You begin by looking at the entire series of numbers. What you notice is:
- that the last digit of every number is 5,
- that the numbers become greater and smaller alternately and
- that the differences between the numbers become greater and greater.
Your next step is to take a closer look at pairs of neighbouring numbers. Develop a hypothesis as to a
possible arithmetical operation with which the one number could be derived from the other. In the process,
you can begin at any random place within the numerical series; frequently (but not always!) it is easiest
to begin with the first two numbers.
What arithmetical operation can be used to derive 35 from 25? Begin with a simple calculation, here, for
example +10 (/5 x7 would also be possible – but more complicated. Check this hypothesis only if you
have determined that the simpler hypothesis doesn’t work.)
Now check the next two numbers. What arithmetical operation can be used to derive 15 from 35? A simple
possibility is -20.
Checking the third pair of numbers: What arithmetical operation can be used to derive 45 from 15? A simple
possibility is +30.
In many cases you can develop an assumption about the rule governing the numerical series after checking
three pairs of numbers.
In the case of this problem, you now have hypotheses about the first three arithmetical operations: +10,
-20, +30
A possible assumption about the rule would be: Addition and subtraction are carried out alternately, using
a number that increases by 10 each time.
The following arithmetical operations, therefore, would be -40, +50, -60, +70, etc.
Now test your assumption: 45 - 40 = 5; 5 + 50 = 55
The numerical series is therefore based on the rule you assumed. Now you must apply that rule once more,
to the last number: 55 - 60 = - 5
You have thus solved the problem. The solution is - 5.
On your answer sheet, you accordingly have to mark the "-" and the 5.
