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If A*B is the greatest common factor of A and B, A$B is defi

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If A*B is the greatest common factor of A and B, A$B is defi [#permalink] New post 18 Apr 2018, 12:12
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If A*B is the greatest common factor of A and B, A$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?

(A) 42
(B) 45
(C) 48
(D) 52
(E) 60
[Reveal] Spoiler: OA

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Re: If A*B is the greatest common factor of A and B, A$B is defi [#permalink] New post 08 May 2018, 04:56
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The question requires attention to details and this is what GRE loves to play us with(even in the RC questions)

So here we are given 12∩15 in the formula of (A*B) $ (A$B)

A*B = 12*15 =180
and A$B is the LCM of 12 and 15 is 60 NOW

180 $(LCM) 60 = 60 which is E
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Re: If A*B is the greatest common factor of A and B, A$B is defi [#permalink] New post 08 May 2018, 20:10
Little confused here. Does ' * ' mean multiplication sigh here or just a symbol like ' $ '? And please explain the solution? Took me 5 mins and I guessed the answer
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Re: If A*B is the greatest common factor of A and B, A$B is defi [#permalink] New post 09 May 2018, 03:44
kruttikaaggarwal wrote:
Little confused here. Does ' * ' mean multiplication sigh here or just a symbol like ' $ '? And please explain the solution? Took me 5 mins and I guessed the answer



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 :)
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Re: If A*B is the greatest common factor of A and B, A$B is defi [#permalink] New post 09 May 2018, 08:26
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* is not multiplication, it is a symbol which means the GCF of 2 numbers.
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Re: If A*B is the greatest common factor of A and B, A$B is defi [#permalink] New post 09 May 2018, 12:40
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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?
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Re: If A*B is the greatest common factor of A and B, A$B is defi [#permalink] New post 09 May 2018, 14:00
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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.

Quote:
If A*B is the greatest common factor of A and B


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.

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


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

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


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.

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Re: If A*B is the greatest common factor of A and B, A$B is defi [#permalink] New post 13 May 2018, 16:42
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Carcass wrote:
If A*B is the greatest common factor of A and B, A$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?

(A) 42
(B) 45
(C) 48
(D) 52
(E) 60


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
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Re: If A*B is the greatest common factor of A and B, A$B is defi   [#permalink] 13 May 2018, 16:42
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