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Ballparking in GRE Math-Geometry

The Ballparking technique works really well on the Geometry questions asked on the GRE. It involves eliminating answer choices of wrong size and estimating the right answer by doing some approximation. Whenever you get stuck or are running out of time on your exam, you should try to use this technique to get your answer right.

Let’s see an example and try finding areas of the shaded region.

1. In the circle given below with centre O, the diameter is 12 and the smaller angle AOB is 150˚ as shown. What is the area of the shaded region?

circlea) 27π

b) 18π

c) 15π

d)12π

e)9π

Well this involves knowing the relationship between sector area and central angle and for that you need to know the formula. However you can solve this just by doing some Ballparking!

Now since the diameter is 12, the radius becomes 6. The area of the circle is 36π (Everyone knows area of Circle formula is πr2). That means area of semicircle would be 18π. Well since the shaded region is less than the area of a semicircle the answer choices A and B get eliminated. As the area of the shaded region is surely more than the area of a quarter circles, that is 9π, answer choice E too gets eliminated.

Now we are left with answer choices C and D as both are between 9π and 18π. A closer observation of the diagram will tell you that the area of the shaded region is surely more than 1/3rd the area of circle, that is more than 12π. Hence the answer choice D gets eliminated and C is the answer!

Ballparking works well in Coordinate Geometry question as well.

2. In the rectangular coordinate system line y = x is the perpendicular bisector of the line segment AB and the X – axis is the perpendicular bisector of the line segment BC. If the coordinates of A are (3, 4), what are the coordinates of point C?

a) (-4,-3)

b) (-4, 3)

c) (3, -4)

d) (4,-3)

e) (4, 3)

Now this question involves drawing the X and Y axes, plotting the point A and the line y = x as shown below. As the line y = x is the perpendicular bisector of the line segment AB, the coordinates of B will be (4,3) (mirror image)as shown below.

Image-1

 

 

 

 

 

 

 

 

 

 

 

As it is given that the X – axis is the perpendicular bisector of the line segment BC, it clearly means that the point C will be in the fourth quadrant with the x coordinate being positive and the y coordinate being negative. That means we can eliminate choices A, B and E.

A closer look at the diagram will tell us that (3, -4) is just the mirror image of point A in the X – axis and not point B. Hence eliminate C and the answer is D!

The diagram below shows points A, B and C.

Image-2

 

 

 

 

 

 

 

 

 

 

 

 

 

This same question would have involved slope, equation of line and other formulae if you had solved it normally. However Ballparking makes it look pretty simple!

 

 

 

 

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