Provincial Finalist Exam for 4th Year/ TY Students Do not turn the page until you are instructed to do so. Answer each question in the box provided next to the question on this sheet. Only one answer should be given unless the question states otherwise. There is no need to explain your answer or show your work. You may use a separate piece of paper to complete your workings. You will have 40 minutes to complete 8 problems of varying difficulty. You may not leave until the exam has finished. USE BLOCK CAPITAL LETTERS Name: ____________________ Student ID: ____________________ School: ____________________ County: ____________________ THIS IS ON YOUR BADGE Write your final answer in the box next to each question î 1. One of the five children cooked dinner for their mother. Alan said: ‘It was either Bob or Ciaran’. Bob said: ‘It was neither me nor Eddie’. Ciaran said: ‘You are both lying’. Mark said: ‘No, one of them told the truth and the other one lied’. Eddie said: ‘No, Mark, you are lying’. The mother knows that three of her children always tell the truth. Who cooked the dinner? 2. 𝐼𝑓 𝑥 = !! ! !! ! !! !! ! and y = ! , find x3 + y3 3. Two people stand back to back next to the rails in a small railway station. As the head of the express train that passes the station reaches them, they start to walk parallel to the rails in opposite directions. As the tail of the train reaches each of them, they stop, having walked 30m and 40m respectively. If they both walked with identical, constant speed and the train kept its speed as well, can you tell how long the train was? 4. I am thinking of three different positive whole numbers. The smallest is 2 less that half the largest, the average of the 3 numbers is 16, and one is a two-‐digit prime number. What are the numbers? 5. A tournament took place between 5 badminton players. Every player played exactly one game with each of the other 4 players. A player gets 1 point for a win and 1/2 a point for a draw and 0 for a loss. It is known that at the end of the event, no two players had the same number of points, the player in first place didn’t have a single draw, the one in second place didn’t lose a single game, and the one in fourth place didn’t win a single game. How many games ended in a draw? 6. Find the number to replace the question mark 7. Aine, Barbara, Catherine, Deirdre and Evelyn are on a lunch break in the school canteen. Each writes down her name on a separate piece of paper. The five pieces of paper are then shuffled and placed in an empty box. Each girl then randomly draws out a piece of paper from the box. What is the probability that no girl selects her own name? Give your answer correct to four decimal places. 8. What is the units digit of 32015?