The Sixth Annual West Windsor-Plainsboro Mathematics Tournament

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1 The Sixth Annual West Windsor-Plainsboro Mathematics Tournament Saturday October 27th, 2018 Grade 6 Test RULES The test consists of 25 multiple choice problems and 5 short answer problems to be done in 40 minutes. All multiple choice answers should be marked on the Scantron mark sheet. No marks on this paper will be graded. All short answers you write should be in exact, simplified form, unless otherwise stated in the question, following the rules below: All fractions must be simplified. All fractional answers must be expressed in the form a b where a and b share no common factors other than 1. For example, if the answer is 9 5, then (mixed fraction) or 10 are NOT ACCEPTABLE. Any question that involves the number π in the answer must be written using the symbol π. In particular, decimal approximations of π are NOT ACCEPTABLE. All radicals must be simplified. Radicals in the denominator of a final answer, a perfect n th power under a n th root, or fractions/decimals under a radical are NOT ACCEPTABLE. You can ask your proctor a question, but if they think answering your question will give you an unfair advantage on the test over other contestants, they don t have to respond. After the testing has completed, please go to your selected mini-event rotation (directions will be given for this after the main contest is over). DO NOT FLIP THIS PAGE TO BEGIN THE TEST UNTIL INSTRUCTED TO DO SO BY YOUR PROCTOR(S).

2 Multiple-Choice Questions Answers to this section of the test should go on the scantron multiple-choice form given to you. NOTHING WRITTEN ON THIS TEST PAPER WILL BE SCORED. 1. What is ( )/9? A. 99 B. 100 C. 101 D. 123 E Compute the following: A. 72 B. 72 C. 73 D. 145 E Claude goes to the school store and buys a pencil and an eraser. If the total cost of his purchase is $5.50 and the pencil cost $5 more than the eraser, how much did the eraser cost? A. $0.00 B. $0.25 C. $5.00 D. $5.25 E. $ David and his dad share their birthday on the same day! David just turned 17, and his dad is now exactly 3 times David s age. How old was his dad when David was born? A. 17 B. 18 C. 34 D. 35 E Bill is making a new fish tank. He takes a box with dimensions 6 cm by 4 cm by 4 cm, but places a sphere inside with a volume of 32 cubic centimeters, how many cubic centimeters of water is needed to fill the tank? A. 36 B. 45 C. 64 D. 72 E In Math Club, there are three types of animals: Snakes, Cats, and Cows. Exactly 20% of Snakes attend every meeting, 30% of Cats attend every meeting, and 90% of Cows attend every meeting. Given that the number of each type of animal present is an natural number, what is the least amount of total members in Math Club? A. 13 B. 25 C. 30 D. 33 E Bessie the Cow escapes from the farm. She heads 5 miles north and 12 miles east. Farmer Joe then goes in a straight line from his farm to Bessie s current location. How much more distance did Bessie travel than farmer Joe? A. 3 miles B. 4 miles C. 5 miles D. 6 miles E. 7 miles 8. Jimmy is baking cake, which has only flour, sugar, and baking soda. The recipe calls for three times as much flour as sugar, and half as much baking soda as sugar. If Jimmy uses 2/3 cups of baking soda, how many cups of ingredients did Jimmy use in total? A. 6 cups B. 7 cups C. 8 cups D. 9 cups E. 10 cups 9. In Mathville, for every dollar earned by a citizen, they must pay 15 cents to the government, but every $15 paid to the government results in a $1 refund. If Adam earns $1500 dollars, how much money does he have to pay to the government? A. $200.0 B. $ C. $ D. $ E. $210.00

