Here's one approach:
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) √2
d) √3
e) (√2)/2
So, s = 1
Answer: B
Cheers,
Brent
PS - Geometry
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So, s = 1
Answer: B
Cheers,
Brent
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Mathsbuddy
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If we superimpose the graph on an Argand diagram, by dividing by SQRT(-1) we arrive at co-ordinates that superimpose back to (1, SQRT(3))
Therefore Answer = 1
ONLY GOOD FOR THOSE WHO UNDERSTAND COMPLEX NUMBERS, BUT VERY QUICK TO DO MENTALLY
Therefore Answer = 1
ONLY GOOD FOR THOSE WHO UNDERSTAND COMPLEX NUMBERS, BUT VERY QUICK TO DO MENTALLY
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Hi kartikc11,
Geometry questions on the GMAT are designed around a limited number of standard formulas and math concepts. You'll become more efficient at solving these types of questions as you learn to spot the patterns involved.
Here, there are a few patterns/rules that immediately come to mind:
1) ANY diagonal line in a graph IS the hypotenuse of a right triangle. You can draw that right triangle by adding the two other sides to the picture. Here, you can draw a line "down" from each point to the X-axis. This will form 2 right triangles.
2) Right triangles on Test day are usually meant to test your knowledge of either the Pythagorean Theorem (A^2 + B^2 = C^2) or your understanding of angles and sides (30/60/90 and 45/45/90).
3) The angles on a line add up to 180 degrees.
4) Circles are always about the radius.
These rules/concepts are what are needed to answer the question (as Brent's explanation shows). During your studies, your ability to spot the rules that apply will help you to work faster and more efficiently.
GMAT assassins aren't born, they're made,
Rich
Geometry questions on the GMAT are designed around a limited number of standard formulas and math concepts. You'll become more efficient at solving these types of questions as you learn to spot the patterns involved.
Here, there are a few patterns/rules that immediately come to mind:
1) ANY diagonal line in a graph IS the hypotenuse of a right triangle. You can draw that right triangle by adding the two other sides to the picture. Here, you can draw a line "down" from each point to the X-axis. This will form 2 right triangles.
2) Right triangles on Test day are usually meant to test your knowledge of either the Pythagorean Theorem (A^2 + B^2 = C^2) or your understanding of angles and sides (30/60/90 and 45/45/90).
3) The angles on a line add up to 180 degrees.
4) Circles are always about the radius.
These rules/concepts are what are needed to answer the question (as Brent's explanation shows). During your studies, your ability to spot the rules that apply will help you to work faster and more efficiently.
GMAT assassins aren't born, they're made,
Rich
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GMATinsight
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We know that perpendicular lines have relations between slopes as given below:
m1 x m2 = -1
The slope of OP line is 1/√3 = m1
therefore, (-1/√3) x m2 = -1 which means m2 = √3/1
But since OP = OQ (both are redie of the given circle) and OP has actual values in the slope being 1 as y-co ordinate and -√3 as X-co ordinate therefore the values of co-ordinate of OQ also will be actual values
m2 = y coordinate/X coordinate = √3/1 therefore co-ordinates of Q (1, √3) ANSWER
therefore
m1 x m2 = -1
The slope of OP line is 1/√3 = m1
therefore, (-1/√3) x m2 = -1 which means m2 = √3/1
But since OP = OQ (both are redie of the given circle) and OP has actual values in the slope being 1 as y-co ordinate and -√3 as X-co ordinate therefore the values of co-ordinate of OQ also will be actual values
m2 = y coordinate/X coordinate = √3/1 therefore co-ordinates of Q (1, √3) ANSWER
therefore
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