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a-b+c=-b+c when a=0 and not equal for other values.. So both are insufficient.. Am I missing something here?

If # represents one of the operations +, - and *, is a#(b-c)=(a#b)-(a#c)for all numbers a, b and c.

(1) a#1 is not equal to 1#a for some numbers a.

# is neither addition (as a+1=1+a) not multiplication (as a*1=1*a), so # is a subtraction. Then LHS=a#(b-c)=a-b+c and RHS=(a#b)-(a#c)=(a-b)-(a-c)=c-b, so the question becomes "is a-b+c=c-bfor all numbers a, b and c?" --> "is a=0". So when a=0 (and # is a subtraction) then a#(b-c)=(a#b)-(a#c) holds true but not for other values of a, so not for all numbers a, b and c. Answer to the question is NO. Sufficient.

(2) # represents subtraction --> the same as above. Sufficient.

If # represents one of the operations +,- and *, is a # (b-c) = (a#b) – (a#c) for all numbers a, b and c.

(1) a#1 is not equal to 1#a for some numbers a

(2) # represents subtraction

Mods, please to DS section...posted by mistake in PS - apologies

You're told that "#" is either addition, subtraction, or multiplication, and then asked if "#" satisfies the distributive property. Of these three, distribution only holds for multiplication, so if "#" is "*", it holds, and if "#" isn't "*", then it does not hold.

All we really need to know is what operation "#" really is.

(1) This is only true of subtraction, so # is subtraction and the distributive property does not hold. Sufficient. (2) Same as above. Sufficient.