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

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M7MBA: Moderator; Posts: 2058; Joined: Sun Oct 29, 2017 4:24 am; Thanked: 1 times; Followed by:5 members

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

by M7MBA » Fri Mar 09, 2018 9:56 am

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

The OA id d.

I need some help here. Experts, can clarify to me how to solve this PS question?

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Source: Beat The GMAT — Problem Solving | Fri Mar 09, 2018 9:56 am

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[email protected]: Elite Legendary Member; Posts: 10392; Joined: Sun Jun 23, 2013 6:38 pm; Location: Palo Alto, CA; Thanked: 2867 times; Followed by:511 members; GMAT Score:800

by [email protected] » Fri Mar 09, 2018 12:30 pm

Hi M7MBA,

We're told that a large pizza has a radius that is 30% larger that that of a medium pizza. We're asked for the percent increase in AREA between a medium and a large pizza. This question can be solved by TESTing VALUES.

IF....
The radius of a medium pizza is 10, then it's area = (pi)(10^2) = 100pi....
then the radius of a large pizza would be 13, so it's area = (pi)(13^2) = 169pi....

Percentage Change = (New - Old)/(Old) = (169pi - 100pi)/(100pi) = 69/100 = a 69% increase in area

Final Answer: D

GMAT assassins aren't born, they're made,
Rich

Contact Rich at [email protected]

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Vincen: Legendary Member; Posts: 2898; Joined: Thu Sep 07, 2017 2:49 pm; Thanked: 6 times; Followed by:5 members

by Vincen » Sun Mar 11, 2018 7:45 am

Hello M7MBA.

Let's suposse that the radius of the medium pizza is equal to r. This implies that the radius of the large pizza is r+0.3r=1.3r.

Now, the area of the medium pizza is $$\pi\cdot r^2$$ and the radius of the large pizza is $$\pi\cdot (1.3r)^2=1.69\pi\cdot r^2.$$ Therefore, the difference between them is $$1.69\pi\cdot r^2 - \pi\cdot r^2\ =\ 0.69\pi\cdot r^2.$$ Now, we have to find what percent represents this to the area of the medium pizza.

$$\pi\cdot r^2----------100\%$$ $$0.69\pi\cdot r^2----------x\%$$ Hence $$x=69\%.$$ Thus, the answer is d .

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Scott@TargetTestPrep: GMAT Instructor; Posts: 8086; Joined: Sat Apr 25, 2015 10:56 am; Location: Los Angeles, CA; Thanked: 43 times; Followed by:29 members

by Scott@TargetTestPrep » Sun Jun 09, 2019 5:59 pm

M7MBA 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 radius of the medium pizza = 10, and thus the radius of the large pizza = 13. Therefore, we have:

Area of medium pizza = 100Ï€

Area of large pizza = 169Ï€

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

(169Ï€ - 100Ï€)/100Ï€ x 100 = 69/100 = 69%

Answer: D

Scott Woodbury-Stewart
Founder and CEO
[email protected]