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The symbol # represents one of the four arithmetic operation

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The symbol # represents one of the four arithmetic operation  [#permalink]

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New post 09 Jan 2011, 08:49
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64% (01:17) correct 36% (01:18) wrong based on 444 sessions

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The symbol # represents one of the four arithmetic operations: addition, subtraction, multiplication, and division. Is (5 # 6) # 2 = 5 # ( 6 # 2)?

(1) 5 # 6 = 6 # 5
(2) 2 # 0 = 2

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Re: if the symbol represents one of the four operations  [#permalink]

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New post 09 Jan 2011, 09:22
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The symbol # represents one of the four arithmetic operations: addition, subtraction, multiplication, and division. Is (5 # 6) # 2 = 5 # ( 6 # 2)?

(1) 5 # 6 = 6 # 5 --> # represents either addition or multiplication in any case (5 # 6) # 2 = 5 # ( 6 # 2) is true: (5 + 6) + 2 = 5 + ( 6 + 2) and (5 * 6) * 2 = 5 * ( 6 * 2). Sufficient.

(2) 2 # 0 = 2 --> # represents either addition or subtraction, if it's addition then the answer is YES (as shown above) but if it's subtraction then the answer is NO: (5 - 6) - 2 =-3 and 5 - ( 6 - 2) = 1. Not sufficient.

Answer: A.

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Re: if the symbol represents one of the four operations  [#permalink]

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New post 12 Jan 2011, 17:57
you can rephrase the question as "does # have associative property i.e does # => + (addition) or *(multiplication)"
Note: only + and * [out of all 4 basic operations] have the associative property.

A : a # B = B # A ==> i.e # is either + or * ==> what is asked
B: 2 # 0 = 2 ==> i.e # is + or - | not what we want

Hope this helps.
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Re: The symbol # represents one of the four arithmetic operation  [#permalink]

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New post 17 Oct 2019, 02:54
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Re: The symbol # represents one of the four arithmetic operation   [#permalink] 17 Oct 2019, 02:54
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