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Joined: 04 Jan 2015
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Question of the Week- 8 (In the quadrilateral shown above,........)
[#permalink]
Updated on: 16 Aug 2018, 00:56
Updated on: 16 Aug 2018, 00:56
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33%
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wrong
based on 228
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e-GMAT Question of the Week #8
In the quadrilateral shown above, the length of AB and CD is 6 units and 8 units respectively. If the length of AC is 10 units, then which of the following can be the perimeter of quadrilateral ABCD?
To access all the questions: Question of the Week: Consolidated List
In the quadrilateral shown above, the length of AB and CD is 6 units and 8 units respectively. If the length of AC is 10 units, then which of the following can be the perimeter of quadrilateral ABCD?
- a) 20 units
b) 35 units
c) 48 units
d) 52 units
e) 60 units
To access all the questions: Question of the Week: Consolidated List
Originally posted by EgmatQuantExpert on 20 Jul 2018, 05:03.
Last edited by EgmatQuantExpert on 16 Aug 2018, 00:56, edited 6 times in total.
Last edited by EgmatQuantExpert on 16 Aug 2018, 00:56, edited 6 times in total.
e-GMAT Representative
Joined: 04 Jan 2015
Posts: 3703
Given Kudos: 165
Re: Question of the Week- 8 (In the quadrilateral shown above,........)
[#permalink]
Updated on: 13 Aug 2018, 00:42
Updated on: 13 Aug 2018, 00:42
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Solution
Given:
- • AB= 6 units
• CD= 8 units
• AC= 10 units
To find:
- • The option which can be the correct diameter of quadrilateral ABCD.
Approach and Working:
Perimeter of ABCD= AB+BC+CD+DA= 8+6+AD+BC= 14+AD+BC
- • Hence, we will get the minimum value of perimeter when AD and BC are minimum
• And, we will get the maximum value of perimeter when AD and BC are maximum.
In ∆ ADC,
- • 10-8 < AD < 10+8
• 2 < AD < 18
In ∆ ABC,
- • 10-6 < BC < 10+6
• 4 < BC < 16
Hence, 6 < AD+BC < 34
Thus, 20<Perimeter of ABCD< 48
The only option which lies between 20 and 48 is 35.
Hence, the correct answer is option B.
Answer: B
Originally posted by EgmatQuantExpert on 20 Jul 2018, 05:08.
Last edited by EgmatQuantExpert on 13 Aug 2018, 00:42, edited 2 times in total.
Last edited by EgmatQuantExpert on 13 Aug 2018, 00:42, edited 2 times in total.
General Discussion
Joined: 05 Feb 2016
Posts: 128
Given Kudos: 69
Location: India
Concentration: General Management, Marketing
WE:Information Technology (Computer Software)
Re: Question of the Week- 8 (In the quadrilateral shown above,........)
[#permalink]
20 Jul 2018, 05:33
20 Jul 2018, 05:33
EgmatQuantExpert
e-GMAT Question of the Week #8
In the quadrilateral shown above, the length of AB and CD is 6 units and 8 units respectively. If the length of AC is 10 units, then which of the following can be the perimeter of quadrilateral ABCD?
To access all the questions: Question of the Week: Consolidated List
In the quadrilateral shown above, the length of AB and CD is 6 units and 8 units respectively. If the length of AC is 10 units, then which of the following can be the perimeter of quadrilateral ABCD?
- a) 20 units
b) 35 units
c) 48 units
d) 52 units
e) 60 units
To access all the questions: Question of the Week: Consolidated List
In triangle ADC ,3<AD<17
In triangle ABC ,5<BC<15
Therefore Max perimeter 8+6+17+15=46
Min perimeter 6+8+3+5=22
22<P<46
So B
