John and Nora met at a health club.

(A) John started going to the health club on the first Monday in January and thereafter, he went every fifth day.

(B) Nora started going to the health club on the first Tuesday in January and thereafter, she went every fourth day.

(C) John and Nora went to the health club on the same day just once in January; it was on that day that they met.

On which day of January did John and Nora meet?

If the first of January is a Sunday (1) through Saturday (7), the first line in each group shows Joe's days and the second line shows Nora's days. 1, 2, 4, 5, 6 and 7 (i.e., all except Jan 1 being Tuesday) have two simultaneoud visits. If January began on a Tuesday there was only one simultaneous visit, which was on Nora's 5th visit, making the date 1 + 4*4 = 17 of January.

 1
 x    x    x    x    x    x
  x   x   x   x   x   x   x   x

 2
x    x    x    x    x    x    x
 x   x   x   x   x   x   x   x

 3
      x    x    x    x    x
x   x   x   x   x   x   x   x

 4
     x    x    x    x    x    x
      x   x   x   x   x   x   x

 5
    x    x    x    x    x    x
     x   x   x   x   x   x   x

 6
   x    x    x    x    x    x
    x   x   x   x   x   x   x

 7
  x    x    x    x    x    x
   x   x   x   x   x   x   x

Posted by Charlie on 2012-11-05 14:17:04