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22 Mar 2023, 11:30
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D
Be sure to select an answer first to save it in the Error Log before revealing the correct answer (OA)!
Difficulty:
35%
(medium)
Question Stats:
67% (01:35) correct
33%
(02:02)
wrong
based on 46
sessions
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Is the quadrilateral ABCD a trapezium?
(1) The angles A, B, C, D of quadrilateral ABCD are in the ratio 2:3:6:7
(2) The angles A, B, C, D of quadrilateral ABCD are in the ratio 1:4:5:8
(1) The angles A, B, C, D of quadrilateral ABCD are in the ratio 2:3:6:7
(2) The angles A, B, C, D of quadrilateral ABCD are in the ratio 1:4:5:8
Pure algebraic questions like this one are no longer part of the GMAT Data Sufficiency syllabus.
For relevant Data Sufficiency questions, please check the Data Sufficiency forum:
Data Sufficiency Forum
Data Sufficiency Forum
26 Mar 2023, 14:14
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We need to find out if ABCD is a trapezium or not.
In a trapezium, the sum of adjacent angles is 180 degrees (because they are co-interior angles made by a transversal on 2 parallel sides)
1. The first part says angles A, B, C, D are in the ratio of 2:3:6:7. As the internal angles of a quadrilateral sum up to 360 degrees, A=40, B= 60, C= 120, D=140.
The angles adjacent to A and B would always be D and C respectively and the sum of adjacent angles is 180 degrees here.
Hence we can say sides AB and CD are parallel to each other while sides BC and AD are not parallel, so it will be a trapezium.
2. Similarly, angles A, B, C, D are in the ratio 1:4:5:8. So, A=20, B=80, C=100, D=160.
Here, again the adjacent angles are giving the sum 180. so we can say AB is parallel to CD while BC is not parallel to AD. So it will be trapezium.
ANSWER=D
In a trapezium, the sum of adjacent angles is 180 degrees (because they are co-interior angles made by a transversal on 2 parallel sides)
1. The first part says angles A, B, C, D are in the ratio of 2:3:6:7. As the internal angles of a quadrilateral sum up to 360 degrees, A=40, B= 60, C= 120, D=140.
The angles adjacent to A and B would always be D and C respectively and the sum of adjacent angles is 180 degrees here.
Hence we can say sides AB and CD are parallel to each other while sides BC and AD are not parallel, so it will be a trapezium.
2. Similarly, angles A, B, C, D are in the ratio 1:4:5:8. So, A=20, B=80, C=100, D=160.
Here, again the adjacent angles are giving the sum 180. so we can say AB is parallel to CD while BC is not parallel to AD. So it will be trapezium.
ANSWER=D
12 Apr 2023, 08:02
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Bunuel
Solution:
Pre Analysis:
- We are asked if ABCD is trapezium or not
- This is YES-NO question
Statement 1: The angles A, B, C, D of quadrilateral ABCD are in the ratio 2:3:6:7
- Let the angles be 2x, 3x, 6x and 7x
- Sum \(2x + 3x + 6x + 7x = 180\) or \(18x = 180\) or \(x=10\)
- Thus, the angles will be \(A=20^o\), \(B=30^o\), \(C=60^o\) and \(D=70^o\)
Attachment:
trap.png [ 3.14 KiB | Viewed 1328 times ]
- We can see that angles A and D and angles B and C are complimentary i.e., adding up to 90 degrees
- From this we can infer that lines AB and CD are parallel to each other while AD and CB are not
- Thus, statement 1 alone is sufficient and we can eliminate options B, C and E
Statement 2: The angles A, B, C, D of quadrilateral ABCD are in the ratio 1:4:5:8
- Let the angles be x, 4x, 5x and 8x
- Sum \(x + 4x + 5x + 8x = 180\) or \(18x = 180\) or \(x=10\)
- Thus, the angles will be \(A=10^o\), \(B=40^o\), \(C=50^o\) and \(D=80^o\)
- Using similar approach, we can say AB and CD are parallel to each other while AD and CB are not
Hence the right answer is Option D
