Check GMAT Club Decision Tracker for the Latest School Decision Releases https://gmatclub.com/AppTrack
GMAT Club

 It is currently 23 Mar 2017, 03:51

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

Events & Promotions

Events & Promotions in June
Open Detailed Calendar

In the attached figure, points P and Q lie on the circle

Author Message
Director
Joined: 06 May 2006
Posts: 792
Followers: 3

Kudos [?]: 32 [0], given: 2

In the attached figure, points P and Q lie on the circle [#permalink]

Show Tags

16 Jun 2006, 00:55
1
This post was
BOOKMARKED
This topic is locked. If you want to discuss this question please re-post it in the respective forum.

In the attached figure, points P and Q lie on the circle with centre O. What is the value of S?

A. 1/2
B. 1
C. sqrt(2)
D. sqrt(3)
E. sqrt(2)/2

I've solved it, checking if there is a better way of doing it...
Attachments

File comment: Graphic.

untitled.GIF [ 2.4 KiB | Viewed 1061 times ]

SVP
Joined: 30 Mar 2006
Posts: 1736
Followers: 1

Kudos [?]: 80 [0], given: 0

Show Tags

16 Jun 2006, 02:06
Took me some time because I had the som many ideas

What I finally chose.

If we draw a line from P to Q we get a 90-45-45 triangle.

Find the distance of OP = 2
Hence PQ must be 2rt(2).

Now take individual values of s and calculate value of t for OQ (=2)

1,sqr(3) and -sqr(3),1 satisifes PQ..........

this is a little long but can be a made short
Manager
Joined: 09 May 2006
Posts: 99
Location: Bangalore, India
Followers: 2

Kudos [?]: 41 [0], given: 0

Show Tags

16 Jun 2006, 05:44
My method:

if two line are perpendicular, product of slopes = -1

Therefore
((t-0)/(s-0))*((1-0)/(srt(3)-0)) = -1
t=s* sqrt(3) ------ A

Also distance of both points from origin is same

Sqrt(t^2 + s^2) = sqrt (3+1) = 2
t^2 + s^2 = 4 -----B

Solving both A & B

3*s^2 + s^2 = 4
s = +1 or -1 (corresponding to Q1 & Q3)

from diagram choose +1
Manager
Joined: 10 May 2006
Posts: 186
Location: USA
Followers: 1

Kudos [?]: 5 [0], given: 0

Show Tags

16 Jun 2006, 07:04
First calculate the distance between [-sqr(3), 1] and the origin

= sqt ( -sqr(3)^2 + 1^2) = sqt (3+1) = 2

This distance must be equal to the distance between the (s,t) and the origin since it's a circle.

2 = sqt (s^2 + t^2) 4 = s^2 + t^2

Next calculate the slopes. Slope of [-sqr(3), 1] and origin = 1/-sqt(3)
Perpindicular slope must be sqt (3).
Therefore, formula of the line is t = sqt(3)*s + 0

Plug in t = sqt(3)*s inot the above distance equation:
4 = s^2 + [sqt (3)*s]^2
4 = s^2 (1+3)
1 = s

Checking the formulas and eyeballing the graph confirms the answer.
Director
Joined: 06 May 2006
Posts: 792
Followers: 3

Kudos [?]: 32 [0], given: 2

Show Tags

16 Jun 2006, 08:10
OA is B.

Thx all. I used the method by shobhitb and tl372.

jaynayak, could you elaborate on your method plz? i did not quite get it.
Senior Manager
Joined: 07 Jul 2005
Posts: 404
Location: Sunnyvale, CA
Followers: 2

Kudos [?]: 13 [0], given: 0

Show Tags

16 Jun 2006, 09:07
Another approach is to use sin/cos functions.
Given P's coordiantes and radius = 2, you can find out that it makes an angle of 30 degrees with X axis, then Q must make an angle of 60 degrees with X axis, which gives s = 1 (cos 60 = 1/2)
CEO
Joined: 20 Nov 2005
Posts: 2909
Schools: Completed at SAID BUSINESS SCHOOL, OXFORD - Class of 2008
Followers: 25

Kudos [?]: 278 [0], given: 0

Show Tags

16 Jun 2006, 12:10
I solved it in under 1 minute.

OP = OQ = 2
Angle of OP with -ve side of x-axis = 30 (because Sin30 = 1/2). So angle of OQ with +ve side of x axis = 60

So s/OQ = Cos60 i.e s/2 = 1/2 i.e s = 1
_________________

SAID BUSINESS SCHOOL, OXFORD - MBA CLASS OF 2008

Manager
Joined: 31 May 2006
Posts: 56
Followers: 1

Kudos [?]: 4 [0], given: 0

Show Tags

26 Jun 2006, 06:28
Intersting Question
_________________

Learn and let others learn

Director
Joined: 06 May 2006
Posts: 792
Followers: 3

Kudos [?]: 32 [0], given: 2

Show Tags

26 Jun 2006, 16:39
ps_dahiya, sgrover - great method! thx
_________________

Uh uh. I know what you're thinking. "Is the answer A, B, C, D or E?" Well to tell you the truth in all this excitement I kinda lost track myself. But you've gotta ask yourself one question: "Do I feel lucky?" Well, do ya, punk?

26 Jun 2006, 16:39
Display posts from previous: Sort by