Beth's pizzeria offers x different toppings. What is the

[BTGmoderatorDC]

Beth's pizzeria offers x different toppings. What is the value of x?

(1) There are an equal number of different pizzas that can be made with (x − 2) toppings as there are different pizzas with just 2 toppings.

(2) If the pizzeria were to add one additional topping, the number of different pizzas that could be made with 4 toppings would double.

OA B

Source: Princeton Review

[Jay@ManhattanReview]

Beth's pizzeria offers x different toppings. What is the value of x?

(1) There are an equal number of different pizzas that can be made with (x − 2) toppings as there are different pizzas with just 2 toppings.

(2) If the pizzeria were to add one additional topping, the number of different pizzas that could be made with 4 toppings would double.

OA B

Source: Princeton Review

Let's take each statement one by one.

(1) There are an equal number of different pizzas that can be made with (x − 2) toppings as there are different pizzas with just 2 toppings.

# of (x - 2) topping pizzas that can be made out of x toppings = xC(x - 2);
# of 2 topping pizzas that can be made out of x toppings = xC2 = xC(x - 2); note that nCr = nC(n - r)

Since both the expressions are the same, we can't get x. Insufficient.

(2) If the pizzeria were to add one additional topping, the number of different pizzas that could be made with 4 toppings would double.

=> (x + 1)C4 = 2*xC4

(x + 1)! / [4! * (x + 1 - 4)] = 2 * x! / [4! * (x - 4)!]

Upon solving, we get x = 7. Sufficient.

The correct answer: B

Hope this helps!

-Jay
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