I12-01

Question

A pizza shop sells only two types of pizza: Margarita and Pepperoni. On a particular day, the shop sold 70 Margaritas and 100 Pepperonis.
 
If it is known that none of the customers purchased more than one pizza of a particular type, and each customer purchased at least one pizza, then select for  Minimum number of customers  the least possible customers the shop could have received and for  Maximum number of customers  the maximum possible customers the shop could have received. Make only two selections, one for each.

Bunuel · Answer

Official Solution:

To minimize the number of customers, we should maximize the number of pizzas each customer could have bought. Since a customer could only buy one pizza of each type, the maximum a customer could purchase is 1 Margarita and 1 Pepperoni. In this case, 70 customers would account for 70 Margaritas and 70 Pepperonis, leaving 30 Pepperonis remaining. These 30 Pepperonis would require 30 additional customers, making the minimum number of customers equal to 70 + 30 = 100.
 
To maximize the number of customers, we need to minimize the number of pizzas each customer could have bought. Given that each customer purchased at least one pizza, the fewest pizzas a customer could buy is 1. Since a total of 170 pizzas were sold, the maximum number of customers would be 170, with each customer buying just 1 pizza.

Correct answer:

Minimum number of customers  "100"

Maximum number of customers  "170"

swapnilnichat1818 · Answer

Why cant the minimum no of customers be 70? as for only one type of pizza customer can by only  Margaritas,and as we are looking for a minimum number.Technically 70 must be answer for minimum number of customers

Bunuel · Answer

No, because we are told that none of the customers purchased more than one pizza of a particular type. So, 70 customers could buy a maximum of 70 Margaritas and 70 Pepperonis, leaving 30 Pepperonis still unpurchased.

Bunuel · Answer

I have revised the question, solution, and formatting by adding more details to enhance clarity.

yuv_20 · Answer

I like the solution - it’s helpful.

anonymousmouse56 · Answer

I don’t quite agree with the solution. Q says "none   purchased more than one pizza of a particular type"
A says "a customer could only buy one pizza of each type,   1 M and 1 P."

This seems to be a discrepancy?

Bunuel · Answer

There's no discrepancy. The question states that  no customer bought more than one pizza of a particular type , meaning a customer  could buy at most one Margarita and one Pepperoni  but not, for example, two Margaritas or two Pepperonis.

The solution correctly follows this rule: when minimizing the number of customers, each customer buys  one Margarita and one Pepperoni  if possible, maximizing the number of pizzas per customer within the given constraint. When maximizing the number of customers, each customer buys  only one pizza  (either Margarita or Pepperoni), which results in the highest possible number of customers.

The misunderstanding comes from misinterpreting "one pizza of a particular type" as limiting each customer to only  one pizza total , which is incorrect. They are allowed  one of each type , not more than one of the same type.

anonymousmouse56 · Answer

Understood - thank you for the clarification Bunuel.

godinero · Answer

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emperordanzy · Answer

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Fettysgurl · Answer

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rtakahashi · Answer

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LAVKESH · Answer

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LAVKESH · Answer

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minnieminnoon · Answer

I like the solution - it’s helpful.

MyGMATbuddy · Answer

To minimize customers, we want maximum overlap, i.e., customers who bought both pizzas.

Let’s pair as many Margarita + Pepperoni combos as possible.

There are only 70 Margaritas → so at most 70 people could have bought both types.

So:

* 70 customers buy 1 Margarita + 1 Pepperoni
* Remaining 100 – 70 = 30 customers buy only Pepperoni

→ Total customers = 70 (both) + 30 = 100

Minimum customers = 100

To maximize customers, we want no overlap, i.e., every pizza goes to a different person.

→ 70 Margarita buyers + 100 Pepperoni buyers = 170 customers

Maximum customers = 170

—

PUJABIN · Answer

I like the solution - it’s helpful.

PUJABIN · Answer

I like the solution - it’s helpful.

apreps · Answer

I like the solution - it’s helpful.

I12-01

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Minimum number of customers	Maximum number of customers
		30
		50
		70
		100
		170
		200