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I am not sure about option 1 as I think it should read "k # l is not equal to l # k for some numbers k" rather than "k # l is not equal to 1 # k for some numbers k". Please correct me if I am wrong.

However Statement 2: Tells us that # repeasents "-". SO k # (l+m) = (k#l) + (k#m) => k - (l+m) = (k-l) + (k-m) => k -l -m = 2k - l - m, which can be true if k=0 and untrue if k is not equal to true. So this statement alone is not sufficient to answer the question.

Hi, I believe the correct answer is E, Statement 1 should read'1#k is not equal to k#1' this is true if # is - and when the value of k is negative. This is insufficient though as if k =0 then the RHS =LHS, if k is greater than or less than zero then the wo two sides are unequal.

My answer is D (both are sufficient), if 1 option is corrected to l # k. Here is my reasoning... We have to access if k # (l+m) = (k#l) + (k#m). We also have to identify if # is representing one of the operation- +,-,or *. Lets look at option 2

2) # represents subtraction Which means that k # (l+m) = k#(l+m)= k-(l+m)=k-m-n which is not equal to (k#l) + (k#m), because latter expression will sum up to 2k-l-m. Hence 2 is sufficient. Now the answer choices is limited to B or D

Lets consider statement 1 1) k # l is not equal to l#k for some numbers k. Now only in multiplication and addition that nxm=mxn (additionally n+m=m+n), which means # stands for subtraction. Hence, by above logic if # represents subtraction, it is sufficient to answer the problem. Hence this statement also works fine.

My answer is D (both are sufficient), if 1 option is corrected to l # k. Here is my reasoning... We have to access if k # (l+m) = (k#l) + (k#m). We also have to identify if # is representing one of the operation- +,-,or *. Lets look at option 2

2) # represents subtraction Which means that k # (l+m) = k#(l+m)= k-(l+m)=k-m-n which is not equal to (k#l) + (k#m), because latter expression will sum up to 2k-l-m. Hence 2 is sufficient. Now the answer choices is limited to B or D

Lets consider statement 1 1) k # l is not equal to l#k for some numbers k. Now only in multiplication and addition that nxm=mxn (additionally n+m=m+n), which means # stands for subtraction. Hence, by above logic if # represents subtraction, it is sufficient to answer the problem. Hence this statement also works fine. Therefore D

First of all If K=0, then k-m-n=2k-l-m, so statement 2 is not sufficient.

Secondly substraction is not the only sign for which k # l is not equal to l#k for some numbers k. Divison is another such operation. Moreover statement is saying "k # l is not equal to 1 # k for some numbers k" and not "k # l is not equal to l#k for some numbers k.", which even I doubted but cannot assume this in GMAT.