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Math Challenge Math Challenge 1. Hailey added the product of 9 and 12 to the product of 7 and 5. She then subtracted the product of 4 and 6 from the result. What was her final answer? Math Challenge Answer: 119 Math Challenge 2. Set A = {B, R,E,A,K,S} Set B = {R, A, I, S, E,D} How many proper subsets does A ∩ B contain ? Math Challenge Answer: 15 Hint: Find the letters in common. Count them. Use this number as the exponent of 2. Two to the 4th power results in 16 subsets. Subtract one to get the number of proper subsets. Math Challenge What is the area of a rhombus with diagonals of 10 cm and 28 cm ? 3. Math Challenge Answer: 140 The area of a rhombus equals the product of the diagonals divided by 2. Math Challenge 4. Two numbers are relatively prime if their only common factor is one. How many positive integers less than 21 are relatively prime to 21 ? Math Challenge Answer: 12 For the #15, eliminate all multiples of 3 and 7. Math Challenge 5. What is the area of a triangle with a base of fourteen and a height of ten? √49 Math Challenge Answer: 70 The area of a triangle is base times height divided by 2. Math Challenge 6. On a 12-hour clock, what is the measure of the acute angle between the hour and minute hand at 4:30? Math Challenge Answer: 45 degrees A circle contains 360 degrees. There are 12 hours on the face of the clock. Divide 360 by 12, so 30 degrees separate each number on the clock. At 4:30, the minute hand points to the 6, and the hour hand is exactly half-way between the 4 and the 5. So, 30+15 = 45. Math Challenge 7. Subtract the cube of five from the square of 17. The result is 6 less than ____ . Math Challenge Answer: 170 Hint: Cube means “to the third power.” Square means “to the second power.” Math Challenge What is the units digit of 4 th to the 97 power? 8. Math Challenge Answer: 4 Hint: Write the first four powers of 4, which are 4, 16, 64, and 256. Notice that 4 and 6 repeat, so every odd power would end in a 4 and every even power would end in a 6. The units digit is another name for the one's place. Math Challenge 9. If A#B = 14 x A + B - 2 then what is the value of 8#17 ? Math Challenge Answer: 127 Hint: Substitute 8 for A and 17 for B. Math Challenge 10. What is the least common multiple of 16 and 18? Math Challenge Answer: 144 Hint: The least common multiple (LCM) is the first multiple that occurs on both lists of multiples. List the multiples of 16 and 18. The first multiple on both lists is 144. Shortcut: The LCM = (the product of the numbers) divided by the GCF Math Challenge How many prime numbers are between 1 and 80? 11. Math Challenge Answer: 22 There are 25 primes between 1 and 100. Fifteen of these are between 1 and 50. Ten of these are between 51 and 100. 97, 89, and 83 are prime, so 25 – 3 = 22. Math Challenge What is the sum of the perimeters of 4 triangles and 5 squares if all sides measure 6 inches? 12. Math Challenge Answer: 192 The perimeter of a polygon is the sum of the lengths of its sides. Math Challenge 13. 67.5 hm = _____ dm Math Challenge Answer: 67,500 King Henry Doesn't Mind Drinking Chocolate Milk Km, hm, dam, meter, dm, cm, mm Math Challenge 14. What is the sum of the factors of 120 ? Math Challenge Answer: 360 Hint: The prime factorization of 120 is 2³ x 3 x 5. To find the sum, (2³+2²+2+2°)x(3+3°)x(5+5°), which is 15x4x6 which equals 360. You could also just write the 16 factors and add them. Math Challenge 15. What is product of the units digit and the tens digit of 54,702 ? Math Challenge Answer: 0 Math Challenge 16. What is the prime factorization of 280 ? Math Challenge Answer: Two to the third power times five to the first power times seven to the first power. Make a factor tree for 280. Math Challenge 17. What is the perimeter of a square with an area of 289 square inches ? Math Challenge Answer: 68 Hint: 289 is a perfect square. 17²=324, so each side of the square is 17. The perimeter is 68. Math Challenge 18. If f(M) = 4M + 12, what is the value of f(15) ? Math Challenge Answer: 72 Hint: Substitute 15 for the letter M. The expression 3M means 3 times M. In algebra, when a number is directly beside a letter, it indicates multiplication. Math Challenge 19. If 12 men can make 60 widgets in 3 days, how many men will need to work at the same rate to make 20 widgets in 6 days? Math Challenge Answer: 2 Hint: Multiply 12 x 3 = 36. It takes 36 man-days to produce 60 widgets. Therefore, it only takes 12 man-days to make 20 widgets. So, 6 days times 2 men would equal 12 man days. The answer is 2. Math Challenge 20. Which of these is an irrational number: A: 6.7389 B: the square root of 144 C: 3/5 D: π Math Challenge Answer: D An irrational number is not an integer and not a fraction. An irrational number can be represented by a decimal value that is never ending and never repeats a pattern. A,B, and C are rational. Only D is irrational. Math Challenge THE END Math Challenge Answer: Math Challenge 22. Math Challenge Answer: Math Challenge 23. Math Challenge Answer: Math Challenge 24. Math Challenge Answer: Math Challenge 25. Math Challenge Answer: Math Challenge 26. Math Challenge Answer: Math Challenge 27. Math Challenge Answer: Math Challenge 28. Math Challenge Answer: Math Challenge 29. Math Challenge Answer: Math Challenge 30. Math Challenge Answer: Math Challenge 31. Math Challenge Answer: Math Challenge 32. Math Challenge Answer: Math Challenge 33. Math Challenge Answer: Math Challenge 34. Math Challenge Answer: Math Challenge 35. Math Challenge Answer: Math Challenge 36. Math Challenge Answer: Math Challenge 37. Math Challenge Answer: Math Challenge 38. Math Challenge Answer: Math Challenge 39. Math Challenge Answer: Math Challenge 40. 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