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If the figure above is a quarter circle and AC is 5, what is the perim

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If the figure above is a quarter circle and AC is 5, what is the perim  [#permalink]

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New post 18 Sep 2018, 22:12
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If the figure above is a quarter circle and AC is 5, what is the perimeter of the shaded region?

(1) The perimeter of the rectangle ABDF is 14.
(2) AB = 4/5*AF


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Re: If the figure above is a quarter circle and AC is 5, what is the perim  [#permalink]

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New post 19 Sep 2018, 05:13

Solution


Given:
    • The radius of the circle = 5

To find:
    • The perimeter of the shaded region

Approach and Working:

Perimeter of the shaded region = length of arc CE + EF + BF +BC
    • Length of arc EC = 2ᴨr/4 = 5ᴨ
    • EF = AE – AF = 5 – AF
    • FB = AD = 5
    • BC = AC – AB = 5 – AB

Thus, the perimeter of the shaded region = 5ᴨ + (5 - AF) + 5 + (5 - AB) = 5ᴨ + 15 – (AB + AF)

Analysing Statement 1
“The perimeter of the rectangle ABDF is 14”

    • Implies, ABDF is a rectangle and 2(AB + AF) = 14
      o AB + AF = 7
    • Therefore, perimeter of the shaded region = 5ᴨ + 15 – (AB + AF) = 15 + 5ᴨ – 7 = 8 + 5ᴨ

Therefore, Statement 1 is sufficient to arrive at a unique answer

Analysing Statement 2
“AB = 4/5 * AF”

    • Perimeter of the shaded region = 5ᴨ + 15 – (AB + AF)
    • However, we cannot find the value of AB or AF from the given information

Therefore, Statement 2 is NOT sufficient to arrive at a unique answer

Hence, the correct answer is option A.

Answer: A

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Re: If the figure above is a quarter circle and AC is 5, what is the perim  [#permalink]

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New post 19 Sep 2018, 09:20
EgmatQuantExpert wrote:

Solution


Given:
    • The radius of the circle = 5

To find:
    • The perimeter of the shaded region

Approach and Working:

Perimeter of the shaded region = length of arc CE + EF + BF +BC
    • Length of arc EC = 2ᴨr/4 = 5ᴨ
    • EF = AE – AF = 5 – AF
    • FB = AD = 5
    • BC = AC – AB = 5 – AB

Thus, the perimeter of the shaded region = 5ᴨ + (5 - AF) + 5 + (5 - AB) = 5ᴨ + 15 – (AB + AF)

Analysing Statement 1
“The perimeter of the rectangle ABDF is 14”

    • Implies, ABDF is a rectangle and 2(AB + AF) = 14
      o AB + AF = 7
    • Therefore, perimeter of the shaded region = 5ᴨ + 15 – (AB + AF) = 15 + 5ᴨ – 7 = 8 + 5ᴨ

Therefore, Statement 1 is sufficient to arrive at a unique answer

Analysing Statement 2
“AB = 4/5 * AF”

    • Perimeter of the shaded region = 5ᴨ + 15 – (AB + AF)
    • However, we cannot find the value of AB or AF from the given information

Therefore, Statement 2 is NOT sufficient to arrive at a unique answer

Hence, the correct answer is option A.

Answer: A

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I think answer is D. because using AB=4/5 AF, we can substitue in AB^2+ AF^2 = 25 and get both AB and AF. and then find the perimeter.
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Re: If the figure above is a quarter circle and AC is 5, what is the perim  [#permalink]

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New post 19 Sep 2018, 11:39
1
sandesh87 wrote:
I think answer is D. because using AB=4/5 AF, we can substitue in AB^2+ AF^2 = 25 and get both AB and AF. and then find the perimeter.


Hey sandesh87,
when you say {AB}^2 + {AF}^2 = 25, are you assuming ABDF as a rectangle?
Ideally when you analyse a statement individually, you should not consider the information present in the other statement. The information that ABDF is a rectangle is present in statement 1 only, and hence should not be considered at the time of analyzing statement 2.
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If the figure above is a quarter circle and AC is 5, what is the perim  [#permalink]

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New post 19 Sep 2018, 11:59
chetan2u Bunuel

Experts can you please confirm what's the OA? Is it D or A?
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If the figure above is a quarter circle and AC is 5, what is the perim  [#permalink]

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New post 19 Sep 2018, 20:26
EgmatQuantExpert wrote:
sandesh87 wrote:
I think answer is D. because using AB=4/5 AF, we can substitue in AB^2+ AF^2 = 25 and get both AB and AF. and then find the perimeter.


Hey sandesh87,
when you say {AB}^2 + {AF}^2 = 25, are you assuming ABDF as a rectangle?
Ideally when you analyse a statement individually, you should not consider the information present in the other statement. The information that ABDF is a rectangle is present in statement 1 only, and hence should not be considered at the time of analyzing statement 2.


Thank you for pointing the mistake. I think these are the errors which usually happen during the actual exam.
I think its a very good question.
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If the figure above is a quarter circle and AC is 5, what is the perim &nbs [#permalink] 19 Sep 2018, 20:26
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