Data Sufficiency

tpr-becky wrote:This is a permutation combination problem becuase and the base formula for those is n!/(n-r)! r! - here we put the r! in the denominator becuase it is a combination problem and order does not matter - therefore we have to divide out any duplicated groups.

1) the nubmer of pizzas that can be made with 2 toppings is x!/(x-2)!2! and the number that can be made with x-2 toppings is x!/(x-(x-2)!2! which equals x!/2!2!

these two equations are equal according to the statment so x!/4= X!/(x-2)!2 you can then divide out the x! and get 1/4= 1/(x-2)!(2) thus 1/2 = 1/(x-2)! and so (x-2)! = 2 so x is equal to 4

Thus 1 is sufficient and the answers are AD

2. same functionality:

(x!)(2)/(x-4)!4! = (x+1)(x!)/(x-3)!(4!)

here I know that you can multiply the top number of a factorial times the rest of the number - thus (x+1)! = (x+1)(x!) etc..

therefore = 2(x!)/(x-4)!4! = (x+1)(x!)/(x-3)(x-4!)(4!) - cancel out to get x+1 = 2(x-3) which can be solved

So I believe the answer is actually D.

In fact the technique to this one is to see that it is asking for the value of a variable so you know it is about solving equations -

each statement gives you a complete equation with only one variable and no squares, therefore they are solveable.

Anurag@Gurome wrote:

akshatgupta87 wrote:Q.) 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.

Someone pls. explain..

(1) x - 2 = xC2, which cannot be solved further.
So, (1) is NOT SUFFICIENT.

(2) (x + 1)C4 = 2* xC4
(x + 1)(x)!/4!*(x - 3)(x - 4)! = 2 * (x!)/(4!)(x - 4)!
(x + 1) = 2(x - 3), which can be solved for x.
So, (2) is SUFFICIENT.

The correct answer is B.