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Question of the Week- 8 (In the quadrilateral shown above,........)

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Updated on: 15 Aug 2018, 23:56
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55% (hard)

Question Stats:

64% (02:39) correct 36% (02:48) wrong based on 105 sessions

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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?

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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Originally posted by EgmatQuantExpert on 20 Jul 2018, 04:03.
Last edited by EgmatQuantExpert on 15 Aug 2018, 23:56, edited 6 times in total.
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Re: Question of the Week- 8 (In the quadrilateral shown above,........)  [#permalink]

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Updated on: 12 Aug 2018, 23:42
2
2

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:

• 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.

• 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.

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Originally posted by EgmatQuantExpert on 20 Jul 2018, 04:08.
Last edited by EgmatQuantExpert on 12 Aug 2018, 23:42, edited 2 times in total.
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Re: Question of the Week- 8 (In the quadrilateral shown above,........)  [#permalink]

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20 Jul 2018, 04:33
EgmatQuantExpert wrote:
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?

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 ABC ,5<BC<15

Therefore Max perimeter 8+6+17+15=46
Min perimeter 6+8+3+5=22
22<P<46
So B
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Re: Question of the Week- 8 (In the quadrilateral shown above,........)  [#permalink]

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Updated on: 20 Jul 2018, 22:26
EgmatQuantExpert wrote:
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?

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.

Originally posted by rahul16singh28 on 20 Jul 2018, 08:32.
Last edited by rahul16singh28 on 20 Jul 2018, 22:26, edited 1 time in total.
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Re: Question of the Week- 8 (In the quadrilateral shown above,........)  [#permalink]

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20 Jul 2018, 21:58
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.

AD < AC + DC, Hence, AD < 10+8 = 18 ---- (1)
(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,........)  [#permalink]

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Updated on: 12 Aug 2018, 23:48

Originally posted by EgmatQuantExpert on 20 Jul 2018, 22:20.
Last edited by EgmatQuantExpert on 12 Aug 2018, 23:48, edited 1 time in total.
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Re: Question of the Week- 8 (In the quadrilateral shown above,........)  [#permalink]

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20 Jul 2018, 22:23
EgmatQuantExpert wrote:
Hey kunalcvrce,

But, can you please tell me, how you arrived at:
In triangle ABC ,5<BC<15"

It should be 2<AD<18 and 4<BC<16

Regards,
Ashutosh
e-GMAT

Hi EgmatQuantExpert

I 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,........)  [#permalink]

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20 Jul 2018, 22:33
EgmatQuantExpert wrote:
Hey kunalcvrce,

But, can you please tell me, how you arrived at:
In triangle ABC ,5<BC<15"

It should be 2<AD<18 and 4<BC<16

Regards,
Ashutosh
e-GMAT

EgmatQuantExpert
It’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,........)  [#permalink]

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Updated on: 12 Aug 2018, 23:45

Originally posted by EgmatQuantExpert on 22 Jul 2018, 13:28.
Last edited by EgmatQuantExpert on 12 Aug 2018, 23:45, edited 1 time in total.
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Re: Question of the Week- 8 (In the quadrilateral shown above,........)  [#permalink]

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23 Jul 2018, 04:19
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Re: Question of the Week- 8 (In the quadrilateral shown above,........)  [#permalink]

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21 Oct 2019, 05:07
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Re: Question of the Week- 8 (In the quadrilateral shown above,........)   [#permalink] 21 Oct 2019, 05:07
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