The two digits of a two-digit number add up to 12. When the digits are swapped round, the new number is 18 more than the original. What is the original number?

Swapping the digits changes the number by 9 times the difference between the digits, so that difference must be 18 ÷ 9 = 2, and the units digit must be the bigger one. Digits adding to 12 and differing by 2 are 5 and 7, giving 57 (and indeed 75 − 57 = 18). Every option has digits adding to 12, which is the trap: 39 grows by 54 when swapped, 48 grows by 36, and 75 is the swapped number itself — it becomes 18 smaller, not larger.