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Statement (1) by itself is insufficient. A rhombus also satisfies the condition.

Statement (2) by itself is insufficient. It is possible to pick arbitrary sides that would result in an area of a rhombus or even a rectangle that is a multiple of 10. For example sides of 4 and 5 produce an area of 20 and sides of 10 and 10 produce an area equal to 100.

Statements (1) and (2) combined are insufficient. Combining both statements together still does not help answer the question.

I think this is a poor-quality question and the explanation isn't clear enough, please elaborate. why both statements combined doesn't solve the question

I think this is a poor-quality question and the explanation isn't clear enough, please elaborate. why both statements combined doesn't solve the question

Why is the question poor-quality?

As for the solution, we could have a square with an area which is a multiple of 10 as well as a rhombus with an area which is a multiple of 10.
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A Quadrilateral to be Sqaure requires two condition: All sides to be equal and angles to be right angle. But none of the solution state anything about the angle so we dont have complete information to judge if it is square or not. So option E