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In the rectangular coordinate system shown, ABCD is a quadrilateral. T

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In the rectangular coordinate system shown, ABCD is a quadrilateral. T  [#permalink]

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New post Updated on: 06 Jan 2019, 19:29
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Difficulty:

  45% (medium)

Question Stats:

54% (01:09) correct 46% (01:50) wrong based on 68 sessions

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In the rectangular coordinate system shown, ABCD is a quadrilateral. The coordinates of the points A , B , C, and D are (0, 2), (a, b), (a, 2), and (0, 0), respectively. Is the quadrilateral ABCD a parallelogram?

(1) a = 3
(2) b = 5

Source: Nova GMAT
Difficulty Level: 650

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Originally posted by SajjadAhmad on 06 May 2017, 11:10.
Last edited by SajjadAhmad on 06 Jan 2019, 19:29, edited 2 times in total.
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Re: In the rectangular coordinate system shown, ABCD is a quadrilateral. T  [#permalink]

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New post 06 May 2017, 11:25
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SajjadAhmad wrote:
Source: Nova GMAT

In the rectangular coordinate system shown, ABCD is a quadrilateral. The coordinates of the points A , B , C, and D are (0, 2), (a, b), (a, 2), and (0, 0), respectively. Is the quadrilateral ABCD a parallelogram?

(1) a = 3
(2) b = 5


For a parallelogram, opposite sides are parallel and equal.

Statement 1: we get the x co-ordinates of point B & C but as we know nothing about point's B y co-ordinate "b", hence we cannot calculate the lengths of AB & BC. hence not sufficient

Statement 2: this gives us y co-ordinate of point B. So BC = 5-2 = 3 units whereas AD = 2-0 = 2 units. Clearly BC is not equal to its opposite side AD. hence it is not a parallelogram. Sufficient.

Hence option B
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Re: In the rectangular coordinate system shown, ABCD is a quadrilateral. T  [#permalink]

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New post 18 Dec 2018, 22:20
Statement 1. Now the points of quadrilateral are (0,2) , (3,b) , (3,2) and (0,0). This will be a parallelogram if b = 4. Otherwise the points won’t make a parallelogram. Hence, Insufficient.
Statement 2. Now the points are (0,2) , (a,5) , (a,2) ,(0,0). This could never be a parallelogram irrespective of the value of a. Hence, Sufficient.
Hence, b is the answer.
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Re: In the rectangular coordinate system shown, ABCD is a quadrilateral. T  [#permalink]

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New post 19 Dec 2018, 06:08
For ABCD to be a parallelogram, a pair of opposite sides have to be parallel and equal.

i.e their slopes have to be equal and their lengths have to be same

From St 1 : a = 3 , We cannot find the length or the slope of the sides AB or BC

So we cannot compare the values for any of the two pairs

Not Sufficient

From St 2 : b = 5

Length of AD = 2

Length of BC = 5-2 = 3 , Since the x-coordinates are same

Since the lengths are different, it is definitely not a parallelogram

Sufficient

Choice B
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Re: In the rectangular coordinate system shown, ABCD is a quadrilateral. T &nbs [#permalink] 19 Dec 2018, 06:08
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In the rectangular coordinate system shown, ABCD is a quadrilateral. T

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