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

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EgmatQuantExpert
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Question of the Week- 8 (In the quadrilateral shown above,........) [#permalink] New post  Updated on: 16 Aug 2018, 00:56
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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?

    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, 05:03.
Last edited by EgmatQuantExpert on 16 Aug 2018, 00:56, edited 6 times in total.
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Re: Question of the Week- 8 (In the quadrilateral shown above,........) [#permalink] New post  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


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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.
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kunalcvrce
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Re: Question of the Week- 8 (In the quadrilateral shown above,........) [#permalink] New post  20 Jul 2018, 05:33
EgmatQuantExpert wrote:
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?

    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
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Re: Question of the Week- 8 (In the quadrilateral shown above,........) [#permalink] New post  Updated on: 20 Jul 2018, 23:26
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EgmatQuantExpert wrote:
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?

    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, 09:32.
Last edited by rahul16singh28 on 20 Jul 2018, 23:26, edited 1 time in total.
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Re: Question of the Week- 8 (In the quadrilateral shown above,........) [#permalink] New post  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,........) [#permalink] New post  Updated on: 13 Aug 2018, 00:48
Expert Reply
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
e-GMAT


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Originally posted by EgmatQuantExpert on 20 Jul 2018, 23:20.
Last edited by EgmatQuantExpert on 13 Aug 2018, 00:48, edited 1 time in total.
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kunalcvrce
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Re: Question of the Week- 8 (In the quadrilateral shown above,........) [#permalink] New post  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
e-GMAT


Hi EgmatQuantExpert

I missed the equal sign considering sides are integer. Thanks for correcting.
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kunalcvrce
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Re: Question of the Week- 8 (In the quadrilateral shown above,........) [#permalink] New post  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
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 .


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Re: Question of the Week- 8 (In the quadrilateral shown above,........) [#permalink] New post  Updated on: 13 Aug 2018, 00:45
Expert Reply
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
e-GMAT
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Originally posted by EgmatQuantExpert on 22 Jul 2018, 14:28.
Last edited by EgmatQuantExpert on 13 Aug 2018, 00:45, edited 1 time in total.
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Re: Question of the Week- 8 (In the quadrilateral shown above,........) [#permalink] New post  23 Jul 2018, 05:19
Expert Reply
Hello everyone,

Thanks for participation.

We have posted the official answer to the question.

Regards,
Ashutosh
e-GMAT
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Re: Question of the Week- 8 (In the quadrilateral shown above,........) [#permalink] New post  09 Feb 2024, 15:43
EgmatQuantExpert wrote:

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


­

We have 2 equations 2<AD<18  &  4<BC<16
That means AD∈ [3,17]  &  BC∈ [5,15]

So, the highlighted part is wrong. It should be AD+BC∈ [8, 32] or  \(8\leq{AD+BC}\leq{32}\)

So, perimeter is bound be between (8+14) and (32+14) i.e, perimeter∈ [22, 46]

Only option is this range is 35 (Option B)
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Re: Question of the Week- 8 (In the quadrilateral shown above,........) [#permalink]
09 Feb 2024, 15:43
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