Prove (by contradiction) that it can't be the case that both A and B are odd numbers....
A proof should be something memorised for the exam.
Back when I rode a dinosaur to school my maths teacher would tell us to 'Pray for a hard paper' (RC Girls' school if relevant, she also told us to use our feminine intuition).
Most people look at a hard paper and panic for 5-10 mins, that is mins you don't waste if you are expecting it.
Every mark and half mark counts so attempt everything you can, even if it is just to put the first line down or in this case, state the theorem.
Let A and B be integers. If A + B is an odd number, then A and B cannot both be odd.
Once that is down is there anything else you can do? Yes - do it or No- move on to another question but come back to this later.
I know for the young people who took this yesterday it feels like the end of the world, it isn't, it is a hard paper, no more no less. I assume there is a paper 2 so time to make up the grade.
It happens sometimes, on my mock physics paper there was a question about a kettle with a heating element, it could be taken as a kettle on a hob or an electric kettle.
The cohort who did this were marked as if it was the way they had drawn the diagram regardless of which way they did it.