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ASB is a quarter circle. PQRS is a rectangle with sides PQ = 8 and PS : Problem Solving (PS)
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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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Bunuel wrote:

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.

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]
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 = $$\frac{90 * 2 * 10 * \pi}{360}$$ = $$5\pi$$

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

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.

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
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Re: ASB is a quarter circle. PQRS is a rectangle with sides PQ = 8 and PS [#permalink]
Top Contributor
Kimberly77 wrote:
BrentGMATPrepNow wrote:
Bunuel wrote:

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.

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

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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Re: ASB is a quarter circle. PQRS is a rectangle with sides PQ = 8 and PS [#permalink]
Great explanation always and crystal clear now. Thanks Brent BrentGMATPrepNow
Re: ASB is a quarter circle. PQRS is a rectangle with sides PQ = 8 and PS [#permalink]
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