# Question: Total Number of Balls

## Comment on Total Number of Balls

### to save some time and exempt

to save some time and exempt ourselves from conducting the quadratic equation all the way through, we can say that the equation wit N and N-1 in the denominator can be cross multiplies with 1/12 to receive that n(n-1) = 6*12 = 72. since there is only one option to solve this product which is 8*9 - we can already tell that n=9 and we are done! Great approach!

### It seems like using

It seems like using quadratics to solve problems is a reoccurring method in gmat problems. Solving quadratic equations is an important skill to have on test day.

### hi Brent

hi Brent ### You're right to say the

If you derived the equation N² - N - 72 = 0 , then the solutions cannot be 8 and -9.
We can verify this by plugging N = 8 and N = -9 into the equation.
For example, if N = 8, we get: 8² - 8 - 72 = 0
Simplify to get: -16 = 0. Doesn't work.

To solve the equation N² - N - 72 = 0 we must first...
Factor the left side to get: (N - 9)(N + 8) = 0
So, either N = 9 or N = -8

Does that help?

Cheers,
Brent