Yeah, right it took me too almost 5 mins to come up with the answer but the

sign * means --multiplication. $ sigh means LCM of output of A*B and the least common multiple of LCM of A and B.

Hope I have cleared your doubt

* is not multiplication, it is a symbol which means the GCF of 2 numbers.

Okay, so I tried this question again. And from what I know, * is not multiplication. @IshanGRE, I am not sure how you got the LCM of 180 and 60 to be 60. You might wanna re-check that. This is how it will be done:
A=12 and B=15.
Step 1: A*B= 12*15=GCF of 12 and 15=3
Step 2: A$B=12$15= LCM of 12 and 15= 60
Step 3: A∩B=(A*B) $ (A$B)= 12∩15= (12*15) $ (12$15). This is basically asking for LCM of GCF and LCM of 12 and 15= 3 (step 1) $ 60 (step 2) = LCM of 3 and 60= 60

Moderators, please let me know if this is the right way. Also, my main question here is, on test how do we know whether its a symbol of a multiplication sign?

What is making this question challenging (to some extent, however, it is not the hardest question on the planet) is the wording of the question itself.

The same is when you are approaching a test such as GRE: it is tricky, NOT difficult.

Back to the question: always, always break it into chunks. Do not think for a moment to the goal (the question's solution) you have to reach but the way to go through. You will be there without believing you are already in your end zone.



This means that we do have two numbers and we do have the GCF of these. A*B is simply a representation of these numbers. We could call them X and Y or Tom and Jerry. The symbol * is impossible of being a multiplication.



Is the same of above, only that here we do have the LCM



this actually means: the common area (the interception) between A and B. Our A is A*B and our B is A$B: GCF $ LCM where $ is just a symbol to show the LCF.
Actually, we have to find the GCF of A*B, the LCM of A$B and then the LCM of the two combined.

A= 12 and B = 15. The GCF of 12 and 15 is 3. The LCM of 12 and 15 is 60. The LCM of both (3 and 60) is 60. E is the answer.

is it not easy to look this way ??

Ask for further assistance.

Regards

12&15 = (12?15) ~ (12~15)

12?15 = GCF(12, 15) = 3

12~15 = LCM(12, 15) = 60

Thus:

(12?15) ~ (12~15) = 3~60 = LCM(3, 60) = 60

Answer: E

PLEASE BE CAREFULL------
your approach is not correct coz A*B = 12*15 =180 its' not correct. They mean here A*B is (A*B is the greatest common factor of A and B)

If A*B is the greatest common factor of A and B, A$B is defined as the least common multiple of A and B, and A∩B is defined as equal to (A*B) $ (A$B), then what is the value of 12∩15? Is this means, at last, we need the LCM? But as far as I remember 12∩15 this symbol means we need to take the GCM. This means the common only. Confused me it.

This questions is Based on LCM and GCD and Custom Characters

A∩B is defined as equal to (A*B) $ (A$B)

12∩15 = (12*15) $ (12$15) [Check out following video to know about Custom Character]

A*B is the greatest common factor of A and B

12*15 = GCD(12,15) = 3 (Check out this video to know about how to find GCD using multiple methods)

A$B is defined as the least common multiple of A and B

12$15 = LCM(12,15) = 3*4*5 = 60

(12*15) $ (12$15) = 3 $ 60 = LCM(3,60) = 60

So, Answer will be E
Hope it helps!

Check out following videos for Functions and Custom Characters and LCM and GCD

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