The symbol # represents one of the four arithmetic operation

Question

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

Bunuel · Answer

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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pushkarajg · Answer

you can rephrase the question as "does # have associative property i.e does # => + (addition) or *(multiplication)" 
Note: only + and *   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.

SchruteDwight · Answer

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

MathRevolution · Answer

Forget conventional ways of solving math questions. For DS problems, the VA (Variable Approach) method is the quickest and easiest way to find the answer without actually solving the problem. Remember that equal numbers of variables and independent equations ensure a solution. 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) 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.

Basshead · Answer

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.

GMATWhizTeam · Answer

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.

Momsspaghetti · Answer

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.

bumpbot · Answer

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The symbol # represents one of the four arithmetic operation

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