Alabama School of Fine Arts Invitational Mathematics Tournament January 14, Sixth Grade Exam

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1 Alabama School of Fine Arts Invitational Mathematics Tournament January 14, 2012 Sixth Grade Exam 1. The Friday tribe is known for its tennis skills. The tribe s secret to winning tennis matches is eating the Bukugi nut, which grows on one tree in the rainforest. This Bukugi nut tree only gives 7 Bukugi nuts every three years. The first harvest season, the Friday tribe stores 4 Bukugi nuts. Three years later, they store 6 Bukugi nuts; and three years after that, the Friday tribe stores only 2 Bukugi nuts. What is the average number of nuts stored per harvest? A B. 2 C D. 4 E. NOTA 2. A Nelson series is a series such that each term, after the first, is some multiple of two plus the previous term. Which of the following could be the first four terms of a Nelson series? A: 4, 4, 36, 39 B: 2, 34, 34, 39 C: 7, 18, 20, 16,000 D: 1, 9, 11, 2197 E: NOTA 3. What is the missing number in this sequence 1, 1, 2, 6,, 120, 720 A. 27 B. 56 C. 24 D. 18 E. NOTA 4. Cynthia gave Stephanie 8 blops. Given that there are 4 bloops in 1 blop. 8 bleeps in 1 bloop, and 4 hoots in two bleeps, how many hoots did Cynthia give? A.1024 hoots B. 512 hoots C.1022 hoots D hoots E. NOTA 5. The Attwood tribe lives in the jungle and loves to eat nuts. The leader of the Attwood tribe, Emma, goes digging for buried nuts. If the hole she digs in has 9 oak-nuts, 7 maple-nuts, and 3 redwood-nuts, then what is the probability that on her first try Emma will pick an oak-nut, and on her second try she pulls out a maple-nut (without replacing the nuts already picked)? A B. 1 3 C D E. NOTA

2 6. Find the mean of the following sequence of numbers: 72, 63, 41, 5, 29, 59, 18 A: 48 B: 53 C: 41 D: 38 E: NOTA 7. How many positive integral divisors does 24 have? A: 10 B: 8 C: 6 D: 4 E: NOTA 8. A cube has a side length of 9. What is the ratio of this cube s volume to its surface area? A: 3: 1 B: 5: 2 C: 2: 3 D: 3: 2 E: NOTA 9. Which of the following is/are true: I. There are three even prime numbers II. aa(bb + cc) = aaaa + bbbb III. nn! = nn(nn 1)(nn 2) (1) A: II only B: I and II C: II and III D: I, II, and III E: NOTA 10. Lemurs and Zhilis are famous for squabbling over nuts. The lemur tribe stored 3 3 nuts for winter, and the Zhili tribe has stored 4 2 nuts for winter. The Zhili tribe needed more nuts though, so they stole 1/3 of the Lemurs nuts. Then, that night, a foul wind blew, causing the Zhili tribe to lose 1/5 of their nuts and the Lemur tribe to lose 1/3 of their nuts. If the Lemur and Zhili tribes decide to work together and pool their nut stores for winter, how many nuts will they have? A: 32 B: 27 C: 35 D: 25 E: NOTA 11. A fair coin is flipped 8 times. What is the probability of getting heads 8 times in a row? A B. 1 4 C D E. NOTA 12. Solve the following system of equations for x: 2xx + 3yy = 7 xx + yy = 4 A: 3 B: 1 C: 3 D: 1 E: NOTA

