1. When are two magnitudes said to be directly proportional? 2. What condition must be met for two magnitudes to be inversely proportional? 3. Are the side of a square and its respective area directly proportional? Justify. 4. If magnitude A increases and as a consequence magnitude B decreases, are they inversely proportional? Why? 5. If A is DP to B (when C is constant) and A is IP to C (when B is constant), what is the relationship between B and C? BLOCK II 6. The square of A is directly proportional to B. When A is 6, B is 4. Find the value of A when B is 25. A) 12 B) 15 C) 14 D) 18 E) 24 7. The magnitude A is directly proportional to the square of B, proportional to C and inversely proportional to D. When A is 3, B is 6, C is 12 and D is 8. Determine the value of C when A is 16, B is 12 and D is 5. A) 6 B) 8 C) 10 D) 12 E) 15 8. The magnitudes A and B are proportional. Find the initial value of A knowing that if it increases by 6 units, the value of B varies by half. A) 16 B) 10 C) 8 D) 20 E) 12 9. The price of a jewel is proportional to the square of its weight. A jewel worth S/ 9,800 is broken into two pieces whose weights are 4 to 3. How much is received for the sale of the two pieces? A) S/4,800 B) S/6,000 C) S/5,200 D) S/5,000 E) S/6,400 10. A wheel A with 80 teeth meshes with another wheel B with 50 teeth; fixed to the axle of B is another wheel C with 15 teeth that meshes with a fourth wheel D with 40 teeth. With wheel A making 120 revolutions per minute, how long will it take wheel D to make 18,000 revolutions? A) 4 h 10 min B) 4 h C) 4 h 15 min D) 4 h 18 min E) 5 h 11. A is inversely proportional to the square root of B. When A is 12, B is 16. What will be the value of B when A is 6? A) 36 B) 49 C) 64 D) 60 E) 81 12. A is directly proportional to B (when C is constant), and inversely proportional to the square of C (when B is constant). When A is 5, B is 20, and C is 6. Find the value of A when B is 28 and C is 3. A) 24 B) 30 C) 36 D) 28 E) 40 13. According to Boyle’s Law, pressure is inversely proportional to the volume held by a given quantity of gas. What pressure (in atmospheres) is a gas subjected to if, when this pressure is increased by 2 atmospheres, the volume varies by 2/5 of its value? A) 1 B) 2 C) 3 D) 4 E) 5 14. The price of diamonds varies proportionally to the square of their weight. A diamond that costs S/36,000 breaks into two pieces, one of which is 2/3 of the other. What is the loss suffered when the diamond breaks? A) S/16,000 B) S/5,760 C) S/17,280 D) S/12,960 E) S/18,720 15. Wheels A, B, C, and D have 50, 60, 48, and 72 teeth respectively. A and B are in mesh, B and C are attached to the same axle, and C and D are in mesh. If A makes 45 turns, how many turns does wheel D make? A) 25 B) 40 C) 36 D) 48 E) 32 1. In a building, the volume of water carried to a certain floor is IP at Tn, where T is the time it takes for the water to reach floor n. If when 80 liters are carried to the second floor the delay is 4 seconds, how long will it take to carry 5 liters to the fourth floor? A) 4 s B) 4.5 s C) 5 s D) 6 s E) 8 s 2. A is directly proportional to the square of B, inversely proportional to C, and inversely proportional to the square root of D. When A is 360, B is 4, C is 6, and D is 25. Find the value of A when B is 12, C is 10, and D is 16. A) 1,675 B) 1,440 C) 2,430 D) 3,240 E) 1,800 3. In a company, the efficiency of a worker is directly proportional to his years of experience and inversely proportional to the square root of his age. Carlos, 25 years old, has 1 year of experience and 2 efficiency points. What will Carlos’ efficiency be at age 36? A) 15 B) 20 C) 24 D) 30 E) 36 4. A worker’s salary in a job is directly proportional to the square of his age. In how many years will an employee who is currently 17 years old have a salary that is 16 times the current salary? A) 52 B) 55 C) 60 D) 51 E) 59 5. A and B are proportional magnitudes. When A is 32, B is 24. Calculate B when A is 48. A) 34 B) 35 C) 36 D) 37 E) 38 1. A taxi driver usually charges in proportion to the number of passengers as well as the distance traveled. He charged 3 passengers S/30 for traveling 45 km. How much will he charge 6 passengers for traveling 48 km? A) S/30 B) S/64 C) S/48 D) S/100 E) S/75 2. Let the magnitudes be A and B where A is IP squared of B. When A is 200, B is 6. Find the value of B when A is 18. A) 18 B) 19 C) 21 D) 20 E) 22 3. A 24-tooth gear A meshes with a 60-tooth gear B. Gear B is in turn attached to the axle of a 48-tooth gear C. If gear A has 90 teeth, how many turns will gear C make? A) 30 B) 40 C) 45 D) 36 E) 60