q25: Let x and y be positive integers such that 3x+7y is divisible by 11. Which of the following must also be divisible by 11?
Is there a fast method for solving this type of question?
3x+7y=0 (mod 11)
Multiplying by 5,
15x+35y=0 (mod 11)
4x+2y=0 (mod 11)
4x-9y=0 (mod 11)
The problem is that it takes a while to guess that we need to multiply by 5 (so this problem might end up taking more than 2 minutes)
Thanks a lot.