Data Sufficiency

In the quadrilateral PQRS, side PS is parallel to side QR. Is PQRS a parallelogram?

(1) PS = QR

(2) PQ = RS

plz post explanation.

i think answer would be A.

IMO E

PS is parallel to QR

From 1, PS = QR

But for a parallelogram, PQ and RS has be to parallel and equal.

The PS and QR being parallel and equal, does not ensure that PQ and RS are also parallel.
PQ and RS are equal but need not be parallel

In sufficient.

From 2, PQ = RS, Same explanation as 1. we need to know that PQ and RS are parallel

Together, Does not give you the information required

Hence E.

If the parallel sides are of equal length, then how can the remaining two sides not also be of equal length and parallel?

I would say 1) alone is sufficient, but 2) alone is not.

Answer A.

crazy4gmat wrote:In the quadrilateral PQRS, side PS is parallel to side QR. Is PQRS a parallelogram?

(1) PS = QR

(2) PQ = RS

plz post explanation.

[spoiler][A][/spoiler]

Hope keeping the following criteria in mind will help solve such DS questions quickly and efficiently:

1) If a quadrilateral has one pair of sides that are both parallel and congruent, then the quadrilateral is a parellelogram.
2) If a the opposite sides of a quadrilateral are congruent, then then quadrilateral is a parallelogram.
3) Opposites sides are parallel.
4) Opposite angles are congruent
5) Diagonals bisect each other.

IMO A

A parrallelagram has 4 parallel sided with oppisite sides and angles being equal. In order for PS=QR and PS ll QR the lengths of the other two sides must be equal and bc PS and QR are equal the other two sides must be parallel

In statement 2 a rhombus would suffice as we don't need PS=QR

i made a mistake,

answer is A

Answer is A. Since the two given sides (PS and QR) are parallel and equal the other two sides have to be parallel and equal to form a quadilateral.

Statement 1: If PS & QR are of equal length & parallel, then automatically, PQ & RS will be of equal length & parallalel. So, this statement alone is sufficient to answer the question.

Statement 2: If PS & QR are parallel & PQ & RS are of equal length, then the quadrilateral can either be a trapezium (one pair of opposite sides are parallel) or a parallelogram. This information is insufficient to answer the question.

Hence answer should be A. What is the OA?

Necessary & minimum condition for a quadrilateral to be a parallelogram is that its two sides should be parallel and equal.
Statement 1. From the question statement we know that two sides of a quadrilateral are parallel and by statement 1 we know that these sides are equal. So, the given quadrilateral is a parallelogram. Hence, sufficient.
Statement 1 & 2 together. from the question statement we know PS is parallel to QR and by statement 2 we know other two sides PO and SR are equal. This could happen in the case of a trapezium and a parallelogram. Hence, Insufficient.