A number of people shared a meal, intending to divide the cost evenly among themselves. However, several of the diners left without paying. When the cost was divided evenly among the remaining diners, each remaining person paid $12 more than he or she would have if all diners had contributed equally. Was the total cost of the meal, in dollars, an integer?

(1) Four diners left without paying.
(2) Six diners paid for the meal.