Problems(2)
A school has 100 students and 5 teachers. In the first period, each student is taking one class, and each teacher is teaching one class. The enrollments in the classes are 50,20,20,5, and 5. Let t be the average value obtained if a teacher is picked at random and the number of students in their class is noted. Let s be the average value obtained if a student was picked at random and the number of students in their class, including the student, is noted. What is t−s?<spanclass=′latex−bold′>(A)</span> −18.5<spanclass=′latex−bold′>(B)</span> −13.5<spanclass=′latex−bold′>(C)</span> 0<spanclass=′latex−bold′>(D)</span> 13.5<spanclass=′latex−bold′>(E)</span> 18.5 Fourty slips of paper numbered 1 to 40 are placed in a hat. Alice and Bob each draw one number from the hat without replacement, keeping their numbers hidden from each other. Alice says, "I can't tell who has the larger number." Then Bob says, "I know who has the larger number." Alice says, "You do? Is your number prime?" Bob replies, "Yes." Alice says, "In that case, if I multiply your number by 100 and add my number, the result is a perfect square. " What is the sum of the two numbers drawn from the hat?<spanclass=′latex−bold′>(A)</span>27<spanclass=′latex−bold′>(B)</span>37<spanclass=′latex−bold′>(C)</span>47<spanclass=′latex−bold′>(D)</span>57<spanclass=′latex−bold′>(E)</span>67 AMCAMC 10AMC 10 B