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?

Cheers,
Brent

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