一道data sufficiency的题 请帮忙

chunzhang

题目： if`represents one of the operations +, -, and x, is k`(l+m) =(k`m) for all numbers k, l, and m?
(1) k`1 is not equal to 1`k for some numbers k.
(2) ` represents subtraction.
请问如何求解？

kazemi

You need to try all operations +, – , and x
so try all operator for:
k.1 is not equal to 1.k for some numbers k.
(-) k-1 is not equal to 1-k , RIGHT , SOME NUMBERS ARE YES
(+) k+1 is not equal to 1+k , WRONG , ALL NUMBERS ARE EQUAL
(x) kx1 is not equal to 1xk , WRONG , ALL NUMBERS ARE EQUAL
so you can get the rigth operator = substraction.

so try the substraction – first:
k. (l+m)=(k.l) + (k.m)
=> k- (l+m)=(k-l) + (k-m)
=> k-l-m = k-l+k-m (move l & m on the left side into the right side)
=> k=k-l+k-m+l+m
=> k=0
so you can get k=0 with substraction.

so the answer is D. EACH statement ALONE is sufficient.