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ASB is a quarter circle. PQRS is a rectangle with sides PQ = 8 and PS

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ASB is a quarter circle. PQRS is a rectangle with sides PQ = 8 and PS  [#permalink]

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New post 14 May 2016, 03:56
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A
B
C
D
E

Difficulty:

  5% (low)

Question Stats:

90% (01:55) correct 10% (02:08) wrong based on 154 sessions

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Re: ASB is a quarter circle. PQRS is a rectangle with sides PQ = 8 and PS  [#permalink]

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New post 14 May 2016, 04:18
Bunuel wrote:
Image
ASB is a quarter circle. PQRS is a rectangle with sides PQ = 8 and PS = 6. What is the length of the arc AQB ?

A. 5π
B. 10π
C. 25
D. 14
E. 28

Attachment:
2016-05-14_1454.png


Clearly A and B are th eONLY valid answer, as pi has to be a part of answer..

the diagonal of rectangle will give us radius of circle..
take triangle PQS-
QS = Hyp = Radius = \(\sqrt{8^2+6^2}=10\)..
ARC = circumference /4 = 2*pi*10/4 = 5pi
A
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Re: ASB is a quarter circle. PQRS is a rectangle with sides PQ = 8 and PS  [#permalink]

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New post 14 May 2016, 07:37
Bunuel wrote:
Image
ASB is a quarter circle. PQRS is a rectangle with sides PQ = 8 and PS = 6. What is the length of the arc AQB ?

A. 5π
B. 10π
C. 25
D. 14
E. 28

Attachment:
The attachment 2016-05-14_1454.png is no longer available


Attachment:
2016-05-14_1454.png
2016-05-14_1454.png [ 3.97 KiB | Viewed 5684 times ]


Radius will be 10 cm

Length of Arc AQB = \(\frac{1}{4}*2π*10\) = 5π

Hence answer will be A. 5π
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ASB is a quarter circle. PQRS is a rectangle with sides PQ = 8 and PS  [#permalink]

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New post 16 Jun 2016, 12:49
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Bunuel wrote:
Image
ASB is a quarter circle. PQRS is a rectangle with sides PQ = 8 and PS = 6. What is the length of the arc AQB ?

A. 5π
B. 10π
C. 25
D. 14
E. 28

Attachment:
2016-05-14_1454.png


As chetan2u pointed out, the correct answer must be in terms of pi. So, we can ELIMINATE C, D, and E

At this point we might remember an important rule: Diagrams in problem solving questions are DRAWN TO SCALE unless stated otherwise.
So, we can use this fact to solve the question by simply "eyeballing" the diagram.

We know that PQ has length 8
How does the length of the arc AQB compare with the length of line segment PQ?
I'd say, the arc is ABOUT twice as long as the line segment.
So, the length of the arc AQB is APPROXIMATELY 16

Now check the two remaining answer choices:
A. 5π ≈ 15.something (pretty close to our approximation!)
B. 10π = 31.something. Too far away from our approximation.

Answer:


Here's a video on the assumptions we can make about diagrams on the GMAT:

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Re: ASB is a quarter circle. PQRS is a rectangle with sides PQ = 8 and PS  [#permalink]

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New post 06 Jul 2017, 17:54
SR=8, QR=6, Triangle SQR is a special right triangle or a multiple of the 3,4,5 right triangle. Hence SQ=10. This is the radius.

With radius we can solve the length of arc AQB = \(\frac{90 * 2 * 10 * \pi}{360}\) = \(5\pi\)

Answer is A
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Re: ASB is a quarter circle. PQRS is a rectangle with sides PQ = 8 and PS  [#permalink]

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New post 06 Jul 2017, 22:09
Length of arc= angle ASR/360 *2*pi*radius
Angle ASR= 90 (angle formed by sides of a rectangle)

Just plug in the values and we get 5pi
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Re: ASB is a quarter circle. PQRS is a rectangle with sides PQ = 8 and PS   [#permalink] 06 Jul 2017, 22:09
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