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Forget conventional ways of solving math questions. For DS problems, the VA (Variable Approach) method is the quickest and easiest way to find the answer without actually solving the problem. Remember that equal numbers of variables and independent equations ensure a solution.

The first step of the VA (Variable Approach) method is to modify the original condition and the question. We then recheck the question.

When we modify the question, ab > bc is equivalent to ab - bc > 0 or b(a-c) > 0. Even though we know a - c > 0 from condition 2), we don't know if b is positive or negative. Thus, both conditions together are not sufficient.

Conditions 1) & 2):
If a = 1, b =1 and c = 0, then ab > bc and the answer is 'yes'.
If a = 1, b =-1 and c = 0, then ab < bc and the answer is 'no'.
Since we don't have a unique solution, both conditions together are not sufficient.

Therefore, E is the answer.
Answer: E

Question : ab > bc ?
Statement 1 : abc = 0
ab > bc
ab - bc > 0
b < a - c > 0
If b > 0 then a > c
If b < 0 then a < c
$$but\ b\ne0$$
Given that abc = o, it means that either of a, b or c is 0
$$If\ b\ \ne0\ and\ c\ =\ o\ then\ ab\ >\ bc$$.
Hence, statement 1 is NOT SUFFICIENT because the information given is not enough to have a definite answer.

Statement 2 : a > c
There is no information about b so we cannot express statement 2 in terms of ab and bc.
Hence, statement 2 is NOT SUFFICIENT.
Combining statement 1 and 2 together does not provide information about the variable that has the value of 0 in abc = 0,
$$In\ statement\ 1\ we\ don't\ know\ what\ b\ is,\ in\ statement\ 2\ we\ only\ know\ that\ b\ \ne\ 0.$$
Hence, both statement together are NOT SUFFICIENT.
Option E is CORRECT.