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Coordinate Geometry and Surface area !

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Coordinate Geometry and Surface area !

by Aishwarya1204 » Sun Oct 14, 2012 5:33 am
Have my test soon. Panicking a little bit.
Took the Gmat prep test ans since they don't give solutions, I have no idea how to solve the following 2 questions:

1.

A thin piece of wire 40m long is cut into 2 pieces. One piece is used to form a circle with radius r and the other is used to form a square. No wire was left over. Which of the following represents total area in sqm of the circular and the square regions in terms of r.

answer is : [spoiler] pi r square + (10-1/2 pi r) square[/spoiler]


2.

In the xy plane, what is the y intercept of the line L ?
a) The slope is 3 times its y intercept
b) The x intercept of line L is -1/3
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by Anurag@Gurome » Sun Oct 14, 2012 5:35 am
Aishwarya1204 wrote:Have my test soon. Panicking a little bit.
Took the Gmat prep test ans since they don't give solutions, I have no idea how to solve the following 2 questions:

1.

A thin piece of wire 40m long is cut into 2 pieces. One piece is used to form a circle with radius r and the other is used to form a square. No wire was left over. Which of the following represents total area in sqm of the circular and the square regions in terms of r.

answer is : [spoiler] pi r square + (10-1/2 pi r) square[/spoiler]
The length of one piece = 2(pi)r and the other is a square. Let us assume that each side of the square is "a".
Perimeter of square = 4a
Now, 2(pi)r + 4a = 40
4a = 40 - 2(pi)r
a = [40 - 2(pi)r]/4 = 10 - (pi)r/2

Total area = Area of Circle + Area of Square
= (pi)r² + a²
= [spoiler](pi)r² + (10 - (pi)r/2)²[/spoiler]

The correct answer is [spoiler](pi)r² + (10 - (pi)r/2)²[/spoiler].
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by Anurag@Gurome » Sun Oct 14, 2012 6:38 am
Aishwarya1204 wrote:Have my test soon. Panicking a little bit.
Took the Gmat prep test ans since they don't give solutions, I have no idea how to solve the following 2 questions:

2. In the xy plane, what is the y intercept of the line L ?
a) The slope is 3 times its y intercept
b) The x intercept of line L is -1/3
Equation of line is y = mx + b
We have to find the value of y-intercept, which means when x = 0, y = b

(1) The slope is 3 times its y intercept implies m = 3b, but from here we cannot find y-intercept; NOT sufficient.

(2) The x-intercept of line L is -1/3 implies when y = 0, x = -b/m = -1/3 implies m = 3b; NOT sufficient.

Combining (1) and (2), we do not get any new info; NOT sufficient.

The correct answer is E.
Anurag Mairal, Ph.D., MBA
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