Huey's Hip Pizza sells two sizes of square pizzas: a small pizza that

area of smaller one = 100 sq inches
area of larger one =15^2=225..
max sq inches that can be bought by them individually =225+100=325 sq inches
total between the two=325*2=650

if the money is collected the best scenario will be buying all large pizzas..
so 225*3=675

so extra=675-650=25
ans D

In the first case each can buy one pizza of $10 and one pizza of $20.

In square inches that would be (10*10=100) for the small pizza and (15*15=225) for the large pizza. In total sq inches that would be (100+225)*2= 650 sq inches.

In the second case if they pool their money together they can buy 3 large pizzas. In terms of square inches that would be 3*225= 675 sq inches.

Hence, the difference is 25 square inches more (675-650).

The correct answer is D.

Small pizza - 10 inches in size - costs $10.
Large pizza - 15 inches in size - costs $20.

Case I - when they buy pizzas alone:
A can buy 1 Small and 1 Large, total square inches = (10)^2 + (15)^2 = 100+225 = 325 inch squared.
B can buy 1 Small and 1 Large, total square inches = (10)^2 + (15)^2 = 100+225 = 325 inch squared.

Total inches = 650.

Case II - when they buy together: they can buy one of the following:
(i) 3 Large - 3(15)^2 = 675 inch squared.
(ii) 2 Large + 2 Small = 2(15)^2 + 2(10)^2 = 450 + 200 = 650 inch squared.
(iii) 1 Large + 4 Small = (15)^2 + 4(10)^2 = 225 + 400 = 625 inch squared.

(i) gives the maximum area, so they would get (675-650) = 25 inch squared more. Ans D.

Huey's Hip Pizza sells two sizes of square pizzas: a small pizza that measures 10 inches on a side and costs $10, and a large pizza that measures 15 inches on a side and costs $20. If two friends go to Huey's with $30 apiece, how many more square inches of pizza can they buy if they pool their money than if they each purchase pizza alone?

Solution -

Small pizza size = 100 inch^2 and Large Pizza size = 225 inch^2 -> So buying large pizza gives more cost effective than buying small pizza.

Each friend can buy individually 1 large and 1 small pizza - > 100+225 = 325 inch^2.

So both buy individually 2*325 = 650 inch^2. --------------1

But, both can buy 3 large pizzas combined for $60 = 3*225 = 675 inch^2. -----------------2

2 - 1 -> Both can get extra pizza = 675-650 = 25 inch^2. ANS D.

MANHATTAN GMAT OFFICIAL SOLUTION:

First, figure the area of each pizza: the small is 100 square inches, and the large is 225 square inches. If the two friends pool their money, they can buy three large pizzas, which have a total area of 675 square inches. If they buy individually, though, then each friend will have to buy one large pizza and one small pizza, so they will only have a total of 2(100 + 225) = 650 square inches of pizza.

Answer: D.

Notice it’s a better deal to buy the 15-inch square pizza than the 10-inch square pizza since spending $20 on a 15^2 = 225 in^2 pizza is better than $10 on a 10^2 = 100 in^2 pizza (notice that 225/20 > 100/10).

Thus, when they pool their money, with $60, they should buy three $20 pizzas.

If they were to not pool their money and buy the pizzas separately, each should buy one $20 pizza and one $10 pizza. Thus in total, they should buy two $20 pizzas and two $10 pizzas.

Thus, it’s three $20 pizzas versus two $20 pizzas and two $10 pizzas. However, if we take away the two $20 pizzas from both sides, it’s one $20 pizza against two $10 pizzas.

Since one $20 pizza is 225 in^2 and two $10 pizzas are 2 x 100 = 200 in^2, pooling the money together buys 225 - 200 = 25 in^2 of extra pizza.

Answer: D

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