How would you solve this multiple-choice problem: What is 12345 x 45678?
It always amazes me when people try and multiply the two numbers. In any objective-type test (multiple choice question), the aim is not to solve the problem — it is to pick the correct answer!
Most people don’t seem to realise the difference.
If I had to solve the problem, I’d look for shortcuts. For example,
- All answers have 9 digits. So that’s not going to help.
- 12345 ends with a 5. All multiples of 5 end with 5. So the answer is either (2) or (3).
- Multiplying the first digits, 1 X 4 = 4. So the answer’s got to start with a bit more than 4. (3) starts with 40. That’s too low. C’mon, the second number STARTS with 45. So…
This takes me 10 seconds. Multiplying the two takes me ten times as long.
Let me repeat the point: You DON’T have to get to the answer. You’ve already been given the answer. You just don’t know which one it is. And you don’t have to solve the entire problem to pick the right one.
There are many ways of picking the right answer. One is what I just used: the answer must satisfy some property. In this case, the answer must be a multiple of 5.
In other cases, the answer must be close to something. For example, what’s 37463 x 28438?
Well, let’s just multiply the first two digits: 37 x 28. That’s 1036. So the answer’s got to be close. OK, (2) is the answer.
These are not one-off techniques, nor are these applicable only to numbers. You can always pick the right choice without solving the problem.
A weaker, but more general version of the above rule is: you can always eliminate choices without solving the problem.
I’ll blog more on this shortly.