The answer is E because for a QUad to be a parallelogram .....the diagonals must bisect each other equally none of the conditions hint that

I think answer should be "B" . What is OA?

Ian Stewart wrote:

pradeepss wrote:Tricky Question:

Is the quadrilateral ABCD a parallelogram?
(1) Sides AB and BC are equal in length.
(2) Sides BC, CD and AD are equal in length.

Neither statement is sufficient on its own. From 2, for example, the three equal sides could look like:

\_/

which is clearly not a parallelogram.

Taking both statements together, all four sides are equal; we therefore have, by definition, a rhombus, and all rhombi are parallelograms. So C.

But if we got a square? Should we consider it a parallelogram?

pradeepss wrote:Tricky Question:

Is the quadrilateral ABCD a parallelogram?
(1) Sides AB and BC are equal in length.
(2) Sides BC, CD and AD are equal in length.

Statement (1) ALONE is sufficient, but statement (2) ALONE is not sufficient.

Statement (2) ALONE is sufficient, but statement (1) ALONE is not sufficient.

BOTH statements TOGETHER are sufficient, but NEITHER statement ALONE is sufficient.

EACH statement ALONE is sufficient.

Statements (1) and (2) TOGETHER are NOT sufficient.

A parallelogram is a quadrilateral whose opposite sides are parallel. Note that the opposite sides and opposite angles of a parallelogram are equal.
Statement (1) specifies that 2 adjacent sides of the quadrilateral are equal.
However, nothing is specified about the other 2 sides, which need not be equal.
So, ABCD need not necessarily be a parallelogram.
Thus, statement (1) ALONE is not sufficient.
Statement (2) implies that 3 sides of the quadrilateral are equal.
However, nothing is specified about the fourth side, which need not be equal (so, the angles between the sides may vary).
Thus, statement (2) ALONE is not sufficient.
When considered together, the two statements tell us that the 4 sides of the quadrilateral are equal making it a parallelogram (in fact, a rhombus which is a parallelogram with 4 equal sides).