Anurag@Gurome wrote:
(1) x - 2 = xC2, which cannot be solved further.
That's not what Statement 1 tells you. Statement 1 says that (x)C(x-2) = (x)C(2).
It's useful to understand the following: say you have 10 people. If I ask "how many committees of 2 people could I choose from this group of 10 people?" that's exactly the same question as "how many committees of 8 people can I choose from this group of 10 people?" because if I choose a committee of 8 people, that's exactly like choosing 2 people to *not* include in the committee.
So if you have x people (or, as in this question, pizza toppings), the number of selections of 2 people you can make is always exactly equal to the number of selections of x-2 people you can make. In combinatorial notation, (x)C(2) is always equal to (x)C(x-2). Similarly, as long as x > n, (x)C(n) is always equal to (x)C(x-n). So in this question Statement 1 tells us nothing new at all; it might as well say '5 = 5'.
tpr-becky wrote:
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!
The second part of the above isn't right. The '2!' in the denominator is wrong; it should be (x-2)!. The number of pizzas that can be made with x-2 toppings is equal to x!/{ [x - (x-2)]! * (x-2)! }. Simplifying, you find this is equal to x!/[ (x-2)! * 2! ], which is exactly equal to the number of 2-topping pizzas you can make, and Statement 1 tells us nothing we didn't know already.
tpr-becky wrote:
each statement gives you a complete equation with only one variable and no squares, therefore they are solveable.
I've mentioned in many posts why I find this the most misleading advice that prep books give test takers. There are very simple situations where one can, 'at a glance', tell how many solutions an equation, or system of equations, will produce. In any remotely sophisticated situation (one involving factorials, say), however, it is usually very difficult to tell 'at a glance' how many solutions you will have. If you don't 'do the work', you'll get a lot of GMAT questions wrong.
