In the figure shown, points P and Q lie on the circle with center O. What is the value of S?
A) 1/2
B) 1
C)sqrt(2)
D)sqrt(3)
E)[sqrt(2)]/2
Answer is B
Coordinate Geometry
This topic has expert replies
 amirhakimi
 Senior  Next Rank: 100 Posts
 Posts: 97
 Joined: 14 Oct 2013
 Thanked: 5 times
 Followed by:1 members
 amirhakimi
 Senior  Next Rank: 100 Posts
 Posts: 97
 Joined: 14 Oct 2013
 Thanked: 5 times
 Followed by:1 members
 theCodeToGMAT
 Legendary Member
 Posts: 1556
 Joined: 14 Aug 2012
 Thanked: 448 times
 Followed by:34 members
 GMAT Score:650
 theCodeToGMAT
 Legendary Member
 Posts: 1556
 Joined: 14 Aug 2012
 Thanked: 448 times
 Followed by:34 members
 GMAT Score:650
The solution to this problem lies in the concept of 306090 triangle.amirhakimi wrote:Aren't P and Q symmetry upon yaxis?
 Attachments

R A H U L

 Master  Next Rank: 500 Posts
 Posts: 269
 Joined: 19 Sep 2013
 Thanked: 94 times
 Followed by:7 members
10 Secs Approach:In the figure shown, points P and Q lie on the circle with center O. What is the value of s?
(A) 1/2
(B) 1
(C) âˆš2
(D) âˆš3
(E) 1/âˆš2
Rotate the figure at point O
Q has the coordinates [spoiler](1, âˆš3) and s = 1; answer B[/spoiler]

 Master  Next Rank: 500 Posts
 Posts: 269
 Joined: 19 Sep 2013
 Thanked: 94 times
 Followed by:7 members
Nope they are not symmetric. We should not rely on the GMAT to provide us figures drawn to scale (implying you cannot use a protractor to measure their diagrams )amirhakimi wrote:Aren't P and Q symmetry upon yaxis?
In the figure shown, points P and Q lie on the circle with center O. What is the value of s?
(A) 1/2
(B) 1
(C) âˆš2
(D) âˆš3
(E) 1/âˆš2
Consider the above problem again:
In âˆ†PAO, the sides are 1, âˆš3, and 2. Thus it is a 306090 triangle as shown.
Complete the other angles and drop a perpendicular to B. It is our new 306090 triangle.
The sides are again 1, âˆš3, and 2.
thus Q has the coordinates (s,t) = [spoiler](1, âˆš3) and s = 1[/spoiler]
GMAT/MBA Expert
 [email protected]
 Elite Legendary Member
 Posts: 10392
 Joined: 23 Jun 2013
 Location: Palo Alto, CA
 Thanked: 2867 times
 Followed by:510 members
 GMAT Score:800
Hi amirhakimi,
Since other posters have properly explained the "math" behind this question, I won't rehash it here.
I do want to reiterate certain tactics that you'll find useful in these types of questions:
1) ANY diagonal line on a graph can be determined by drawing a right triangle "around it." This is a useful tactic on most questions involving graphs.
2) The GMAT regularly tests certain right triangles (30/60/90, 45/45/90, 3/4/5, 5/12/13), so be on the look out for those triangles.
GMAT assassins aren't born, they're made,
Rich
Since other posters have properly explained the "math" behind this question, I won't rehash it here.
I do want to reiterate certain tactics that you'll find useful in these types of questions:
1) ANY diagonal line on a graph can be determined by drawing a right triangle "around it." This is a useful tactic on most questions involving graphs.
2) The GMAT regularly tests certain right triangles (30/60/90, 45/45/90, 3/4/5, 5/12/13), so be on the look out for those triangles.
GMAT assassins aren't born, they're made,
Rich
 amirhakimi
 Senior  Next Rank: 100 Posts
 Posts: 97
 Joined: 14 Oct 2013
 Thanked: 5 times
 Followed by:1 members
That was the the first principal of MGMAT on Geometry and I completely forget about that.
"DON'T ASSUME WHAT YOU DON'T KNOW FOR SURE!"
Getting this answer wrong was my punishment for not paying attention to principals
Thanks for the headsup my friend
"DON'T ASSUME WHAT YOU DON'T KNOW FOR SURE!"
Getting this answer wrong was my punishment for not paying attention to principals
Thanks for the headsup my friend
mevicks wrote: Nope they are not symmetric. We should not rely on the GMAT to provide us figures drawn to scale (implying you cannot use a protractor to measure their diagrams )