Exactly 3/5 of the people in the room are under the age of 21, and exactly 5/13 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?
Answers
A) 21
B) 35
C) 39
D) 60
E) 42
The total number of the people in the room must be a multiple of both 5 and 14 (in order 3/5 and 5/14 of the number to be an integer), thus the total number of the people must be a multiple of LCM of 5 and 14, which is 70.   Since, the total number of the people in the room is greater than 50 and less than 100, then there are 70 people in the room.   Therefore there are   3/5*70= 
<gadget id="calculator">  3/5*70</gadget>
<output>42</output>
42 people in the room under the age of 21.   Answer: 42.
<result>E</result>
Exactly 3/5 of the people in the room are under the age of 21, and exactly 5/13 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?