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In the rectangular coordinate system shown, ABCD is a quadrilateral. T
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Updated on: 06 Jan 2019, 19:29
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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
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06 May 2017, 11:25
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 coordinates of point B & C but as we know nothing about point's B y coordinate "b", hence we cannot calculate the lengths of AB & BC. hence not sufficient Statement 2: this gives us y coordinate of point B. So BC = 52 = 3 units whereas AD = 20 = 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
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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
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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 = 52 = 3 , Since the xcoordinates are same Since the lengths are different, it is definitely not a parallelogram Sufficient Choice B
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