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505-555 (Easy)|   Geometry|      
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Bunuel
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ASB is a quarter circle. PQRS is a rectangle with sides PQ = 8 and PS 14 May 2016, 03:56
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15% (low)

Question Stats:

86% (01:47) correct 14% (02:08) wrong based on 220 sessions

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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

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A
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ASB is a quarter circle. PQRS is a rectangle with sides PQ = 8 and PS 14 May 2016, 04:18
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Bunuel

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

Show Spoiler
Attachment:
2016-05-14_1454.png
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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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ASB is a quarter circle. PQRS is a rectangle with sides PQ = 8 and PS 14 May 2016, 07:37
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Bunuel

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

Show Spoiler
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Attachment:
2016-05-14_1454.png
2016-05-14_1454.png [ 3.97 KiB | Viewed 19245 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 16 Jun 2016, 12:49
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Bunuel

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

Show Spoiler
Attachment:
2016-05-14_1454.png
Show more

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:
Show Spoiler
A


Here's a video on the assumptions we can make about diagrams on the GMAT:
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ASB is a quarter circle. PQRS is a rectangle with sides PQ = 8 and PS 06 Jul 2017, 17:54
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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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ASB is a quarter circle. PQRS is a rectangle with sides PQ = 8 and PS 06 Jul 2017, 22:09
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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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ASB is a quarter circle. PQRS is a rectangle with sides PQ = 8 and PS 20 Nov 2022, 08:14
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BrentGMATPrepNow
Bunuel

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

Show Spoiler
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:
Show Spoiler
A


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

Hi BrentGMATPrepNow, not quite sure why radius here is not SR=8 but SQ? Thanks Brent
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ASB is a quarter circle. PQRS is a rectangle with sides PQ = 8 and PS 20 Nov 2022, 10:28
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Kimberly77
BrentGMATPrepNow
Bunuel

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

Show Spoiler
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:
Show Spoiler
A


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

Hi BrentGMATPrepNow, not quite sure why radius here is not SR=8 but SQ? Thanks Brent
Show more

The radius of a circle is equal to the distance from the center to any point on the circumference of the circle.
So, here S is the center of the circle.
Since point R does not lie on the circumference of the circle, the length of SR it's not the radius.
On the other hand, point Q DOES lie on the circumference of the circle, which means SQ is the radius

On the other hand, point B lies on the circumference of the circle, which means SB is the radius as well
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ASB is a quarter circle. PQRS is a rectangle with sides PQ = 8 and PS 20 Nov 2022, 12:45
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Great explanation always and crystal clear now. Thanks Brent BrentGMATPrepNow :thumbsup: :please:
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