What is the sum of the positive integer factors of 12?

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1 1. $ Three investors decided to buy a time machine, with each person paying an equal share of the purchase price. If the purchase price was $6000, how much did each investor pay? $6, What integer is closest to 10π? 3. What is the sum of the positive integer factors of 12? 4. If = 8 and = 4, what is the value of the expression 2 4? 5. If 5x + 2 = 7, what is the value of 15x + 6? 6. What is the range of the four high scores in the table shown here? H S Player PinkNinja FR33DOM Marsh-e-mallow Gator-231 High Score 5,736,750 2,710, , ,500

2 7. Given that 4(n 5) + 2 = 3(n 1), what is the value of n? 8. $ A concession stand sells a 16-ounce drink for $4. If the price is directly proportional to the amount of drink served, what is the price of a 20-ounce drink? 9. What is the product of the greatest common factor of 4 and 10 and the least common multiple of 4 and 10? 10. What is the arithmetic mean of the integers from 16 to 20, inclusive? 11. combinations An ice cream shop offers chocolate, strawberry and vanilla flavors of ice cream and sprinkles for a topping. By choosing one flavor of ice cream and a topping of sprinkles or no sprinkles, how many different combinations are possible? 12. cm In ABC, shown here, AC = 13 cm and BC = 8 cm. If ABC has perimeter 36 cm, what is the length of side AB? A 13 B 8 C

3 13. What is the value of the sum ? 14. quarters Sammy goes to the store and buys $1.80 worth of produce. He gives the clerk a $5 bill and receives change consisting of only quarters, dimes, nickels and pennies. What is the greatest number of quarters he could receive? 15. inches 8 12 An 8-inch by 12-inch piece of cardboard has a 3-inch by 3-inch square cut out of each corner. What is the perimeter of the resulting figure, shown here? 16. units 2 What is the area of the triangle enclosed by the lines y = 0, x = 8 and y = x? 17. units If A through G are evenly spaced points on the number line shown, what is the value of AC + DG? A 2 B C D E F G What decimal is equivalent to 4 5 percent?

4 19. A fair 10-sided die, with faces numbered 1 through 10, is rolled once. What is the probability that the number rolled will be prime? Express your answer as a common fraction. 20. points Five students had a mean score of 90 points on a test. One test was scored incorrectly, and that particular test score was later raised by five points. What is the new mean score? 21. triangles How many triangles of any size are in the figure shown here? 22. If p is prime and n is even such that p + n = 47 and pn = 210, what is the value of n? 23. If a # b = a 2 (7 b), what is the value of (2 # 5) # 3? 24. number If the permutations of the letters in the word SURE are numbered 1 through 24 in alphabetical order, what number is RUSE?

5 25. A line contains the points (6, 10) and (15, 22). If the line intersects the y-axis at (0, b), what is the value of b? 26. What is the value of k in the equation shown? = 10 k 27. Samhir writes down all of the odd numbers between 500 and 700 that are divisible by both 7 and 9. What is the sum of the numbers Samhir writes? 28. Sasha s secret passcode is a nine-digit number that begins and ends with 6. The sum of every three consecutive digits in the number is 14. What is the fifth digit of Sasha s passcode? 29. cm Coco buys a very large rectangular chocolate bar and decides that each day, she will cut the largest possible square off of the bar and eat it. When the remaining part of the chocolate bar is a square, she will eat all that is left. The table shows the area, in square centimeters, of the square Coco eats on each day. If Coco finishes the chocolate bar on Day 6, what was the length of the longer side of the chocolate bar when Coco bought it? Day Eaten Area (cm 2 ) This figure shows five shaded circles within a circle of radius 7 units. The four small congruent shaded circles are tangent to the outer circle and to the large shaded circle. The radius of each of the smaller shaded circles is 1 the radius of the 5 large shaded circle. What fraction of the largest circle s area is shaded? Express your answer as a common fraction.

