Please help me understand the solution to this question

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The question asks, “x could be which of the following”, which tells us that we only need to find one instance where x is equal to one of the answer choices. I choose a simple example of p = 13, and see if I can identify possible values of x and y. We can see that x=2 and y=11 works, so the answer is A.


Some concepts to consider as well:

  • p must be odd (because all primes > 11 are odd)
  • x and y must have one be odd and one be even (must have one odd and one even to get an odd #, p)
  • the only even prime number is 2
  • then, I should look for examples of prime numbers that are 2 apart (11 and 13, 17 and 19, etc etc)