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

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Math Expert
Joined: 02 Sep 2009
Posts: 51215
If a large pizza has a radius that is 30% larger that that of a medium  [#permalink]

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17 Aug 2018, 11:20
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Difficulty:

15% (low)

Question Stats:

81% (00:48) correct 19% (01:18) wrong based on 57 sessions

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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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17 Aug 2018, 11:31
1
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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18 Aug 2018, 08:11
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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18 Aug 2018, 09:53
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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18 Aug 2018, 10:18
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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20 Aug 2018, 10:08
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, 10:08
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# If a large pizza has a radius that is 30% larger that that of a medium

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