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Is quadrilateral PQRS a parallelogram?

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Is quadrilateral PQRS a parallelogram?  [#permalink]

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New post 21 Feb 2012, 00:39
11
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A
B
C
D
E

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Question Stats:

64% (00:53) correct 36% (01:04) wrong based on 181 sessions

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Is quadrilateral PQRS a parallelogram?

(1) PQ is parallel to SR.
(2) QR and PS have the same length.
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Re: Is quadrilateral PQRS a parallelogram?  [#permalink]

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New post 21 Feb 2012, 00:51
eybrj2 wrote:
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:
Attachment:
Isosceles trapezoid.PNG
Isosceles trapezoid.PNG [ 3.19 KiB | Viewed 4460 times ]
Answer: E.

Hope it's clear.
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Re: Is quadrilateral PQRS a parallelogram?  [#permalink]

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New post 21 Feb 2012, 02:39
Bunuel wrote:
eybrj2 wrote:
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:
Attachment:
Isosceles trapezoid.PNG
Answer: E.

Hope it's clear.



Hi Bunuel,

What is the naming convention to be followed during the GMAT?

I was focusing on the clock & made my parallelogram look like a rectangle & choose C.

Thanks in advance
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Re: Is quadrilateral PQRS a parallelogram?  [#permalink]

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New post 21 Feb 2012, 02:48
boomtangboy wrote:
Bunuel wrote:
eybrj2 wrote:
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:
Attachment:
Isosceles trapezoid.PNG
Answer: E.

Hope it's clear.



Hi Bunuel,

What is the naming convention to be followed during the GMAT?

I was focusing on the clock & made my parallelogram look like a rectangle & choose C.

Thanks in advance


The vertices are given in order. The order of the vertices on the diagram is the same as in the stem PQRS.

Hope it's clear.
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Re: Is quadrilateral PQRS a parallelogram?  [#permalink]

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New post 21 Feb 2012, 08:58
Bunuel wrote:
eybrj2 wrote:
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:
Attachment:
Isosceles trapezoid.PNG
Answer: E.

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...
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Re: Is quadrilateral PQRS a parallelogram?  [#permalink]

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New post 21 Feb 2012, 09:30
JubtaGubar wrote:
Bunuel wrote:
eybrj2 wrote:
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:
Attachment:
Isosceles trapezoid.PNG
Answer: E.

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...


Welcome to GMAT Club.

You must be talking about some other problem, since the stem in the original questions doesn't say that opposite sides PS and QR are parallel.
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Re: Is quadrilateral PQRS a parallelogram?  [#permalink]

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New post 21 Feb 2012, 22:14
could be a rhombus, a square - which would meet the criteria for being a parallelogram. But, could also be a trapezium with opposite angles equal to 180.
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Re: Is quadrilateral PQRS a parallelogram?  [#permalink]

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New post 28 Nov 2019, 07:18
chetan2u, VeritasKarishma, Bunuel, gmatbusters
Hi I'm having tough time solving this.
Statement1 says that PQ is parallel to SR: diagram can be rhombus,square,rectangle....All belong to parallelogram sub group.
please help me solve this problem
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Is quadrilateral PQRS a parallelogram?  [#permalink]

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New post 28 Nov 2019, 07:36
SonGoku wrote:
chetan2u, VeritasKarishma, Bunuel, gmatbusters
Hi I'm having tough time solving this.
Statement1 says that PQ is parallel to SR: diagram can be rhombus,square,rectangle....All belong to parallelogram sub group.
please help me solve this problem



PQ is parallel to SR, but what about the second pair of opposite sides QR and PS.
If QR||PS, then surely it is a parallelogram, and if NOT, it will be a trapezium.
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Re: Is quadrilateral PQRS a parallelogram?  [#permalink]

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New post 28 Nov 2019, 22:45
SonGoku wrote:
chetan2u, VeritasKarishma, Bunuel, gmatbusters
Hi I'm having tough time solving this.
Statement1 says that PQ is parallel to SR: diagram can be rhombus,square,rectangle....All belong to parallelogram sub group.
please help me solve this problem


In addition to what chetan2u said above, note two things:

1. A parallelogram has both pairs of opposite sides parallel to each other. So PQ should be parallel to SR AND PS should be parallel to QR for it to be a parallelogram. With only one pair of sides parallel, it may not be a parallelogram.
2. Rhombus, square and rectangle are all parallelograms. So if you have a rectangle, that is a parallelogram too. A square is a parallelogram too etc. Then, given a square, if you are asked, "Is it a parallelogram?", your answer would be "yes".
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Re: Is quadrilateral PQRS a parallelogram?   [#permalink] 28 Nov 2019, 22:45
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