3 10. Andrew likes to build scale models in his free time. Recently, he decided to build a replica of the Empire state building, which is 1440 feet tall, at a scale of 1 inch to 40 feet. How tall is his scale model in inches? A. 3 inches B. 10 inches C. 36 inches D. 432 inches E inches 11. Tommy joined cross-country in his school. In the first practice, he was able to run 8 miles in an hour. After a week of practicing, Tommy could run 10 miles in the same amount of time. If Tommy continued to increase the amount he could run by the same amount every week thereafter, how many miles would he be able to run after 4 more weeks? A. 10 miles B. 12 miles C. 14 miles D. 16 miles E. 18 miles 12. Jack and Jill are rounding numbers. They are given a number, 49.49, and decide to round it. Jack rounds it by first rounding to the hundredths place, then the tenths place, then the ones place, then the tens place, then the hundreds place. Jill rounds by rounding it to the nearest hundreds place. What is the difference between Jack s final number and Jill s final number? A. 0 B. 50 C. 100 D. 150 E The company SGSS is a massive company with 4 branches in each of the 9 biggest countries. In addition, each branch has 20 buildings each employing 20 workers. If SGSS pays all of their employees equally, and raised their wages by $0.20, then how much more money will they have to pay their employees? A B C D E Al is taking a test he did not study for. He can only correctly answer 10% of the problems, and will guess the answer for the rest. If the test is 120 multiple choice with four choices per answer, how many problems can he expect to get right? A. 12 B. 30 C. 36 D. 39 E Given a 5x5 grid, how many ways are there to color exactly 5 cells yellow, such that each row and each column contain exactly one yellow cell? A. 120 B. 240 C. 360 D. 720 E Fields on a farm are numbered 1 to 50. Bessie the cow goes around eating fields that are multiples of 2. Then she goes around and eats multiples of 3, then 4, then 5. How many fields are still full of grass? (Note: If Bessie ate the grass on a field, it is no longer full). A. 11 B. 12 C. 13 D. 14 E You and a friend are playing a game with dice. If the dice lands on an even number, your friend gives you $3. If the dice lands on an odd number, you have to give your friend $2.37. You have time to play exactly 10 rounds. If you won exactly 6 rounds, how much money did you win? A. $7.26 B. $7.89 C. $8.52 D. $9.15 E. $9.88

4 18. Todd owns a restaurant with 20 tables. The tables can seat either 4 or 6 people. If 92 people can be seated at Todd s cafe, how many 4 people tables are there in Todd s restaurant? A. 14 B. 15 C. 16 D. 17 E What is the units digit of ? A. 0 B. 2 C. 4 D. 6 E A diagonal is defined as a line connecting two non-adjacent vertices of a polygon. How many diagonals does a polygon with 19 sides have? A. 152 B. 171 C. 304 D. 323 E Two sides of a triangle have lengths 13 and 15. If the altitude to the third side is 12, what is the length of the third side? A. 11 B. 12 C. 13 D. 14 E How many digits does have? A. 9 B. 10 C. 11 D. 12 E I have a broken calculator that can only do two operations: divide by 3, or subtract 1. What is the minimum amount of operations it takes to get from 2018 to 0? A. 14 B. 16 C. 18 D. 20 E A cat is walking on the vertices of triangle ABC. The cat starts at vertex A and walks to an adjacent vertex at random every second. What is the probability that the cat is back at vertex A after 5 seconds? A. 1/16 B. 2/16 C. 3/16 D. 4/16 E. 5/ What is the tens digit of 5! + 6! + 7! !? (The! is a factorial, and n! = n (n 1) (n 2) 2 1. For example, 4! = = 24) A. 4 B. 5 C. 6 D. 7 E. 8

5 Short Answer Questions Answers to this section of the test should go on the short answer questions answer form given to you. NOTHING WRITTEN ON THIS TEST PAPER WILL BE SCORED. 1. Adam has to buy a birthday present for two of his friends, but he s forgotten which one wants which gift. He knows that one of them wants cat food, one wants an iphone 10, but he also remembers someone asking him for a hockey stick. If Adam randomly gives one of the three gifts to each of the two friends, what is the probability that both of them get the gift they want? (Note: Both friends do not want the same gift) 2. The numbers on the opposite faces of a die add up to 7. What is the sum of the numbers on the 4 faces touching the face with the number 1? 3. How many distinct ways can the letters B, E, S, S, I, E be rearranged such that it does not form the word Bessie? 4. Let x be the answer to this problem. If x is positive, what is x 2 6? 5. A bee is riding on a train heading west. Once another train heading east on the same track is within 200 miles, the bee begins to fly to and from the two trains until they meet. The first train travels at 40 mi/h but stops for 3 minutes at a station before crossing paths with the other train, while the second train travels at 61 mi/h. If the bee travels 200 mi/h, how much distance does the bee travel?

The Sixth Annual West Windsor-Plainsboro Mathematics Tournament

The Sixth Annual West Windsor-Plainsboro Mathematics Tournament Saturday October 27th, 2018 Grade 6 Test RULES The test consists of 25 multiple choice problems and 5 short answer problems to be done in