quantskillsgmat wrote:square ABCD lie in first quadrant of xy plane.A(4,6),B(8,6), C(8,2) ,D(4,2). point p lie on x axis and its coordinate is (6,0). A certain computer programe randomly generates equation of line is form of y=mx+b.If point p is a point on a line generated by this prog, what is prob that line does not pass through ABCD.
a)3/4 b)3/5 c)1/2 d)2/5 e)1/4
DRAW the figure:
]
Any line through point P that does NOT pass through the two shaded regions will NOT pass through the square.
Any line through point P that passes through one of the shaded regions must pass through the other.
The slope of line L = (2-0)/(4-6) = -1.
The slope of line M = (2-0)/(8-6) = 1.
Since the slopes are negative reciprocals, line L is perpendicular to line M.
The intersection of lines L and M forms four 90 degree angles.
The sum of these four angles is 360.
Thus, the fraction of the coordinate plane taken by the two shaded regions = 180/360 = 1/2.
Thus, the probability that a line through point P will NOT pass through the two shaded regions = 1-1/2 = 1/2.
The correct answer is
C.
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