3 13. Find the solution in base 10: =?10 A: 1143 B: 41 C: 1243 D: 60 E: NOTA 14. Let A = The sum of the first 6 composite numbers B = The median of the series {9, 13, 7, 4, 9, -2, 1} C = 3! 2! Find AAAA BB A: B: 42 C: D. 21 E: NOTA 15. Harry Potter and his friends are casting spells in the meadow. Harry has the fastest spell casting time, clocking in at 14 ssssssssssss. If Harry decides to cast mmmmmmmmmmmm spells over the course of two and a half minutes, how many spells will he have cast at the end of this time period? A. 34 spells B spells C. 35 spells D. 33 spells E. NOTA 16. N = the first composite number. M = the N th prime number. Find (M+N)(MN) A. 30 B. 180 C. 70 D. 308 E. NOTA 17. Huey, the Horsey Horse, lives in a barn that is 3 yards by 8 feet. What is the area of the barn? A. 24 feet 2 B. 72 yards 2 C. 24 yards 2 D. 11 yards 2 E. NOTA 18. Ms. Cantwell s jet flies at 200 miles per hours, and Mrs. Lugemwa s bus goes three hundred and sixty miles per hour. If the two vehicles leave ASFA at the same time, how much farther will Mrs. Lugemwa s bus have traveled than Ms. Cantwell s jet after two hours and 15 minutes? A. 360 miles B. 200 miles C. 240 miles D. 450 miles E. NOTA

4 19. A silver statue of Pooja is leaning against a wall. The top of her head touches the wall at 40 feet. If the base of the statue is 9 feet away from the wall, how tall is Pooja s statue, in feet? A: 41 B: 42 C: 41 D: 39 E: NOTA 20. Ash wants to purchase max repel but has no money. He finds a ditto and decides to trade it for goods. If a max repel costs $200 dollars, and Ash knows that for 1 ditto, he can get 10 poke balls, and for 1 poke ball, he can get 2 revives, and he can sell 1 revive at the store for $30 dollars, how many max repels can he get? A. 1 B. 3 C. 5 D. 2 E. NOTA 21. Evaluate: (42 6)3 8 + ( 1) ( 6 4)4 A: 3 2 B: 7 4 C: 29 8 D: 3 10 E: NOTA 22. The Zhou tribe is very vain, and prides itself on always winning the annual Shiniest Nuts award. The year, however, the award is in 2 hours, and the Zhou tribe still has 18 of its prize nuts to transport to the judging area. If the Zhou tribe can transport 3 nuts per person, per hour, how many people do they need transporting nuts to get all 18 of their shiniest nuts to the judging area on time? A: 6 B: 9 C: 2 D: 5 E: NOTA 23. Solve for x: 7xx > 8xx A: xx > 1 3 B: xx > 3 C: xx > 1 45 D: xx > 1 45 E: NOTA 24. What is 50% of 60% of 10% of 240? A. 20 B. 7.2 C. 2 D. 2.7 E. NOTA

5 25. Given 8 9 Use the remaining numbers from 1-9 to fill in the grid such that each row, column, and diagonal sums to 15. What number must be placed in the center? A: 2 B: 6 C: 3 D: 5 E: NOTA TB1: Numair, Deanna, Karan, and Stephen are sitting at a table discussing their favorite movies, snacks, and drinks. They make a list of them for future reference; however, a mysterious cat in a hat shreds the list up. The four friends are depressed, because they cannot recall their favorite items. Later on that day, an anonymous package appears at their doorstep and contains a list of clues that they can use to find out their favorite items. They do have a scratch sheet of paper with some of the information on it and know what items are in each category, though. The paper reads: Movies: Kung Fu Panda 2, Cinderella, Bambi, and Up Snacks: Jolly Ranchers, Gummy Bears, Honey Buns, and Nestle Crunch Drinks: Pepsi, Coke, Protein Shake, and Dr. Pepper. The clues are given in the following order: 1. Karan enjoys watching movies involving bears while eating gummy bears and drinking coke, which is commonly associated with polar bears. 2. Stephen is working to be the world s strongest man and regularly consumes protein shakes. However, he cannot stand Nestle Crunch. 3. Deanna is fond of princesses, who lose their slippers at large social gatherings, but her favorite movie is Up. 4. Numair often dreams of being a princess, which is why his favorite movie is Cinderella. 5. Stephen and Deanna both suffer from a potentially fatal allergy to Jolly Ranchers, which is why Jolly Ranchers are NOT their favorite snack. 6. Numair has always been afraid of the doctor, which is why he is utterly disgusted by Dr. Pepper. What is the number of consonants in the name of Deanna s favorite snack? TB2: What is the sum of 3 billion and two? TB3: A circle has a radius equal to the second prime number. What is the area of the circle?