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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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Math Expert
Joined: 02 Sep 2009
Posts: 52297
If A?B is the greatest common factor of A and B, A~B is defined as the  [#permalink]

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10 May 2018, 00:48
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Difficulty:

5% (low)

Question Stats:

92% (01:41) correct 8% (02:03) wrong based on 73 sessions

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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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Re: If A?B is the greatest common factor of A and B, A~B is defined as the  [#permalink]

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10 May 2018, 03:35
(12?15)= 3
(12~15)= 60
3~60= 60
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Joined: 23 Nov 2017
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GMAT 1: 720 Q51 V36
Re: If A?B is the greatest common factor of A and B, A~B is defined as the  [#permalink]

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10 May 2018, 04:32
1
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]

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13 May 2018, 16:53
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

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Re: If A?B is the greatest common factor of A and B, A~B is defined as the &nbs [#permalink] 13 May 2018, 16:53
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