For all positive integers m, m* = 3m when

[Guest]

For all positive integers m, m* = 3m when m is odd and m* = m/2 when m is even. Which of the foll is equivalent to (9*) x (6*)

NOTE: ANSWER CHOICES EDITED BY RON ON JULY 9, 2009
1. 81*
2. 54*
3. 36*
4. 27*
5. 18*

Answer : 27*

I got 81 as the answer. Am i missing something ?

[Khalid]

For all positive integers m, m* = 3m when m is odd and m* = m/2 when m is even. Which of the foll is equivalent to (9*) x (6*)

NOTE: ANSWER CHOICES EDITED BY RON ON JULY 9, 2009
1. 81*
2. 54*
3. 36*
4. 27*
5. 18*

Answer : 27.

I got 81 as the answer. Am i missing something ?

Tricky question. They are asking which one of the below is equal to the above>
27*= 3 x 27 = 81 = 9*x6*

[RonPurewal]

For all positive integers m, m* = 3m when m is odd and m* = m/2 when m is even. Which of the foll is equivalent to (9*) x (6*)

NOTE: ANSWER CHOICES EDITED BY RON ON JULY 9, 2009
1. 81*
2. 54*
3. 36*
4. 27*
5. 18*

Answer : 27.

I got 81 as the answer. Am i missing something ?

Tricky question. They are asking which one of the below is equal to the above>
27*= 3 x 27 = 81 = 9*x6*

yes.
you have to apply the definition to the answer choices, too. be careful! they pull dirty little tricks like this all the time. always read problem statements very, very carefully.
and, in the case of short problems like this one, read them again, just to be sure. you really don't want to miss a problem that you understand completely, just because you weren't paying attention.

[Ksenia]

All the answer choices should be in squares in the original question, in your question square = star sign ("*").
So, the correct answer is 27*

[JonathanSchneider]

Note squares, exactly, because 27^2 is a much larger number. BUT we do need to see that there is an * after each of the numbers in the answer choices, or else 81 is in fact correct.

(The original problem actually shows a * symbol before and after the m, and again before and after each of the answer choices. As posted above, however, the problem would yield the answer that the poster originally came up with. Be careful how you read problems - and post them : )

[commit.gmat]

From the other people's comments, I see that the question is posted incorrectly. Can someone please correct the problem. it is very misleading.

thanks

[RonPurewal]

From the other people's comments, I see that the question is posted incorrectly. Can someone please correct the problem. it is very misleading.

thanks

done. see above.

jonathan was quite new as a moderator when he posted on this thread; he may not have been aware that he had the capacity to edit the other posters' posts.

[goutam.datta]

i AM STILL MISSING THE ANSWER, how the answer is 27.

could some one help here please. thx.

[RonPurewal]

i AM STILL MISSING THE ANSWER, how the answer is 27.

could some one help here please. thx.

it's not 27, it's 27*, with the star. if you follow the directions for the star, you'll find that 27* is 81, which is the answer to the problem.

[rustom.hakimiyan]

For all positive integers m, m* = 3m when m is odd and m* = m/2 when m is even. Which of the foll is equivalent to (9*) x (6*)

NOTE: ANSWER CHOICES EDITED BY RON ON JULY 9, 2009
1. 81*
2. 54*
3. 36*
4. 27*
5. 18*

Answer : 27.

I got 81 as the answer. Am i missing something ?

Tricky question. They are asking which one of the below is equal to the above>
27*= 3 x 27 = 81 = 9*x6*

yes.
you have to apply the definition to the answer choices, too. be careful! they pull dirty little tricks like this all the time. always read problem statements very, very carefully.
and, in the case of short problems like this one, read them again, just to be sure. you really don't want to miss a problem that you understand completely, just because you weren't paying attention.

Hi Ron,

I'm a little confused by this question as a whole. I can easily follow this in retrospect but i'm still not certain as to WHY:

9* X 6* =>

9*=3m
m=3

6*=1/2m
m=12

Therefore: 12*3 = 36*

I'm a little confused as to what information in the question stem dictates that you are supposed to plug in 9 for m vs. solve for m with the 9*? More importantly, why do we convert it back to the "*" in the end?

Thanks

[RonPurewal]

9* X 6* =>

9*=3m
m=3

6*=1/2m
m=12

These are both backwards.

The * sign is an operator. That means it does something to the number attached to it.

You can express this operator in words: "The star multiplies odds by 3, but cuts evens in half."
That might help, because it seems to be the presence of the letter "m" that's giving you grief here.

So, 9* and 6* just mean that you should follow the directions with 9 and 6, respectively.
9* = 3 times 9 = 27
6* = half of 6 = 3.

Since the star is on all the answer choices, you just have to follow the same directions for those.

[RonPurewal]

This is a lot like the "√" sign. If I ask you what √9 is, you'll say 3; √16, you'll say 4; etc.

You don't have to solve for anything (= do the process in reverse) unless the sign/symbol is on an unknown, and the RESULT is what you're given.

E.g., if I tell you that √x = 9, then x is not 3; it's 81. ("√x = 9" means "If you take unknown thing x and follow the directions, THEN you'll GET 9.")

So, if I told you that x* = 10, then x would be 20. (As opposed to 10* = 5.)
If I told you that x* = 9, then x would be 3. (As opposed to 9* = 27.)

Hope that helps.