GMAT Question of the Day - Daily to your Mailbox; hard ones only

 It is currently 23 Apr 2019, 17:20

### GMAT Club Daily Prep

#### Thank you for using the timer - this advanced tool can estimate your performance and suggest more practice questions. We have subscribed you to Daily Prep Questions via email.

Customized
for You

we will pick new questions that match your level based on your Timer History

Track

every week, we’ll send you an estimated GMAT score based on your performance

Practice
Pays

we will pick new questions that match your level based on your Timer History

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

Author Message
TAGS:

### Hide Tags

Math Expert
Joined: 02 Sep 2009
Posts: 54493
ASB is a quarter circle. PQRS is a rectangle with sides PQ = 8 and PS  [#permalink]

### Show Tags

14 May 2016, 03:56
00:00

Difficulty:

5% (low)

Question Stats:

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

### HideShow timer Statistics

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 [ 1.33 KiB | Viewed 7292 times ]

_________________
Math Expert
Joined: 02 Aug 2009
Posts: 7579
Re: ASB is a quarter circle. PQRS is a rectangle with sides PQ = 8 and PS  [#permalink]

### Show Tags

14 May 2016, 04:18
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

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
_________________
Board of Directors
Status: QA & VA Forum Moderator
Joined: 11 Jun 2011
Posts: 4426
Location: India
GPA: 3.5
Re: ASB is a quarter circle. PQRS is a rectangle with sides PQ = 8 and PS  [#permalink]

### Show Tags

14 May 2016, 07:37
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:
The attachment 2016-05-14_1454.png is no longer available

Attachment:

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

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

Hence answer will be A. 5π
_________________
Thanks and Regards

Abhishek....

PLEASE FOLLOW THE RULES FOR POSTING IN QA AND VA FORUM AND USE SEARCH FUNCTION BEFORE POSTING NEW QUESTIONS

How to use Search Function in GMAT Club | Rules for Posting in QA forum | Writing Mathematical Formulas |Rules for Posting in VA forum | Request Expert's Reply ( VA Forum Only )
CEO
Joined: 12 Sep 2015
Posts: 3588
ASB is a quarter circle. PQRS is a rectangle with sides PQ = 8 and PS  [#permalink]

### Show Tags

16 Jun 2016, 12:49
1
Top Contributor
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:

_________________
Test confidently with gmatprepnow.com
Manager
Joined: 22 Nov 2016
Posts: 205
Location: United States
GPA: 3.4
Re: ASB is a quarter circle. PQRS is a rectangle with sides PQ = 8 and PS  [#permalink]

### Show Tags

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

_________________
Kudosity killed the cat but your kudos can save it.
Director
Joined: 02 Sep 2016
Posts: 663
Re: ASB is a quarter circle. PQRS is a rectangle with sides PQ = 8 and PS  [#permalink]

### Show Tags

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
_________________
Help me make my explanation better by providing a logical feedback.

If you liked the post, HIT KUDOS !!

Don't quit.............Do it.
Re: ASB is a quarter circle. PQRS is a rectangle with sides PQ = 8 and PS   [#permalink] 06 Jul 2017, 22:09
Display posts from previous: Sort by