

Bunuel · Answer

I think you misunderstood the question.

*  = 27*3 =  81 .

Which of the options also give 81?

D.   = 3*27 = 81.
 81 = 81 .

B.   = 1/2*54 = 27.
 27 ≠ 81

Alvarito · Answer

Bunuel, you are THE MASTER, i really got confused trying to understand the problem.

thank for your explanation, i have it clear now.

nishantkurup · Answer

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   (in which case you would apply m/2) or   (in which case you would apply 3m). Since the only answer choice available is     in this case, D is your answer.

CrackverbalGMAT · Answer

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

!

Devmitra Sen
GMAT SME

! Devmitra Sen GMAT SME

SOLVE55555 · Answer

*  = 3*3 * 12/2
 = 9*6
 = 54
 m is even
 = 54/2
 = 27

Hence the correct option id D i.e 27.

kinshukdudeja · Answer

For these type of questions you always have to remember this quote...

shubham4MBA · Answer

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.

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

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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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