Question: At a certain pizza parlor, the diameter of a large pizza is 40% larger than the diameter of a small pizza. What is the percent increase in total amount of pizza, from a small to a large?

(A) 20%
(B) 40%
(C) 64%
(D) 80%
(E) 96%

Solutions and Explanation
Approach Solution : 1
Let A = pi*[r^2], We can rewrite it as A = pi*[(1/2d) ^2]
Therefore, the Area (small) = pi*[(1 / 2d)^2] will become Area (small) = pi*[(1 / 4d)]
=>Area (large) = pi*[(1/2*1.4d)^2]
=>Area (large) = pi*[(1/2*7/5d)^2]
=>Area (large) = pi*[(49/100d)]
So, now we write that the radius of the large pizza is approximately 50% larger than the smaller pizza.
Let us substitute a number for d so that we can analyse the difference in sizes.
=> Area (small) = pi*[(1/4d)] = pi*[(1/4 * 36)] = pi(9)
=> Area (large) = pi*[(49/100d)] = pi*[(49/100 * 36)] = pi(18)
As a result we can say that the area of the larger pizza is approximately 100% greater
The value 96% in the last option is near to the approximation value.
Correct Answer: (E)

Approach Solution : 2
Consider the small pizza diameter as 100
Consider the Large pizza diameter would be as 140
The Area of Circle = π∗[(d2)^2] = (π/4) ∗ (d^2)
We know that the above has only variable as the diameter
Therefore,
=> 100^2 = 10000
=> 140^2 = 19600
The difference = 9600 which can also be assessed as 96%
Correct Answer: (E)

Approach Solution : 3
We will have to determine the areas of the pizzas.
We know that the area of circle = pi*[r^2] and 2r =d
Now let us pick the smart numbers
Diameter of small pizza is 10 and then the diameter of big pizza is 14
And then,
Area of small pizza = 25pi and area of big pizza = 49pi
As a result, the percent increase can be calculated as, => 49/25 = 1.96 = 96 % bigger
Correct Answer: (E)

“At A Certain Pizza Parlor, The Diameter Of A Large Pizza Is 40% Larger Than The Diameter Of A Small Pizza” - is a subject covered in the GMAT quantitative reasoning section. A student needs to be knowledgeable in a wide range of qualitative skills in order to successfully complete GMAT Problem Solving questions. There are 31 questions in the GMAT Quant section overall. Calculative mathematical problems must be solved in the GMAT quant topics' problem-solving section using appropriate mathematical skills.

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