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If a large pizza has a radius that is 30% larger that that of a medium

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If a large pizza has a radius that is 30% larger that that of a medium  [#permalink]

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New post 17 Aug 2018, 12:20
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If a large pizza has a radius that is 30% larger that that of a medium pizza, what is the percent increase in area between a medium and a large pizza?

A. 30
B. 36
C. 60
D. 69
E. 90

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Re: If a large pizza has a radius that is 30% larger that that of a medium  [#permalink]

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New post 17 Aug 2018, 12:31
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Bunuel wrote:
If a large pizza has a radius that is 30% larger that that of a medium pizza, what is the percent increase in area between a medium and a large pizza?

A. 30
B. 36
C. 60
D. 69
E. 90


If radius of medium pizza is 'r', then radius of larger pizza is 1.3r.
So, \(A_{L}=\pi*(1.3r)^2\) & \(A_{M}=\pi*r^2\)

%increase in area=\(\frac{\pi*(1.3r)^2-\pi*r^2}{\pi*r^2}\)*100=(1.69-1)*100=69%

Ans. (D)
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If a large pizza has a radius that is 30% larger that that of a medium  [#permalink]

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New post 18 Aug 2018, 09:11
Bunuel wrote:
If a large pizza has a radius that is 30% larger that that of a medium pizza, what is the percent increase in area between a medium and a large pizza?

A. 30
B. 36
C. 60
D. 69
E. 90

I. Assign values

Radius and area
Let radius of medium pizza, \(r=10\)
AREA of medium pizza: \(a=πr^2=100π\)

Radius of large pizza, \(R=(10*1.3)=13\)
OR
\(R=(r+.30r)=1.3r=(1.3*10)=13\)
AREA of large pizza, \(A=(π* 13^2)=169π\)

[Percent increase, mental math: 169 is 69% greater than 100 - Answer D]

Percent increase in area = percent change

Percent change: \(\frac{Change}{Original}*100\)

Change: \((169π-100π)=69π\)
Original (area of medium pizza) = \(100π\)

Percent increase in area:
\((\frac{69π}{100π})*100=(.69*100)=69\) %

Answer D

II. Shortcut formula for overall percent change

We have successive percent changes because the radius increases by 30% TWICE
(\(r*r*π\)) => \((R*R*π)\)

SHORTCUT formula
Overall percent change for two successive percent changes:
\(A+B+\frac{A*B}{100}\) percent

\(A\) = first percent change
\(B\) = second percent change

\(30+30+\frac{30*30}{100}\)

\((60+\frac{900}{100})=(60+9)=69\) percent increase

Answer D
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Re: If a large pizza has a radius that is 30% larger that that of a medium  [#permalink]

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New post 18 Aug 2018, 10:53
Bunuel wrote:
If a large pizza has a radius that is 30% larger that that of a medium pizza, what is the percent increase in area between a medium and a large pizza?

A. 30
B. 36
C. 60
D. 69
E. 90




Large Area = (169/100) Medium Area
%Increase = 69
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Re: If a large pizza has a radius that is 30% larger that that of a medium  [#permalink]

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New post 18 Aug 2018, 11:18
Bunuel wrote:
If a large pizza has a radius that is 30% larger that that of a medium pizza, what is the percent increase in area between a medium and a large pizza?

A. 30
B. 36
C. 60
D. 69
E. 90


\(30 + 30 + \frac{30*30}{100}\)

= 69, Answer must be (D) 69
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Re: If a large pizza has a radius that is 30% larger that that of a medium  [#permalink]

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New post 20 Aug 2018, 11:08
Bunuel wrote:
If a large pizza has a radius that is 30% larger that that of a medium pizza, what is the percent increase in area between a medium and a large pizza?

A. 30
B. 36
C. 60
D. 69
E. 90


We can let the medium pizza = 10 and the large = 13; thus:

Area of medium = 100π

Area of large = 169π

Using the percent change formula: (New - Old)/Old x 100 we obtain:

(169π - 100π)/100π x 100 = 69/100 = 69%

Answer: D
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Re: If a large pizza has a radius that is 30% larger that that of a medium &nbs [#permalink] 20 Aug 2018, 11:08
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