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If A?B is the greatest common factor of A and B, A~B is defined as the

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Bunuel
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If A?B is the greatest common factor of A and B, A~B is defined as the [#permalink] New post   Updated on: 15 Jul 2019, 02:59
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E

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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

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Difficulty Level: 500
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E

Originally posted by Bunuel on 10 May 2018, 01:48.
Last edited by Sajjad1994 on 15 Jul 2019, 02:59, edited 1 time in total.
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Re: If A?B is the greatest common factor of A and B, A~B is defined as the [#permalink] New post   10 May 2018, 04:35
(12?15)= 3
(12~15)= 60
3~60= 60
Answer is E
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Re: If A?B is the greatest common factor of A and B, A~B is defined as the [#permalink] New post   10 May 2018, 05:32
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1. If A?B is the greatest common factor of A and B
2. A~B is defined as the least common multiple of A and B
3. A&B is defined as equal to (A?B)~(A~B)

From 3: 12&15 = (12?15)~(12~15)
From 1: (12?15) = HCF (12, 15) = 3
From 2: (12~15) = LCM (12, 15) = 60

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

Choice E
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Re: If A?B is the greatest common factor of A and B, A~B is defined as the [#permalink] New post   13 May 2018, 17:53
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Bunuel 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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If A?B is the greatest common factor of A and B, A~B is defined as the [#permalink] New post   28 Oct 2022, 09:26
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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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If A?B is the greatest common factor of A and B, A~B is defined as the [#permalink]
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