In the quadrilateral PQRS, side PS is parallel to side QR.

Question

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

(1) PS = QR

(2) PQ = RS

suraabhi · Answer

Hi,

Can someone please explain the answer A?

from both A & B each considered alone we can say that they can be rectangel, rhoumbus, IIogram or trapeizium. Hence INSUFFICIENT

Combining them also does not change the situation. HENCE INSUFFICIENT.

I would normally go for E and not A.

Cheers

vyassaptarashi · Answer

well Option A says PS = QR and according to the question PS ll QR ...

hence PQ has to be equal and parallel to RS ....since connecting two equal and ll lines.

Otherwise the easiest way to find out whether it is a parallelogram or not draw two lines parallel and equal to each other and connect them with other two lines and see it will form a parallelogram

Therefore, this option is sufficient

Attachment:

2.jpg [ 24.01 KiB | Viewed 96702 times ]

Option B tells us that PQ = RS
Now, it does not tell us anything about PS and QR ... they can be unequal ... hence this option is insufficient to answer

Attachment:

3.jpg [ 20.34 KiB | Viewed 96583 times ]

Hence answer option A

ssruthi · Answer

So if 2 opp sides are equal means it is ||gram? not matter it is square or rohbus or rectangle?

catfreak · Answer

If two opposite sides are parallel and equal, then its definitely a parallelogram. It could be a square,rhombus or rectangle ( all are types of parallelogram)

WholeLottaLove · Answer

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

(2) PQ = RS

I'm having a tough time seeing how this wouldn't be a parallelogram.

We know that a.) the figure has 4 sides and b.) that PS || PR. In addition, we are told that PQ=RS. I cannot construct a four sided figure with these constraints that doesn't have two pairs of parallel sides. Can someone please explain what I am missing and the logic behind how to solve these kinds of problems?

mau5 · Answer

Refer to the image, where PQ=SR and PS || QR.

WholeLottaLove · Answer

Good God I don't know how I missed that. :shock:

jlgdr · Answer

In statement 1 couldn't figure be a rectangle? Is a rectangle a type of parallelogram? I guess so right? Thanks Cheers J

gmatacequants · Answer

Hi J, You are Right.

Actually, the statement 1 could well yield a simple parallelogram or a rectangle or a rhombus or a square . All these are types of parallelogram: Simple parallelogram - a quadrilateral with opposite sides equal and parallel Rectangle - a parallelogram with adjacent sides at 90 degrees Rhombus - a parallelogram with all sides equal Square - a parallelogram with adjacent sides at 90 degrees and all sides equal Kudos is the best form of appreciation

LakerFan24 · Answer

(basic) properties of a parallelogram:

a) opposite sides are parallel and of the same length

b) interior angles add up to 360 degrees

c) opposite angles are equal, and adjacent angles sum to 180

Knowing the above:

1) PS=QR. Given: PS//QR. Textbook definition of //gram. sufficient.

2) PQ=RS. Does not mention whether PQ//RS, whether PS=QR, etc. insufficient.

--> A

bumpbot · Answer

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In the quadrilateral PQRS, side PS is parallel to side QR.

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