TASK OF THE WEEK |. Solve the following problems by applying Polya's four-step strategy. Briefly explain each step. 1. In how many ways can you answer a 12-question true-false test if you answer each question with either a "true" or a \"false"? 2. In a league of eight football teams, each team plays every other team in the league exactly once. How many league games will take place? 3. The four children in the richest family in Mexico are Aurora. Evelyn. Anita and Asuncion. The ages of the two teenagers are 13 and 15. The ages of the younger children are 5 and 7. From the following clues. determine the age of each of the children: a. Aurora is older than Evelyn. b. Asuncion is younger than Anita. c. Asuncion is 2 years older than Evelyn d. Anita is older than Aurora 4. The cities of Atlanta, Chicago, Philadelphia, and Seattle held conventions this summer for collectors of coins, stamps. comic books. and baseball cards. From the following clues. determine which collectors met in which city. a. The comic book collectors convention was in August. as was the convention held in Chicago. b. The baseball card collectors did not meet in Philadelphia. and the coin collectors did not meet in Seattle or Chicago. c. The convention in Atlanta was held during the week of July 4. whereas the coin collectors convention was held the week after that. cl. The convention in Chicago had more collectors attending it than did the stamp collectors convention 5. Divine has saved money for her dream vacation. She spends half of her money on a plane ticket; she then spends 2500 pesos for a jacket; 1,100 pesos for grab car. and one-third of her remaining money for a hotel room. After her brother gave her an amount of 7500 pesos. Divinefinds that she has 16300 pesos. How much money did she have at the start of her vacation? 6. An investor bought 20 shares of stock for a total cost of 60.000 pesos and then sold all the shares for 70,000 pesos. A few months later the investor bought 25 shares of the same stock for a total cost of 90.000 pesos and then sold all the shares for 95.000 pesos. How much money did the investor earn on these investments? 7. Nothing is known about the personal life of the ancient Greek mathematician Diophantus except for the information in the following epigram. \"Diophantus passed % of his life in childhood. 112 in youth, and i more as a bachelor. Five years after his marriage was born a son who died four years before his father, at % his father's (final) age.\" How old was Diophantus when he died? 8. An airline flies from Manila to Davao with a stopover in Cebu. It charges a fare of 1.800 pesos from Manila to Cebu and a fare of 3,500 pesos from Manila to Davao. In one flight. a total pf 180 passengers boarded the plane in Manila and the collected fare totaled 494.000 pesos. How many passengers got off the plane in Cebu? 9. Palindromlc numbers read the same from left to right. For instance, 37. 573 is a palindromic number. Find the smallest palindromic number larger than 600 that is a multiple of 3. 10. The skyboxes at a large sports arena are equally spaced. around a circle. The 11th skybox is directly opposite the 35th skybox. How many skyboxes are there in the sports arena