Data Sufficiency

This question is from the MBA.com practice test 2.

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

Statement (2) ALONE is sufficient, but statement (1) along in not sufficient.

This is the right answer, but I'm not sure why. Could someone help me with the logic of this?

Thanks!

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

=> n # 0 = n can be : n - 0 = n OR n + 0 = n then # can be + or -

(2) n # n = 0 for all integers n

=> n - n = 0 : ok
=> n + n = 0 :nok
=> n * n = 0 :nok
=> n / n = 0 :nok

Thanks!!!

zozo123 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

=> n # 0 = n can be : n - 0 = n OR n + 0 = n then # can be + or -

(2) n # n = 0 for all integers n

=> n - n = 0 : ok
=> n + n = 0 :nok
=> n * n = 0 :nok
=> n / n = 0 :nok

In 2) - what if n = 0 (because it says for all integers n)?
=> n - n = 0 : ok
=> n + n = 0 :ok
=> n * n = 0 :ok
=> n / n = 0 :nok

so we can't tell what is the function "#".

is there anything wrong in above explanation because I think answer should be E.

mendiratta wrote:
In 2) - what if n = 0 (because it says for all integers n)?
=> n - n = 0 : ok
=> n + n = 0 :ok
=> n * n = 0 :ok
=> n / n = 0 :nok

so we can't tell what is the function "#".

is there anything wrong in above explanation because I think answer should be E.

(2) says n#n = 0, for all integers n. By virtue of being a statement
that is true, the condition HAS to be true for all integers n. This means, for
any value of n, n#n should be = 0. So, if the condition is satisfied
for n=0 and not satisfied for n=1, the above statement doesn't
hold true.