X, Y and Z jump forward 4', 6' and 5', respectively. At 8 AM, they all land on mark 199'. How many times will they all land on the same mark (need not be at the same moment) between mark 195' and 1000', if all of them cross mark 1000' by 9 AM?

X lands on marks 199 + 4k, Y on 199 + 6k, Z on 199 + 5k for non-negative integers k. A common mark must satisfy mark – 199 being a multiple of LCM(4,6,5) = 60. So common marks are 199, 259, 319, 379, 439, 499, 559, 619, 679, 739, 799, 859, 919, 979, 1039, ... Between 195' and 1000' (presumably inclusive): 199, 259, 319, 379, 439, 499, 559, 619, 679, 739, 799, 859, 919, 979 = 14 marks. Excluding the starting mark 199 (already 'landed at 8 AM'), count of additional common marks = 13. Hence 13.