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# Is quadrilateral PQRS a parallelogram?

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Is quadrilateral PQRS a parallelogram? [#permalink]

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21 Feb 2012, 00:39
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Is quadrilateral PQRS a parallelogram?

(1) PQ is parallel to SR.
(2) QR and PS have the same length.
[Reveal] Spoiler: OA
Math Expert
Joined: 02 Sep 2009
Posts: 39051
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Kudos [?]: 106556 [0], given: 11628

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

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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 [ 3.19 KiB | Viewed 2158 times ]
Answer: E.

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

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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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Posts: 39051
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Re: Is quadrilateral PQRS a parallelogram? [#permalink]

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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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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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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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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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29 Jan 2016, 06:13
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Re: Is quadrilateral PQRS a parallelogram?   [#permalink] 29 Jan 2016, 06:13
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# Is quadrilateral PQRS a parallelogram?

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