Question 13382
 [qoute]
 if 2x+1 is a multiple of 5,and if 2x+1<100, how many possible values of x are prime numbers [/quote]

 Sol: Note2x+1 is odd, if 2x+1 = 5q for some positive integer q.
      then q must be odd. We can set q = 2k -1 for some psitive integer k.
      Hence,if 2x+1 = 5(2k-1) = 10 k -5 ,then x = 5k -3. (why?)
      Since 2x+1 <100 and x ( >0)is prime , so x = 5k -3 <= 49 or 5k <= 52. 
      k start from 1, 2,4...,up to 10 as 
     (to make x to be prime,k is not odd >1 ormultiple of3) 
 
       k | x = 5k-3
     ---------------
       1 |  2 (prime(OK)
       2 |  7 (prime(OK)
       4 |  17 (prime(OK)
       8 |  37 (prime(OK)
      10 |  47 (prime(OK)


  Hence, there are 5 such primes x with 0< 2x+1 < 100 and (2x+1) = 0 mod 5.

  The above solution is the shortest way to get the answer withour redundant  
  testing.
 
  Sorry, I won't give further explanations. 
  Try to read carefully to understand the details.

  Kenny