Question: A pizza can be assembled from given choices, with customers' preferences. The crust is available in 3 varieties – cheese burst, classic, and wheat thin; toppings are available in 4 variants – bacon, black olives, pepperoni and sausage; and finally cheese available in 3 types – Cheddar, American, and Swiss. How many various types of pizzas can be made if a customer has the choice of not choosing either of toppings or cheese?

1. 3
2. 9
3. 12
4. 36
5. 60

Correct Answer: E

Solution and Explanation:
Approach Solution 1:
Since we have an option of choosing (not choosing ) any cheese or topping.We can take this as an extra option.

eg. now no. of toppings= 5 (including the no choice option)
now of types of cheese= 4(including the no choice option)
so, the total ways=3x5x4= 60

Approach Solution 2:
Given:
Number of varieties for

• Pizza crust = 3
• Toppings = 4
• Cheese = 3

One have the choice of not choosing either of toppings or cheese

To find:
Number of ways pizza can be customised

So, there are 4 possible cases:

• Choice of only crust, which can be done in ^3C1= 3 ways
• Choice of crust and toppings, which can be done in ^3C1∗^4C1= 3*4= 12 ways
• Choice of crust and cheese, which can be done in ^3C1∗^3C1= 3*3= 9 ways
• Choice of crust, toppings, and cheese, which can be done in ^3C1∗^4C1∗^3C1= 3*4*3= 36 ways

Therefore, the total number of ways pizza can be customised= 3 +12+9+36= 60 ways

Approach Solution 3:
Given that:

Number of varieties for pizza crust= 3
Number of varieties for toppings= 4
Number of varieties for cheese= 3
Customer cannot choose either of toppings or cheese alone
Possible ways in which the pizza can be made :
- Pizza made with crust only= 3C1= 3*1= 3
- Pizza made with crust and toppings= 3C1*4C1
=> (3*1)*(4*1)
=> 3*4= 12
- Pizza made with crust and cheese= 3C1*3C1
=> (3*1)*(3*1)
=> 3*3= 9
- Pizza made with crust, cheese and toppings= 3C1*3C1*4C1
=(3*1)*(3*1)*(4*1)
=> 3*3*4
=> 9*4= 36
Various types of pizzas that can be made= pizza with crust only+pizza with crust and toppings+pizza with crust and cheese+pizza with crust, cheese and toppings
=3+12+9+36= 60 various types of pizzas

“A pizza can be assembled from given choices, with customer’s”- is a topic of the GMAT Quantitative reasoning section of GMAT. To solve GMAT Problem Solving questions a student must have knowledge about a good amount of qualitative skills. GMAT Quant practice papers improve the mathematical knowledge of the candidates as it represents multiple sorts of quantitative problems.

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