6 1. Hal has a positive secret number. He performs a sequence of operations with his secret number. He doubles the number, subtracts 8, divides by 4, adds 2 and squares the result to get 25. What is Hal s secret number? 2. $ Toni goes to a department store and buys two shirts marked the same price. She pays full price for the first shirt but gets a 40% discount on the second shirt. If she pays a total of $32.40 for the two shirts, how much did she pay for the second shirt?

7 3. The table lists the number of Wednesdays on which the Norton Middle School cafeteria served each of four different entrées and each of three different desserts during the previous school year. If the entrée and dessert served each Wednesday were selected independently and randomly, based on this data, what is the probability that the Norton Middle School cafeteria served pizza and lemon cake on the first Wednesday of the previous school year? Express your answer as common fraction. Entree Dessert Pizza 15 Lemon Cake 20 Chicken 8 Apple Pie 8 Fish & Chips 10 Brownies 12 Tacos 7 4. integers How many integers x, with 0 < x 100, are divisible by 2, 3 and 4?

8 5. Two circles, each of radius 5 units, have centers at the origin and at (7, 7), respectively. What is the y-intercept of the line that contains their common chord? 6. ways How many ways are there to choose positive integers a, b and c, not necessarily distinct, so that a + b < c and c 5?

9 7. degrees The figure shows points P and Q inside rhombus ABCD so that segments AP, BP, BQ, CQ, DQ and DP are all congruent. If the measure of angle BAD is 40, what is the degree measure of angle PDQ? B A P Q C D 8. % A company sells popcorn in cylindrical canisters. Marketing indicates that wider canisters will increase sales. If the diameter of the canister is increased by 27% while keeping the volume of the canister the same, by what percent must the height be decreased? Express your answer to the nearest whole number.

10 1. If 11 n = 123,456,787,654,321, what is the value of n? 2. (, ) The point (4, 2) is reflected over the line y = x. What are the coordinates of its image? Express your answer as an ordered pair. 3. The ages, in years, of four members of a family are represented by a, b, c and d, where a < b < c < d. Their mean age is 34, their median age is 33, and the range of their ages is 32. What is the value of a? 4. base 7 What is the value of when written in base 7? 5. Raquel uses six different digits to fill in the blanks below, writing one digit in each blank, so that the resulting addition statement is correct. What is the least possible sum of the six digits? + = 6. If a, b and c satisfy the equations a 2 + b 2 = 313, b 2 + c 2 = 277 and a 2 + c 2 = 302, what is the value of a 2 + b 2 c 2?

11 7. moves A chess knight makes L-shaped moves on a grid of squares. During each move, the knight moves two squares either up, down, left, or right, then one square in a perpendicular direction. The knight starts on the square marked K in the 6-by-6 board shown here, and its two possible first moves are shown. What is the least number of moves the knight must make from the K in order to land at least once on each of the squares marked with a star? K 8. A chess club has 8 girls and 6 boys. Two members, Zig and Zag, are fraternal twins of different genders. If a team of 3 girls and 3 boys is randomly selected for the district championship, what is the probability that exactly one of the twins is on the team? Express your answer as a common fraction. 9. units 2 Triangle ABO is an isosceles right triangle, AC is a diameter of circle O, and AB is a diameter of circle D. If the semicircle centered at O has area 2π, what is the shaded area AEBF (which is called a lune)? E F D B A O C 10. Each cell in the 3-by-3 array of squares shown is filled with a digit from 1 to 9, inclusive. If the four listed conditions are satisfied, what is the resulting three-digit number when diagonal B is read from upper-left to lower-right? (1) Each digit from 1 through 9 is used exactly once. (2) Each row, read from left to right, forms an odd three-digit multiple of 3 that is not a multiple of 9. (3) Each column, read from top to bottom, forms an odd three-digit multiple of 3 that is not a multiple of 9. (4) Diagonal A, read from lower-left to upper-right, forms an odd three-digit multiple of 9. Diagonal B Diagonal A