In the figure above, is quadrilateral PQRS a parallelogram?

Question

https://gmatclub.com/forum/download/file.php?id=5537 In the figure above, is quadrilateral PQRS a parallelogram? (1) The area of ΔPQS is equal to the area of ΔQRS. (2) QR = RS Q2.jpg

JingChan · Answer

E

1 tells us nothing about angles or "parallelogramness"
2 tells us nothing about angles or "parallelogramness"

Together tells us nothing either.

GK_Gmat · Answer

E.

|| gram is a quadrilateral in which opp. sides are equal and parallel. 

Stat 1: 
Tells us nothing about the parallel sides; insuff.

Stat 2: 
These are adjacent sides; insuff.

Stat 1 & 2:
Still doesn't provide us with any useful info.

mrsmarthi · Answer

Is the quadrilateral PQRS a parallelogram where QS is the diagnol.

(1) The area of triangle PQS is equal to the area of triangle QRS.
(2) QR = RS.

I guess it wrong. Just wanted to know whether I am missing any property of a quadrilateral for it to be a parallelogram.

.

I am not sure whether OA is correct. But I will let you know the OA after some replies.

. I am not sure whether OA is correct. But I will let you know the OA after some replies.

Bunuel · Answer

Well my first thought is E. Or there is some catch I cannot notice...

mrsmarthi · Answer

Bunuel,

Well I assumed that when the diagnol of the quadrilateral divedes it into two triangles of equal area, then the quadrilateral must be parallelogram. But I guess this assumption is wrong.

IN a parallelogram, the diagnols divide it into two triangles of equal areas but need NOT be true with quadrilateral.

OA is E.

Bunuel · Answer

Is the quadrilateral PQRS a parallelogram where QS is the diagnol.

(1) The area of triangle PQS is equal to the area of triangle QRS.

Well yes: the area of a parallelogram is twice the area of a triangle created by one of its diagonals. But the opposite is not correct: two triangles can share the same base, have the same area BUT their two corresponding side not necessary to be parallel. --> Not sufficient.

(2) QR = RS. --> QRS is isosceles. For PQRS to be parallelogram QPS also must be isosceles, in this case we get rhombus, but it's OK every rhombus is parallelogram. But we don't know that. --> Not sufficient.

(1)+(2) Area QRS=Area PQS, QRS is isosceles. --> PQS can have the same area as QRS and not be isosceles. So not sufficient.

E.

Parallelogram is a quadrilateral with two sets of parallel sides.

The opposite or facing sides of a parallelogram are of equal length, and the opposite angles of a parallelogram are equal.

Opposite sides of a parallelogram are equal in length.

Opposite angles of a parallelogram are equal in measure.

The area of a parallelogram is twice the area of a triangle created by one of its diagonals.

The diagonals of a parallelogram bisect each other.

Every rhombus is a parallelogram. Opposite is not correct.

Every square is a parallelogram. Opposite is not correct.

mrsmarthi · Answer

Bunuel,

Thank you for the detailed explanation.

GMATinsight · Answer

Statement 1 : The area of ΔPQS is equal to the area of ΔQRS.

The figure may be a Parallelogram or a Kite shape figure (non-parallelogram). Hence,
 NOT SUFFICIENT

Statement 2 : QR = RS

The figure may be a Parallelogram or an Isosceles triangle above the Diagonal and an scalene triangle below the diagonal of quadrilateral (non-parallelogram). Hence,
 NOT SUFFICIENT

Combining the two statements : 
The figure may be a Parallelogram or an Isosceles triangle above the Diagonal and an scalene triangle below the diagonal of quadrilateral (non-parallelogram) such that area of both halves of the Quadrilateral are same. Hence,
 NOT SUFFICIENT

Answer: option E

testcracker · Answer

hi lets consider this logic: area of a triangle = (1/2) * base * height now triangle, (1/2) * 3 * 4 and triangle, (1/2) * 4 * 3 have the same area, but is it necessary that these two triangles are congruent ? Certainly no on this line of reasoning, we can conclude that the the answer is straight "E" please raise your voice if there is anything wrong here thanks, and cheers with +1

bumpbot · Answer

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In the figure above, is quadrilateral PQRS a parallelogram?

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