Math Olympiad 5( Week 20 Quiz 4) 1. Mrs. Smith's class has a music class every 3 school days, an art class once a week, and a P.E. class every 4 school days. If they have all these classes today (Today is Tuesday), how many days later will all of these classes be on the same day? Note that every week has 5 school days. 2. A prime number is a whole number that can only be divided by itself and one. What is the biggest prime number that is less than 195? 3. Using digits 1, 2, 3, 4, and 5 (each digit can be used as many times as you want in a number), how many 3-digit numbers can you make? 4. Using a die(a cube with number of 1 to 6), what is the probability of throwing a 2, 3 and 6 regardless of the order? 5. There are 7 locks and each with a key. However all the keys were messed up. At most how many tries will be needed in order to match each key to its lock? 6. There are 80 balls of 8 different colors in a bag. There are an equal number of balls for each color. At least how many balls need to be taken out from the bag so that there are 4 balls which are the same color? 7. A spinner shown in the diagram has 6 equal sections. The probability of the pointer falling into each section is the same (Assume the pointer will never fall on a line between two sections). What is the probability that the pointer falls on an odd number?
8. There are two types of boxes that can hold either 8 or 7 balls exactly. To put a total of 71 balls into the boxes so that all the boxes are full, what is the smallest number of boxes needed? 11. If 2 laptops out of 10 on an assembly line are non-black, what is the probability that a laptop selected at random from the assembly line will be black? 12. A is a two-digit number. When 239 is divided by this number , there is a remainder of 5. What is the smallest possible value for A? 13. The product of two whole numbers is 448 and their quotient is 7. What is the smaller number? 14. I have 4 three-cent stamps and 2 five-cent stamps. Using one or more of the stamps, how many different amounts of postage can I make? 15. A bag contains 312 beads. All the beads are the same, but in 4 different colors. There are equal number of beads for each color. If Mary is blindfolded and picks beads from the bag, what is the fewest number of beads she has to pick in order to be absolutely sure that there are 10 beads of the same color? |