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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.
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Since we have 3 variables (a, b, and c) and 0 equations, E is most likely the answer. So, we should consider conditions 1) & 2) together first. After comparing the number of variables and the number of equations, we can save time by considering conditions 1) & 2) together first.

Conditions 1) & 2)
We have abc = 100 and 2(ab + bc + ca) = 720 or ab + bc + ca = 360.
If we have a = 10, then we have bc = 100 and ab + bc + ca = 10(b+c) + 100 = 720 or b + c = 62, which yields a + b + c = 72.
If we have a = 5, then we have bc = 200 and ab + bc + ca = 5(b+c) + 200 = 720 or b + c = 104, which yields a + b + c = 5 + 104 = 109.

Since both conditions together do not yield a unique solution, they are not sufficient.

Therefore, E is the answer.
Answer: E

In cases where 3 or more additional equations are required, such as for original conditions with "3 variables", or "4 variables and 1 equation", or "5 variables and 2 equations", conditions 1) and 2) usually supply only one additional equation. Therefore, there is an 80% chance that E is the answer, a 15% chance that C is the answer, and a 5% chance that the answer is A, B or D. Since E (i.e. conditions 1) & 2) are NOT sufficient, when taken together) is most likely to be the answer, it is generally most efficient to begin by checking the sufficiency of conditions 1) and 2), when taken together. Obviously, there may be occasions on which the answer is A, B, C, or D.

Let a, b and c = height, width and length of the rectangular box.
Question is, what is the value of a+b+c? (i.e what is height + weight + length)
Statement 1:
$$The\ volume\ of\ a\ rec\tan gular\ box\ is\ 1000m^3$$
Volume of a rectangular box = a*b*c = height * width * length
$$a\cdot b\cdot c=1000m^3$$
Thw value of a, b and c still remain unknown, hence, statement 1 is NOT SUFFICIENT.

Statement 2:
$$The\ surface\ area\ is\ 720m^2$$
The surface area of a rectangular box = 2(height * weight) + 2(height * length) + 2(width * length)
720 = 2(ab + ac + bc)
360 m^2= ab + ac + bc
Variable a, b, and c are unknown, hence, statement 2 is also NOT SUFFICIENT.

Combining both statements together;
$$Volume=1000m^3$$
$$Area=720m^2$$
$$ab+ac+bc=360m^2$$
a+b+c = ?
Here, variable a, b, and c are not known yet. Therefore, both statements combined together are NOT SUFFICIENT.

Thus, the correct answer is OPTION E.

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