WEEK'S PUZZLE 10

PUZZLE 10 -from the 7th to the 13th of December (to be collected by the 14th of December)

THE MAGIC NUMBER

'Free me, please', Ali begged the genius who had trapped him in a cage.
‘I will free you only if you find a number which obeys certain conditions’, the genius answered.
And these were the conditions:
1.- If the number were multiple of 2, then it would be a number between 50 and 59, both included.
2.- If it were not a multiple of 3, then it would be a number between 60 and 69, both included.
3.- If it were not a multiple of 4, then it would be a number between 70 and 79, both included.
Which was the magic number?

SOLUTION
If the number is a multiple of 2, it could be:
50, 52, 54, 56, 58
If it is not a multiple of 3, the number could be:
61, 62, 64, 65, 67, 68
If it is not a multiple of 4, the possibilities are:
70, 71, 73, 74, 75, 77, 78, 79

By eliminating the only possibility is number 75.