In June of this year there was an outcry amongst UK sixteen-year-olds 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
Test-makers at the public-school level do not have time to plow through great, long, unwieldy answers to basic maths problems.
You may be caught off-guard 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:
n2 – n – 90 = 0
n2 – n = 90
What number, when subtracted from its square, equals 90?
Why, 10 of course!
So now, “Show n2 – 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
I know it’s easy to armchair-quarterback these things when you’re not sweating in a timed test– for what it’s worth, that’s my approach.