Data Sufficiency

Removing the problem as I heard that it is a copyright violation.
Or is it not ?

Hi,

You can follow:
https://www.beatthegmat.com/og-ds-125-t86074.html

rppala90 wrote:If ^ represents one of the operations +, -, and X,
is K ^ ( L + M) = (K ^ L) + (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.

Hi--
Statement 1 -- since it is given that K^1 is not equal to 1^K for some values-- we know that ^ cannot be + or *. Now solving the equn we get

LHS= K-(L+M)
RHS= K-L+K-M = 2K- (L+M)

Now, if K=0 then LHS=RHS
else LHS is not equal to RHS
Therefore, LHS is not equal to RHS for ALL values of K,L,M

Since the question asks us to find the equality for ALLnumbers K,L and M -- Therefore the statement is SUFFICIENT---

Same is the case for Statement 2
SUFFICIENT

THE answer is D

Here ans of the question will be YES if ^ means 'x'.

From Option 1. We know the ^ Not Equal to ' x'
Option to directly says that ^ Not Equal to ' x'

Hence ans is D.