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![If (a*b)*c implies (a + b) is a multiple of c, is [m*(−n)]*12? (1) m](/forum/styles/gmatclub_light/imageset/icon_post_target_unread.svg "If (a*b)*c implies (a + b) is a multiple of c, is [m*(−n)]*12? (1) m"){kind=icon}
17 Jul 2019, 04:43
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C
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Difficulty:
45%
(medium)
Question Stats:
67% (01:54) correct
33%
(01:57)
wrong
based on 152
sessions
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Date
Time
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If (a*b)*c implies (a + b) is a multiple of c, is [m*(−n)]*12?
(1) m = 5n
(2) When a positive integer n is divided by 12, the remainder is 3.
(1) m = 5n
(2) When a positive integer n is divided by 12, the remainder is 3.
18 Jul 2019, 03:22
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This is an interesting question because, although it is a question on functions, you also need to know about divisibility concepts to be able to solve this question.
A number is divisible by 12 if it is divisible by both 3 and 4.
From the question data, (a*b)*c implies (a+b) is a multiple of c. So, the question that we are trying to answer is if (m-n) is a multiple of 12.
From statement I, m = 5n. Therefore, m – n = 4n. From this, we can only say that m-n is a multiple of 4. Depending on the value of n, 4n may or may not be a multiple of 4.
Statement I alone is insufficient. Answer options A and D can be eliminated. Possible answer options are B, C or E.
From statement II, n = 12k + 3, where k is a positive integer. Depending on the values of k, n can take on different values. We don’t have any information about m.
It’s impossible to answer the main question uniquely.
Answer option B can be eliminated. Possible answer options now, are C or E.
Combining statements I and II, from the first statement, we know that m-n = 4n; from the second statement, n = 3 or 15 or 27 and so on.
For any of these values of n, 4n (i.e. m-n) will always be a multiple of 12 since n is definitely a multiple of 3. The combination of statements is sufficient.
The correct answer option is C.
Hope this helps!
A number is divisible by 12 if it is divisible by both 3 and 4.
From the question data, (a*b)*c implies (a+b) is a multiple of c. So, the question that we are trying to answer is if (m-n) is a multiple of 12.
From statement I, m = 5n. Therefore, m – n = 4n. From this, we can only say that m-n is a multiple of 4. Depending on the value of n, 4n may or may not be a multiple of 4.
Statement I alone is insufficient. Answer options A and D can be eliminated. Possible answer options are B, C or E.
From statement II, n = 12k + 3, where k is a positive integer. Depending on the values of k, n can take on different values. We don’t have any information about m.
It’s impossible to answer the main question uniquely.
Answer option B can be eliminated. Possible answer options now, are C or E.
Combining statements I and II, from the first statement, we know that m-n = 4n; from the second statement, n = 3 or 15 or 27 and so on.
For any of these values of n, 4n (i.e. m-n) will always be a multiple of 12 since n is definitely a multiple of 3. The combination of statements is sufficient.
The correct answer option is C.
Hope this helps!
18 Jul 2019, 08:11
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This question makes no sense, notationally or logically. It might look like a question "about functions" as the post above says, but it is not, because the "*" in the question is not a well-defined function at all. Mathematical notation can't be used in the way this question is trying to use it, and Statement 2 doesn't even make sense semantically (do they mean "*the* positive integer n"?). So test takers should just ignore this question. If a GMAT question wants to ask "is m-n divisible by 12", the question will simply ask that, and the question will also tell you in advance that m and n are integers.
