Question: Total Number of Balls

Comment on Total Number of Balls

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!
gmat-admin's picture

Great approach!

It seems like using quadratics to solve problems is a reoccurring method in gmat problems.
gmat-admin's picture

Solving quadratic equations is an important skill to have on test day.

hi Brent

When I'm solving a quadratic equation, why can't the answer be N=8 and N=-9 instead?
gmat-admin's picture

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?


Hi Brent,

What if there is a question where 2 balls are drawn at the same time. How should we approach such questions?
gmat-admin's picture

The answer (and the solution) would be exactly the same. Here's why:

Let's say Person A reaches into the box and grabs 2 balls (1 ball with each hand) and removes them at the EXACT SAME TIME.
For this scenario, P(both balls are white) = some number

Now replace the two balls and restart the experiment.

This time, Person B reaches into the box and grabs 2 balls (1 ball with each hand) and TRIES remove them at the same time, BUT his left hand (holding a ball) leaves the box 0.0000000001 seconds before the right hand leaves the box.
Should it make a difference that the left hand exited the box 0.0000000001 seconds before the right hand?
No. It makes no difference.

So, for any question in which two or more items are selected (without replacement), it makes no difference to our final answer if we assume one object was removed before the other object(s).

Does that help?

Yes, thanks!

Add a comment

Office Hours

Have questions about your preparation or an upcoming test? Need help modifying the Study Plan to meet your unique needs? No problem. Just book a Skype meeting with Brent to discuss these and any other questions you may have. 

Change Playback Speed

You have the option of watching the videos at various speeds (25% faster, 50% faster, etc). To change the playback speed, click the settings icon on the right side of the video status bar.

Have a question about this video?

Post your question in the Comment section below, and a GMAT expert will answer it as fast as humanly possible.

Free “Question of the Day” emails!