In a certain year, 1 January and 31 December fall on the same day of the week. What does that tell you about the year?

In an ordinary year of 365 days, 31 December comes 364 days after 1 January, and $364=52\times 7$ exactly, so the two dates land on the same weekday. In a leap year of 366 days the gap is 365 days, one more than a whole number of weeks, so 31 December falls one weekday later than 1 January. The matching therefore rules out a leap year. The traps: the first option is the exact reverse of the truth, and the last two name particular weekdays, which nothing in the question can pin down — the year could start on any day at all.