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02 Feb 2022, 06:16
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Difficulty:
25%
(medium)
Question Stats:
86% (02:23) correct
14%
(02:01)
wrong
based on 42
sessions
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Not Attempted Yet
The symbols \(\&\) and \(\#\) each denote one of the four arithmetic operations: addition, subtraction, multiplication and division. If the symbols denote different arithmetic operations such that and \(a\&b\#c = c\#b\&a\), where \(a\), \(b\) and \(c\) are distinct positive integers, what is the value of \(4\&5\#4\)?
A. -24
B.-16
C. 16
D. 24
E. 26
A. -24
B.-16
C. 16
D. 24
E. 26
Archived Topic
Hi there,
This topic has been closed and archived due to inactivity or violation of community quality standards. No more replies are possible here.
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02 Feb 2022, 06:40
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Bunuel
There's an issue with the wording of the question. On the GMAT, if a question tells you "a, b and c are distinct positive integers", the question means "a, b and c are different fixed positive integers, and we're just not telling you exactly what they're equal to". But if that's what this question means, then there are several possibilities for the operations "&" and "#". For example, "&" can be subtraction, and "#" can be multiplication, if a = 6, b = 3 and c = 2. Then we get 6 - 3*2 = 2*3 - 6, which is true, and then 4&5#4 = 4 - 5*4 = -16.
But I think the question means to say that the relationship a&b#c = c#b&a is true for any three distinct positive integers a, b and c. Then the operations can't be division or subtraction, because those operations aren't reversible. It can only be that & and # represent addition and multiplication, in one order or the other. Then 4&5#4 = 4*5 + 4 or 4 + 5*4, and either way the answer is 24.
23 Sep 2025, 05:49
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solution please.
Archived Topic
Hi there,
This topic has been closed and archived due to inactivity or violation of community quality standards. No more replies are possible here.
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Thank you for understanding, and happy exploring!
