Is quadrilateral PQRS a parallelogram?
(1) PQ is parallel to SR.
(2) QR and PS have the same length.
Best way to tackle this problem is to draw different cases.
Noe, each statement alone is clearly insufficient. When taken together it's certainly possible PQRS to be a parallelogram but it's also possible it to be isosceles trapezoid:
Hope it's clear.
I had the same logic, however this task was in the Manhattan GMAT
test I took last week. Their answer was A with the following explanation:
A parallelogram is a quadrilateral in which both pairs of opposite sides are parallel. The opposite sides of a parallelogram also have equal length.
(1) SUFFICIENT: We know from the question stem that opposite sides PS and QR are parallel, while this statement tells us that they also have equal lengths. The opposite sides PQ and RS must also be parallel and equal in length. This is the definition of a parallelogram, so the answer to the question is “Yes.”
(2) INSUFFICIENT: We know from the question stem that opposite sides PS and QR are parallel, but have no information about their respective lengths. This statement tells us that the opposite sides PQ and RS are equal in length, but we don’t know their respective angles; they might be parallel, or they might not be. According to the information given, PQRS could be a trapezoid with PS not equal to QR. On the other hand, PQRS could be a parallelogram with PS = QR. The answer to the question is uncertain.
The correct answer is A.
This confused me a lot...