A pizza shop sold small pizzas for $4.5

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BrijNath: Newbie | Next Rank: 10 Posts; Posts: 8; Joined: Mon Jul 30, 2018 4:53 am

by BrijNath » Fri Apr 05, 2019 8:49 am

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A pizza shop sold small pizzas for $4.5 and large pizzas for $12.5 each. One night the pizza shop sold 500 pizzas, for a total of $5050. How many small pizzas were sold?

A.300
B.350
C.125
D.175
E.150

If someone can please explain it in a very simple way also if there is a framework to follow to solve these types of problems.

Thanks!!

Source: Beat The GMAT — Problem Solving | Fri Apr 05, 2019 8:49 am

GMATGuruNY: GMAT Instructor; Posts: 15539; Joined: Tue May 25, 2010 12:04 pmFollowed by: 1906 members; Location: New York, NY; Thanked: 13060 times; GMAT Score:790

by GMATGuruNY » Fri Apr 05, 2019 9:17 am

The GMAT would list the answer choices in ascending or descending order, as follows:

BrijNath wrote:A pizza shop sold small pizzas for $4.5 and large pizzas for $12.5 each. One night the pizza shop sold 500 pizzas, for a total of $5050. How many small pizzas were sold?

A.125
B.150
C.175
D. 300
E. 350

We can PLUG IN THE ANSWERS, which represent the number of small pizzas.
The average cost per pizza = 5050/500 ≈ $10.
Since the average cost ($10) is much closer to the price of a large pizza ($12.50) than to the price of a small pizza ($4.50), more than half of the 500 pizzas must be large pizzas.
Thus, the number of small pizzas must be less than 250.
Eliminate D and E.
When the correct answer is plugged in, the total cost for the 500 pizzas = $5050.

B: 150 $4.50 small pizzas, implying 350 $12.50 large pizzas, for a total of 500 pizzas
Total cost = (150)(4.5) + (350)(12.5) = 675 + 4375 = 5050.
Success!

The correct answer is 150.

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