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28 Sep 2023, 06:06
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E
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Difficulty:
95%
(hard)
Question Stats:
38% (03:05) correct
62%
(02:32)
wrong
based on 61
sessions
History
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A college cafeteria offers three sizes of pizza - small, medium, or large. With a small pizza, up to one topping is included without additional charge; for a medium or large, up to two different toppings are included without additional charge. The cafeteria offers two meat toppings - pepperoni and sausage. If the cafeteria offers N other toppings, then how many ways can someone order a pizza - choosing a size and up to the maximum number of toppings - without having to pay extra? Assume that double toppings are not an option.
A. 3/2N^2 + 9/2N + 3
B. 2N^2 + 7N + 6
C. N^2 + 7/2N + 3
D. 3N^2 + 9N + 6
E. N^2 + 4N + 4
Please let me know your reasoning as I cannot find a proper answer to this question anywhere.
Thanks
A. 3/2N^2 + 9/2N + 3
B. 2N^2 + 7N + 6
C. N^2 + 7/2N + 3
D. 3N^2 + 9N + 6
E. N^2 + 4N + 4
Please let me know your reasoning as I cannot find a proper answer to this question anywhere.
Thanks
28 Sep 2023, 07:57
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Given: A college cafeteria offers three sizes of pizza - small, medium, or large. With a small pizza, up to one topping is included without additional charge; for a medium or large, up to two different toppings are included without additional charge. The cafeteria offers two meat toppings - pepperoni and sausage.
Asked: If the cafeteria offers N other toppings, then how many ways can someone order a pizza - choosing a size and up to the maximum number of toppings - without having to pay extra? Assume that double toppings are not an option.
Small pizza - one extra topping without additional charge
Medium or large pizza - two different toppings without additional charge
Two meat toppings - pepperoni and sausage
Other toppings - N toppings
Case 1: Small pizza
Number of toppings = N+2
Case 2: Medium or large pizza
Number of toppings = (N+2)(N+1) = N^2 + 3N + 2
Total number of ways to order pizza = (N+2) + (N^2 + 3N + 2) = N^2 + 4N + 4
IMO E
Asked: If the cafeteria offers N other toppings, then how many ways can someone order a pizza - choosing a size and up to the maximum number of toppings - without having to pay extra? Assume that double toppings are not an option.
Small pizza - one extra topping without additional charge
Medium or large pizza - two different toppings without additional charge
Two meat toppings - pepperoni and sausage
Other toppings - N toppings
Case 1: Small pizza
Number of toppings = N+2
Case 2: Medium or large pizza
Number of toppings = (N+2)(N+1) = N^2 + 3N + 2
Total number of ways to order pizza = (N+2) + (N^2 + 3N + 2) = N^2 + 4N + 4
IMO E
28 Sep 2023, 08:35
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Hi, Could you please let me know the source of this question?
Thanks
Thanks
