VJesus12 wrote:If # denotes one of the four arithmetic operations addition, subtraction, multiplication and division, what is the value of 1 # 2?
(1) n # 0 = n for all integers n
(2) n # n = 0 for all integers n
[spoiler]OA=B[/spoiler]
Source: GMAT Prep
Let's take each statement one by one.
(1) n # 0 = n for all integers n
"¢ # as addition
We see that n # 0 = n + 0 = n;
So, 1 # 2 = 1 + 2 = 3.
"¢ # as subtraction
We see that n # 0 = n - 0 = n;
So, 1 # 2 = 1 - 2 = -1.
No unique value of 1 # 2. Insufficient.
(2) n # n = 0 for all integers n
"¢ # as subtraction
We see that n # n = n - n = 0
No other operator can be #.
So, 1 # 2 = 1 - 2 = -1. Sufficient.
The correct answer:
B
Hope this helps!
-Jay
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