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GMATPrep Q - XY Plane

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by krnverma » Mon Aug 08, 2011 2:55 am
Image

Q: In the figure above, points P and Q lie on the circle with center O. What is the value of S.

a)1/2
b)1
c)Root 2
d)Root 3
e)(Root 2)/2

OA: B

Another question where I fell in the trap of the classic mistake - "predictable wrong choice in the answer choices". Could some one explain the Math behind the answer?

Thank you!
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by GMATGuruNY » Mon Aug 08, 2011 3:21 am
krnverma wrote:Image

Q: In the figure above, points P and Q lie on the circle with center O. What is the value of S.

a)1/2
b)1
c)Root 2
d)Root 3
e)(Root 2)/2

OA: B

Another question where I fell in the trap of the classic mistake - "predictable wrong choice in the answer choices". Could some one explain the Math behind the answer?

Thank you!
The sides of a 30-60-90 triangle are proportioned x : x√3 : 2x.
Whenever you see √3 in a geometry question, look for -- or DRAW -- a 30-60-90 triangle.
Given (-√3, 1), y=1 and |x|=√3 represent the legs of a 30-60-90 triangle in which the sides are 1:√3:2.
Thus, we get the following drawing:

Image

The correct answer is B.
Last edited by GMATGuruNY on Mon Aug 08, 2011 7:54 am, edited 2 times in total.
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by gmatboost » Mon Aug 08, 2011 7:31 am
For a step-by-step explanation check out my previous post here:
https://www.beatthegmat.com/circle-i-can ... tml#393687

Mitch's picture is very helpful to visualize each step.
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by ashhchdg » Sun Aug 14, 2011 11:36 pm
Hi All,
I solved the problem by the below method. Please let me know if this is correct .

Point P(-√3,1)and O (0,0)make a line with slope m1 which is perpendicular to line made by Q(s,t)with slope m2. Since we know that product of slopes of perpendicular lines is -1. Therefore,

m1 * m2 = -1. here m1=-1/√3,

hence m2=√3/1--> implies x=1 as the line is in +ve plane. and the ratio has to be the same as both the lines are radius of the semicircle.
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by gmatboost » Mon Aug 15, 2011 8:15 am
You are correct that the second line has a slope of root(3), and that the length of the line must be the same as the length of the first because they are both radii. It would probably good to double check that the coordinates turn out as you expect by setting up some sort of equation like

x^2 + [x*root(3)]^2 = 2^2

But in the end you got it right, and you didn't make any incorrect assumptions, so it's a good approach.
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