Set T consists of all points (x,y) such that x^2 + y^2 = 1. If point (a,b) is selected from set T at random, what is the probability that b > a + 1?
A)1/4
B)1/3
C)1/2
D)3/5
E)2/3
OA:A
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Probability - Set T consists
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fiza gupta
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Hi fiza gupta,
This question is fairly 'high-concept', but you can solve it with a drawing and a bit of logic.
When you graph the equation X^2 + Y^2 = 1, you will have a circle with a radius of 1 that is centered around the Origin. There are only four points on that circle that are integer values: (0,1), (1, 0), (0, -1) and (-1, 0). All of the other points are positive/negative fractional values. Knowing that, the ONLY way for the inequality Y > X + 1 to occur is when X is NEGATIVE and Y is POSITIVE. That outcome only occurs in the 2nd quadrant of the graph (which is 1/4 of the circle). While you might be unsure about whether every point in that quadrant would 'fit' the inequality or not, the answer choices ARE numbers - and the smallest of them is 1/4. Since there's no smaller possibility, 1/4 must be the answer.
Final Answer: A
GMAT assassins aren't born, they're made,
Rich
This question is fairly 'high-concept', but you can solve it with a drawing and a bit of logic.
When you graph the equation X^2 + Y^2 = 1, you will have a circle with a radius of 1 that is centered around the Origin. There are only four points on that circle that are integer values: (0,1), (1, 0), (0, -1) and (-1, 0). All of the other points are positive/negative fractional values. Knowing that, the ONLY way for the inequality Y > X + 1 to occur is when X is NEGATIVE and Y is POSITIVE. That outcome only occurs in the 2nd quadrant of the graph (which is 1/4 of the circle). While you might be unsure about whether every point in that quadrant would 'fit' the inequality or not, the answer choices ARE numbers - and the smallest of them is 1/4. Since there's no smaller possibility, 1/4 must be the answer.
Final Answer: A
GMAT assassins aren't born, they're made,
Rich
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GMATGuruNY
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I posted a solution here:
https://www.beatthegmat.com/set-t-consis ... 90340.html
https://www.beatthegmat.com/set-t-consis ... 90340.html
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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].
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fiza gupta
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