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# If Q is a quadrilateral, is Q a rectangle?

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If Q is a quadrilateral, is Q a rectangle?  [#permalink]

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Updated on: 11 Jul 2019, 05:17
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Difficulty:

25% (medium)

Question Stats:

59% (00:45) correct 41% (00:40) wrong based on 169 sessions

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If Q is a quadrilateral, is Q a rectangle?

(1) Opposite sides of Q are parallel.
(2) One of the four angles of Q is 90 degrees.

Source: Nova GMAT
Difficulty Level: 600

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Originally posted by hardnstrong on 09 Jun 2010, 11:15.
Last edited by SajjadAhmad on 11 Jul 2019, 05:17, edited 1 time in total.
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Re: If Q is a quadrilateral, is Q a rectangle?  [#permalink]

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09 Jun 2010, 11:21
IMO E.

A alone is INSUFFICIENT - Could be a parallelogram, a square, a rhombus, or a rectangle.
B alone is INSUFFICIENT - Doesn't tell us anything.

A and B together can give us a square or a rectangle. INSUFFICIENT.
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Re: If Q is a quadrilateral, is Q a rectangle?  [#permalink]

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09 Jun 2010, 11:53
3
sjayasa wrote:
IMO E.

A alone is INSUFFICIENT - Could be a parallelogram, a square, a rhombus, or a rectangle.
B alone is INSUFFICIENT - Doesn't tell us anything.

A and B together can give us a square or a rectangle. INSUFFICIENT.

Square is just a special case of rectangle so answer is C (what I mean is that every square is a rectangle, rhombus and parallelogram but not vise-versa).

For more on this issue check this link: Polygons.

Hope it helps.
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Re: If Q is a quadrilateral, is Q a rectangle?  [#permalink]

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09 Jun 2010, 11:55
Aha! Dint really know that.
Thank you for correcting!
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Re: If Q is a quadrilateral, is Q a rectangle?  [#permalink]

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10 Jun 2010, 00:02
OA is C

Thanks for the info bunuel. I will make a note of this +1
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Re: If Q is a quadrilateral, is Q a rectangle?  [#permalink]

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13 Jun 2010, 00:02
1
Even with the OA i have doubt. Please correct me if I am wrong in this case.
1 is telling that Opposite sides of Q are parallel BUT it is not telling that these sides are equal in lenght.
2 is telling that One of the four angles of Q is 90 degrees. Clearly any one alone is insufficient but when you combine then also there is possibility that it may be a ractangle or a "right angled trapezium". So according to my thinking, the OA must be wrong and the actual answer must be E. Please correct me if I am wrong.

Consider giving me KUDOS if you like my post.
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Re: If Q is a quadrilateral, is Q a rectangle?  [#permalink]

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13 Jun 2010, 05:06
1
2
amitjash wrote:
Even with the OA i have doubt. Please correct me if I am wrong in this case.
1 is telling that Opposite sides of Q are parallel BUT it is not telling that these sides are equal in lenght.
2 is telling that One of the four angles of Q is 90 degrees. Clearly any one alone is insufficient but when you combine then also there is possibility that it may be a ractangle or a "right angled trapezium". So according to my thinking, the OA must be wrong and the actual answer must be E. Please correct me if I am wrong.

Consider giving me KUDOS if you like my post.

(1) Opposite sides of Q are parallel --> note that this means that all opposite sides are parallel --> Q is a parallelogram. Is it a rectangle, special case of parallelogram? We don't know.

(2) One of the four angles of Q is 90 degrees. Not sufficient.

(1)+(2) Parallelogram with one right angle must be a rectangle as in parallelogram opposite angles are equal and not opposite angles sum to 180 degrees.

Hope it's clear.
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Re: If Q is a quadrilateral, is Q a rectangle?  [#permalink]

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13 Jun 2010, 07:18
Thanks bunuel,
My mistake.... I appreciate this forum has such a active and tolerant Moderator.
Keep it up... and thank you very much...
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Re: If Q is a quadrilateral, is Q a rectangle?  [#permalink]

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25 Nov 2018, 11:18
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Re: If Q is a quadrilateral, is Q a rectangle?   [#permalink] 25 Nov 2018, 11:18
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