Problem: exactly 3 / 7 of the people in the room are under the age of 21 , and exactly 5 / 12 of the people in the room are over the age of 65 . if the total number of the people in the room is greater than 50 and less than 100 , how many people in the room are under the age of 21 ?
Rationale: "the total number of the people in the room must be a multiple of both 7 and 12 ( in order 3 / 7 and 5 / 12 of the number to be an integer ) , thus the total number of the people must be a multiple of lcm of 7 and 12 , which is 84 . since , the total number of the people in the room is greater than 50 and less than 100 , then there are 84 people in the room . therefore there are 3 / 7 * 84 = 36 people in the room under the age of 21 . answer : c ."
annotated_formula: divide(multiply(multiply(7, 12), 3), 7)