When divided by 2 the remainder is 1
  →   equation (1)
 

When divided by 3 the remainder is 2
  →   equation (2)
 

When divided by 4 the remainder is 3
  →   equation (3)
 

When divided by 5 the remainder is 4
  →   equation (4)
 

When divided by 6 the remainder is 5
  →   equation (5)
 

• From the above equations, x, A, B, C, D, and E must be whole numbers.
• From equation (1), x must be odd.
• From equation (5), x must be divisible by 5 + the remainder 4.
  • If it ends with 0 + 4 = 4 (even).
  • If it ends with 5 + 4 = 9 (odd)

Thus, x must end with 9.
 

Try x = 9

  →   (not a whole number - not okay)

Try x = 19

  →   (not a whole number - not okay)

Try x = 29

  →   (whole number - okay)
 

  →   (not a whole number - not okay)

Try x = 39

  →   (not a whole number - not okay)

Try x = 49

  →   (not a whole number - not okay)

Try x = 59

  →   (whole number - okay)
 

  →   (whole number - okay)
 

  →   (whole number - okay)

Thus, x = 59           answer