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GMATPrep Q - XY Plane

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krnverma: Junior | Next Rank: 30 Posts; Posts: 25; Joined: Wed Feb 02, 2011 5:17 am; Thanked: 1 times

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

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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Source: Beat The GMAT — Problem Solving | Mon Aug 08, 2011 2:55 am

GMATGuruNY: GMAT Instructor; Posts: 15539; Joined: Tue May 25, 2010 12:04 pmFollowed by: 1906 members; Location: New York, NY; Thanked: 13060 times; GMAT Score:790

by GMATGuruNY » Mon Aug 08, 2011 3:21 am

krnverma wrote:

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 : xâˆš3 : 2x.
Whenever you see âˆš3 in a geometry question, look for -- or DRAW -- a 30-60-90 triangle.
Given (-âˆš3, 1), y=1 and |x|=âˆš3 represent the legs of a 30-60-90 triangle in which the sides are 1:âˆš3:2.
Thus, we get the following drawing:

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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gmatboost: Master | Next Rank: 500 Posts; Posts: 312; Joined: Tue Aug 02, 2011 3:16 pmFollowed by: 33 members; Location: New York City; Thanked: 130 times; GMAT Score:780

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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GMAT Boost offers 250+ challenging GMAT Math practice questions, each with a thorough video explanation, and 100+ GMAT Math video tips, each 90 seconds or less.
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ashhchdg: Junior | Next Rank: 30 Posts; Posts: 14; Joined: Sun Aug 14, 2011 4:25 am; Thanked: 1 times

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(-âˆš3,1)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/âˆš3,

hence m2=âˆš3/1--> 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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gmatboost: Master | Next Rank: 500 Posts; Posts: 312; Joined: Tue Aug 02, 2011 3:16 pmFollowed by: 33 members; Location: New York City; Thanked: 130 times; GMAT Score:780

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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