BREAKING: Target Test Prep releases Brand New 2026 On Demand GMAT prep course

Redeem

Help Needed! GMAT exam next week

This topic has expert replies
Post new topic Post Reply
Previous Topic Next Topic
Source: — Problem Solving |
User avatar
Master | Next Rank: 500 Posts
Posts: 307
Joined: Sun Jul 11, 2010 7:52 pm
Thanked: 36 times
Followed by:1 members
GMAT Score:640

by limestone » Sun Sep 12, 2010 11:09 pm
So big picture!!! Please resize it.
From the given information, we can calculate the radius of the circle : r^2 = x^2 + y^2 = (-sqrt(3)) ^2 + 1^2 = 4, then r = 2
As OP and OQ crosses the original O, the equation of OP and OQ lines must be in the form: y = a*x
Plug in the given point P(-sqrt(3), 1) into OP's equation: 1 = a * -sqrt(3), or a = 1/-sqrt(3)
As line OP is perpendicular to line OQ, a1 ( a of OP's equation) * a2 ( a of OQ's equation) = -1
a2 = -1/ a1 = -1/ (1/-sqrt(3)) = sqrt(3)
the equation of line OQ: y = sqrt(3)*x, plug in Q(s,t) into OQ's equation: t = sqrt(3) * s or t^2 = 3 * s^2
Because Q (s,t) is on the circle, s^2 + t^2 = r^2 or s^2 + t^2 = 2^2
From the two bold equations : 4* s^2 = 4
Or s^2 = 1 or s = +1 or -1
However, Q is to the right the Oy vector, hence s must be equal to 1.
B is the answer.
Top
User avatar
GMAT Instructor
Posts: 15539
Joined: Tue May 25, 2010 12:04 pm
Location: New York, NY
Thanked: 13060 times
Followed by:1906 members
GMAT Score:790

by GMATGuruNY » Mon Sep 13, 2010 2:43 am
Quick approach:

Slope of OP = rise/run = (1)/ (-√3).
To get from the origin to point P (the radius), we need to move up 1 and to the left √3.
OQ is perpendicular to OP because the two lines form a right angle. The slopes of perpendicular lines are negative reciprocals.
Thus the slope of OQ = √3/1.
OQ = radius, so point Q must be the same distance from the origin as point P.
Thus, to get from the origin to point Q, we need to move up √3 and to the right 1. This is the only way to have a slope of √3/1 and be the same distance from the origin as point P.
So s=1.

Second approach:
When you see √3 in a problem, look for a 30-60-90 triangle.
The attached .pdf shows how you could draw a line from P to the x axis and another from Q to the x axis to create two 30-60-90 triangles and determine the value of s.

Good luck on your GMAT!
Attachments
BTG_semicircle.pdf
(24.57 KiB) Downloaded 109 times
Private tutor exclusively for the GMAT and GRE, with over 20 years of experience.
Followed here and elsewhere by over 1900 test-takers.
I have worked with students based in the US, Australia, Taiwan, China, Tajikistan, Kuwait, Saudi Arabia -- a long list of countries.
My students have been admitted to HBS, CBS, Tuck, Yale, Stern, Fuqua -- a long list of top programs.

As a tutor, I don't simply teach you how I would approach problems.
I unlock the best way for YOU to solve problems.

For more information, please email me (Mitch Hunt) at [email protected].
Student Review #1
Student Review #2
Student Review #3
Top
Post new topic Post Reply
• Page 1 of 1