Question

every prime number greater than 10 has a digit in the ones place that is included in which set of numbers below?

Answer 1

So we can start with the full of possibilities and eliminate them one by one.

The full set is {0,1,2,3,4,5,6,7,8,9}.

Now we know that any prime greater than 2 is odd as otherwise it would have 2 as a factor, so we can eliminate all of these digits that would be an even number, leaving:

{1,3,5,7,9}

We also know that any prime greater than 5 cannot be a multiple of 5 and that all numbers with 5 in the digits are a multiple of 5, so we can eliminate 5.

{1,3,7,9}

We know that 11,13,17 and 19 are all primes, so we cannot eliminate any more of these, leaving the set:

{1,3,7,9} as our answer.