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In the quadrilateral PQRS, side PS is parallel to side QR.
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28 Jun 2011, 14:45
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52% (01:09) correct 48% (01:13) wrong based on 381 sessions
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In the quadrilateral PQRS, side PS is parallel to side QR. Is PQRS a parallelogram? (1) PS = QR (2) PQ = RS
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Re: In the quadrilateral PQRS, side PS is parallel to side QR.
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29 Jun 2011, 06:04
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 75162 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 75112 times ]
Hence answer option A




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Re: In the quadrilateral PQRS, side PS is parallel to side QR.
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29 Jun 2011, 04:10
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



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Re: In the quadrilateral PQRS, side PS is parallel to side QR.
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07 Sep 2011, 07:11
So if 2 opp sides are equal means it is gram? not matter it is square or rohbus or rectangle?



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Re: In the quadrilateral PQRS, side PS is parallel to side QR.
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07 Sep 2011, 07:47
ssruthi wrote: So if 2 opp sides are equal means it is gram? not matter it is square or rohbus or rectangle? 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)



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In the quadrilateral PQRS, side PS is parallel
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01 May 2012, 06:43
In the quadrilateral PQRS, side PS is parallel to side QR. Is PQRS a parallelogram?
(1) PS = QR
(2) PQ = RS
could you please share with ur thoughts on this? and how to distinguish a square from a parallelogram in such a task?



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Re: In the quadrilateral PQRS, side PS is parallel
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01 May 2012, 10:17
Galiya wrote: In the quadrilateral PQRS, side PS is parallel to side QR. Is PQRS a parallelogram?
(1) PS = QR
(2) PQ = RS
could you please share with ur thoughts on this? and how to distinguish a square from a parallelogram in such a task? If opposite sides of any quadrilateral are equal then its a parallelogram.But here only a is enough to determine that PQRS is a parallelogram.Bcoz PS=QR implies PQ=RS.But PQ=RS need not imply PS=QR(the isosceles trapezium). We can't determine even using both 1 & 2 that PQRS is a square. A.



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Re: In the quadrilateral PQRS, side PS is parallel
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01 May 2012, 12:22
but square also has equal and parallel sides  i went with E since couldn't determine whether a square or a parallelogram in front of me



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Re: In the quadrilateral PQRS, side PS is parallel
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01 May 2012, 12:32
Galiya wrote: but square also has equal and parallel sides  i went with E since couldn't determine whether a square or a parallelogram in front of me That is correct, but not all parallelogram are squares. Just because the sides are the same does not make it a square. If you were given an angle, which would have to be 90 degrees, that would make it a square. What I do is make a parallelogram with angles that are not all 90 degrees on my paper until I can prove that it is a square. If you do it that way you should not have a problem again.
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Re: In the quadrilateral PQRS, side PS is parallel
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18 Oct 2013, 00:45
Galiya wrote: but square also has equal and parallel sides  i went with E since couldn't determine whether a square or a parallelogram in front of me Square is also a Parallelogram.



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Re: In the quadrilateral PQRS, side PS is parallel
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06 Dec 2013, 09:14
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?



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Re: In the quadrilateral PQRS, side PS is parallel
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06 Dec 2013, 09:31
WholeLottaLove wrote: 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? Refer to the image, where PQ=SR and PS  QR.
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Re: In the quadrilateral PQRS, side PS is parallel
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06 Dec 2013, 09:48
Good God I don't know how I missed that.



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Re: In the quadrilateral PQRS, side PS is parallel
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16 May 2014, 09:52
In statement 1 couldn't figure be a rectangle? Is a rectangle a type of parallelogram? I guess so right? Thanks Cheers J



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Re: In the quadrilateral PQRS, side PS is parallel
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16 May 2014, 11:38
jlgdr wrote: In statement 1 couldn't figure be a rectangle? Is a rectangle a type of parallelogram? I guess so right? Thanks Cheers J 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
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Re: In the quadrilateral PQRS, side PS is parallel to side QR.
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04 Sep 2017, 16:22
(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 Kudos please if helpful



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Re: In the quadrilateral PQRS, side PS is parallel to side QR.
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24 Jul 2018, 04:13
NightFury wrote: Galiya wrote: In the quadrilateral PQRS, side PS is parallel to side QR. Is PQRS a parallelogram?
(1) PS = QR
(2) PQ = RS
could you please share with ur thoughts on this? and how to distinguish a square from a parallelogram in such a task? If opposite sides of any quadrilateral are equal then its a parallelogram.But here only a is enough to determine that PQRS is a parallelogram.Bcoz PS=QR implies PQ=RS.But PQ=RS need not imply PS=QR(the isosceles trapezium). We can't determine even using both 1 & 2 that PQRS is a square. A. How do we know PS=QR implies PQ=RS?



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Re: In the quadrilateral PQRS, side PS is parallel to side QR.
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21 Dec 2018, 21:43
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.



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Re: In the quadrilateral PQRS, side PS is parallel to side QR.
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19 Jan 2020, 16:28
Sorry to say but you committed a simple mistake here two sides. It is opposite sides which must be equal and parallel to form parallelogram. masoomjnegi wrote: 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.




Re: In the quadrilateral PQRS, side PS is parallel to side QR.
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19 Jan 2020, 16:28






