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Re: The symbol # represents one of the four arithmetic operation [#permalink]
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
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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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)
The answer is 'yes'.

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

Therefore, A is the answer.

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

We can rephrase this question as: Does # represent addition/multiplication?

(1) Yes, given the information in this statemen we can conclude # represents addition and multiplication. SUFFICIENT.

(2) This is true for addition or subtraction. INSUFFICIENT.

Answer is A.
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Re: The symbol # represents one of the four arithmetic operation [#permalink]
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Step 1: Analyse Question Stem

The operator # can represent ONE of the four arithmetic operations.
We have to find out if (5 # 6) # 2 = 5 # (6 # 2).

The given equation holds only when the operator represents addition or multiplication. Therefore, the question can be rephrased as “Does the operator represent addition or multiplication?”

Step 2: Analyse Statements Independently (And eliminate options) – AD / BCE

Statement 1: 5 # 6 = 6 # 5

The above equation holds good when the operator represents addition or multiplication.

If # represents addition, 5 + 6 = 6 + 5
If # represents multiplication, 5 * 6 = 6 * 5

The data given in statement 1 alone is sufficient to say that (5 # 6) # 2 = 5 # (6 # 2).
Statement 1 alone is sufficient. Answer options B, C and E can be eliminated.


Statement 2: 2 # 0 = 2

The above equation holds good when the operator represents addition or subtraction.

The data in statement 2 is insufficient to answer the question with a definite YES or NO, since, based on the definition of the operator #, the main question can be answered with a YES and NO.
Statement 2 alone is insufficient. Answer option D can be eliminated.

The correct answer option is A.
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Re: The symbol # represents one of the four arithmetic operation [#permalink]
I got confused by the statement "symbol # represents one of the four arithmetic operations"

In statement 1 it is Multiplication and addition.
And in statement 2 it is subtraction and addition.

I selected Option C.
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Re: The symbol # represents one of the four arithmetic operation [#permalink]
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Re: The symbol # represents one of the four arithmetic operation [#permalink]
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