FORTNIGHT'S PUZZLE 10

PUZZLE 10: 22nd-28th February (to be e-mailed by the 1st March)
POSTED BY IES CAMPANAR

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, 58If it is not a multiple of 3, the number could be:61, 62, 64, 65, 67, 68If it is not a multiple of 4, the possibilities are:70, 71, 73, 74, 75, 77, 78, 79By eliminating the only possibility is number 75.