In June of this year there was an outcry amongst UK sixteenyearolds in the wake of this GCSE probability problem:
So, speaking as a mathematician (and a former college professor), here’s my take on this:
First and foremost, you can be sure of two things:

There is a solution, and

It’s simple.
Testmakers at the publicschool level do not have time to plow through great, long, unwieldy answers to basic maths problems.
You may be caught offguard momentarily, but calm down, use what you know , and Keep It Simple.
So, what do we know? Well …
The first thing that jumps out at me is that quadratic.
It would be easy to write in an equivalent form:
n^{2} – n – 90 = 0
becomes
n^{2} – n = 90
What number, when subtracted from its square, equals 90?
Why, 10 of course!
So now, “Show n^{2} – n – 90 = 0″ becomes the much simpler equivalent statement
“Show n = 10.”
Note: we are talking about a whole number of candies, so a small, simple number like 10 makes sense.
Onwards: back to What You Know.
Pulling one out of 6 orange sweets,and then one of 5 (remaining) orange sweets, from a bag of n (10, remember?) sweets looks like this:
This resolves to
Recall that the probability is one third, and you get
For n = 10 you get the true statement
QED.
I know it’s easy to armchairquarterback these things when you’re not sweating in a timed test– for what it’s worth, that’s my approach.