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Question of the Week 8 (In the quadrilateral shown above,........)
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Updated on: 16 Aug 2018, 00:56
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eGMAT Question of the Week #8In 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
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Re: Question of the Week 8 (In the quadrilateral shown above,........)
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Updated on: 13 Aug 2018, 00:42
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, • 108 < AD < 10+8 • 2 < AD < 18 In ∆ ABC, • 106 < 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
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Re: Question of the Week 8 (In the quadrilateral shown above,........)
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20 Jul 2018, 05:33
EgmatQuantExpert wrote: eGMAT Question of the Week #8In 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<17In triangle ABC , 5<BC<15Therefore Max perimeter 8+6+17+15=46 Min perimeter 6+8+3+5=22 22<P<46So B



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Re: Question of the Week 8 (In the quadrilateral shown above,........)
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Updated on: 20 Jul 2018, 23:26
EgmatQuantExpert wrote: eGMAT Question of the Week #8In 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 The Answer has to be B. From the Property of Traingle (i.e. Sum of two sides is always greater than third side). In Triangle ADC, \(2 < AD < 18\) In Triangle ABC, \(4 < BC < 16.\) Add the Max value of AD & BC + 14. Only option B satisfies.
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Re: Question of the Week 8 (In the quadrilateral shown above,........)
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20 Jul 2018, 22:58
Given , AB = 6, CD = 8, AC = 10 Question : Perimeter = AB + BC + CD + AD = ?, i.e. BC + AC + 14 = ? Required, value of AD and BC to find out perimeter of the quadrilateral.
For Triangle ADC : AD < AC + DC, Hence, AD < 10+8 = 18  (1) And, AD+DC > AC, Hence, AD > 2 (2) (Checking AD + AC > DC not required as already AC> DC)
For Triangle ABC : BC < AB+AC, Hence, BC < 6+10 = 16 (3) And, AB + BC > AC, hence, BC > 4 (4) (Checking BC + AC > AB not required as already AC > AB)
From Eq. (1) & (3) we get P <48 and from Eq. (3) & (4) we get P >24. Only (B) satisfies this. Hence, answer is (B) 35 units.



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Re: Question of the Week 8 (In the quadrilateral shown above,........)
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Updated on: 13 Aug 2018, 00:48
Hey kunalcvrce, Your answer is correct. But, can you please tell me, how you arrived at: "In triangle ADC ,3<AD<17 In triangle ABC ,5<BC<15"It should be 2<AD<18 and 4<BC<16 Regards, Ashutosh eGMAT
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Re: Question of the Week 8 (In the quadrilateral shown above,........)
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20 Jul 2018, 23:23
EgmatQuantExpert wrote: Hey kunalcvrce, Your answer is correct. But, can you please tell me, how you arrived at: "In triangle ADC ,3<AD<17 In triangle ABC ,5<BC<15"It should be 2<AD<18 and 4<BC<16 Regards, Ashutosh eGMATHi EgmatQuantExpertI missed the equal sign considering sides are integer. Thanks for correcting.



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Re: Question of the Week 8 (In the quadrilateral shown above,........)
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20 Jul 2018, 23:33
EgmatQuantExpert wrote: Hey kunalcvrce, Your answer is correct. But, can you please tell me, how you arrived at: "In triangle ADC ,3<AD<17 In triangle ABC ,5<BC<15"It should be 2<AD<18 and 4<BC<16 Regards, Ashutosh eGMAT EgmatQuantExpertIt’s a proper GMAT type question. I will say it’s a simple and tricky question. If triangle property didn’t strike on time then this question will become most difficult to solve . Sent from my iPhone using GMAT Club Forum mobile app



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Re: Question of the Week 8 (In the quadrilateral shown above,........)
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Updated on: 13 Aug 2018, 00:45
Hey kunalcvrce, Thanks for your feedback. We will try our best to give the best GMAT like questions in our Question of the Week series. Regards, Ashutosh eGMAT
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Re: Question of the Week 8 (In the quadrilateral shown above,........)
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23 Jul 2018, 05:19
Hello everyone, Thanks for participation. We have posted the official answer to the question. Regards, Ashutosh eGMAT
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Re: Question of the Week 8 (In the quadrilateral shown above,........)
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