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Manager  Joined: 07 Feb 2010
Posts: 114
The symbol # represents one of the four arithmetic operation  [#permalink]

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Difficulty:   45% (medium)

Question Stats: 63% (01:17) correct 37% (01:18) wrong based on 491 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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Math Expert V
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Re: if the symbol represents one of the four operations  [#permalink]

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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.

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

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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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The easiest way is to check for all different operations

1) multiplication gives you a YES
2) addition gives you a YES
3) division gives you a NO
4) subtraction gives you a NO

statement 1 is only possible with 1) or 2), hence, sufficient

statement 2 is possible with both 2) (YES) and 4) (NO), hence, not sufficient
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Re: The symbol # represents one of the four arithmetic operation  [#permalink]

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anilnandyala wrote:
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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Visit https://www.mathrevolution.com/gmat/lesson for details.

Since we have one operation(#), we can assume we have 1 variable (#) and 0 equations, D is most likely to be the answer. So, we should consider each condition on its own first.

Condition 1)
The possible operations are + and x for condition 1), because 5+6=6+5, 5x6=6x5, but 5-6≠6-5, 5÷6≠6÷5
Both operations have associative properties and we have (5#6)#2=5#(6#2)

Since condition 1) yields a unique solution, it is sufficient

Condition 2)
The possible operations are + and - for condition 1), because 2+0=2, 2-0=2, but 2x0≠2, 2÷0 is not defined.
If # is an addition, then we have (5+6)+2=5+(6+2) and the answer is 'yes'.
If # is a subtraction, then we have (5-6)-2≠5-(6-2) and the answer is 'no'.

Since condition 2) does not yield a unique solution, it is not sufficient

If the original condition includes “1 variable”, or “2 variables and 1 equation”, or “3 variables and 2 equations” etc., one more equation is required to answer the question. If each of conditions 1) and 2) provide an additional equation, there is a 59% chance that D is the answer, a 38% chance that A or B is the answer, and a 3% chance that the answer is C or E. Thus, answer D (conditions 1) and 2), when applied separately, are sufficient to answer the question) is most likely, but there may be cases where the answer is A,B,C or E.
_________________ Re: The symbol # represents one of the four arithmetic operation   [#permalink] 07 Nov 2019, 11:15
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