Math Olympiad 2( Week 51 Quiz 10) 1. Joe is 1 foot shorter than Niconia. The total heights of both is 7 feet. What is the height of Niconia in feet? 2. There are 14 drawings to be exhibited in a long showcase. Each drawing needs to be fixed with pins in the four corners. A pin can be shared by the two adjacent drawings as shown in the figure below.
At least how many pins are needed to fix the drawings? 3. There are 2 metal strips to be connected into a long strip. Each metal strip is 5 feet long and the length of the overlapping area is 1 foot as shown in the figure below.
What is the length of the long strip (in feet)? 4. Larry is currently the same age as Morgan 4 years ago and their total age was 6 years then. What is the age of Larry now? 5. Each face of a cube is uniquely marked from 1 to 6. Some of the faces are shown below. Which of the following is marked on the opposite face of '6'?
6. Each face of a cube has a unique color. Below shows some of the faces of the cube. What is the possible color of the face that is opposite to the face with (green) color?
7. There are two clubs with a total of 26 students. One club has 2 more students than the other one. How many students are there in the smaller club? 8. Nancy and Steve both have a certain number of cookies. If Nancy gives 10 cookies to Steve, then they would have the same number of the cookies. How many more cookies does Nancy have than Steve has now? 9. David is currently the same age as Niconia 3 years ago. The total age of both is now 11 years old. What is the age of David? 10. Each face of a cube is uniquely marked from O to T. Some of the faces are shown below. Which of the following is marked on the opposite face of 'P'?
11. A tournament gave prize money for the competitors. The 1st place got half of all the prize money. The 2nd place got half of the remaining prize money. Each of the next placement competitor got half the remaining prize money. If the 3rd placement got $1, what was the prize for the 1st place (in dollars)? 12. Each face of a cube is uniquely marked from A to F. Some of the faces are shown below. Which of the following is marked on the opposite face of 'E'?
13. If you write down the integers from 1 to 60 inclusively, how many times will the digit "1" be written? 14. A pie can be made in a pan in 2 minutes with 1 minute for each side of the pie. If the pan can make four pies at the same time, at least how many minutes are needed to make 6 pies? 15. 3 students took turns to put books from a bin to a shelf. The 1st student took half of the books from the bin and put them to the shelf. Each of the remaining students took half of the books remained in the bin and put to the shelf. In the end, there were 1 book still left in the bin. How many books in total did all the 3 students put to the shelf? |