Hi there,
this is a problem from the GMAT exam. I've thought it over and over and cannot match my results with the options offered, maybe someone out there can point out, where I am going wrong in my calculations.
Here is the problem:
Two circles (in my diagram they are drawn as sections of a cone, but I don't think it matters or does it?)
Circle C is bigger than Circle B.
The radius of C is called r
The radius of B is called x
We know that x is 20% of r.
The Question: By what percentage is the area of circle C greater than the area of Circle B?
So, here is my favorite solution (which still doesn't match):
To find the percentage of an increase I usually apply the following formula:
New Value = Old Value + Old Value x percentage (works nicely for pricing)
Formula for Area is of course:
A=pi times r squared
So:
A of C = pi times r squared
A of B = pi times x squared
x is 20% of r
so:
x= (r) x (0.2)
Area of C = Area of B + (Area of B x (what?)) (I call it y)
plugging the info in:
pi x (r squared) = pi x (0.2 squared) x (r squared) + pi x (0.2 squared) x (r squared) x (y)
SOLVING FOR y
0.2 SQUARED = 0.04
- (pi x (0.04) x (r squared))
(pi x (r squared)) - (pi x (0.04) x (r squared)) = pi x (0.04) x (r squared) x (y)
DIVIDE BY pi AND r squared
1 - 0.04 = 0.04y
is:
0.96 = 0.04y
is:
y = 24
So I would say the Area of Circle C is 24% bigger than the Area of Circle B.
Alas, the options available are:
250%
400%
500%
2400%
2500%
And my tutor suggested 2,500 or 250% but I can't figure out how he did it and which of the two would be correct.
Plugging numbers in doesn't help:
Let r be 10
thus x is (20% of r) = 2
Area C= pi x 10 sq = 100 pi
Area B = pi x 2 sq = 4 pi
100= 4 + (y x 4)
same situation .... I am baffled.
Thanks a bunch
sang-gye
this is a problem from the GMAT exam. I've thought it over and over and cannot match my results with the options offered, maybe someone out there can point out, where I am going wrong in my calculations.
Here is the problem:
Two circles (in my diagram they are drawn as sections of a cone, but I don't think it matters or does it?)
Circle C is bigger than Circle B.
The radius of C is called r
The radius of B is called x
We know that x is 20% of r.
The Question: By what percentage is the area of circle C greater than the area of Circle B?
So, here is my favorite solution (which still doesn't match):
To find the percentage of an increase I usually apply the following formula:
New Value = Old Value + Old Value x percentage (works nicely for pricing)
Formula for Area is of course:
A=pi times r squared
So:
A of C = pi times r squared
A of B = pi times x squared
x is 20% of r
so:
x= (r) x (0.2)
Area of C = Area of B + (Area of B x (what?)) (I call it y)
plugging the info in:
pi x (r squared) = pi x (0.2 squared) x (r squared) + pi x (0.2 squared) x (r squared) x (y)
SOLVING FOR y
0.2 SQUARED = 0.04
- (pi x (0.04) x (r squared))
(pi x (r squared)) - (pi x (0.04) x (r squared)) = pi x (0.04) x (r squared) x (y)
DIVIDE BY pi AND r squared
1 - 0.04 = 0.04y
is:
0.96 = 0.04y
is:
y = 24
So I would say the Area of Circle C is 24% bigger than the Area of Circle B.
Alas, the options available are:
250%
400%
500%
2400%
2500%
And my tutor suggested 2,500 or 250% but I can't figure out how he did it and which of the two would be correct.
Plugging numbers in doesn't help:
Let r be 10
thus x is (20% of r) = 2
Area C= pi x 10 sq = 100 pi
Area B = pi x 2 sq = 4 pi
100= 4 + (y x 4)
same situation .... I am baffled.
Thanks a bunch
sang-gye