Math Contest Problems : Eighth Grade Test - Excellence in Mathematics Contest – 2011
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Muhammad Yusuf
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1. Included in the Rhind Papyrus from 3600 years ago, the Egyptians used the following rule to determine the area of a circle:
“From the diameter, subtract 1/9 of the diameter. Square your answer.”
Compared to the correct formula for computing the area of a circle, what is the per cent error when using this Egyptian formula? (Note: “per cent error” = “amount of error”/”correct answer”.)
A. 0.60% B. 0.73% C. 0.92% D. 1.28% E. 1.31%
2. In mentioning the phenomenal growth of the Internet, a computer scientist wrote that the capacity is now reaching one yottabyte. If one yottabyte equals one thousand zettabytes; one zettabyte equals one million pettabytes; one pettabyte equals one million gigabytes; one gigabyte equals 210 megabytes; and one megabyte equals 220 bytes; then one yottabyte equals approximately 10N bytes. What is N? (Personally, I’d say, “That’s a lotta bytes!”)
A. 15 B. 18 C. 21 D. 24 E. 27
3. It is 6:00 PM Tuesday in San Francisco when it is 2:00 AM Wednesday in London. Zan at the San Francisco Google office and Alec at the London Google office are scheduled to work together on a project on their computers. Zan contacts Alec at 7:40 AM San Francisco time and they begin working. They work together until Alec shuts down his computer at 7:15 PM London time. For how many minutes did they work together?
A. 35 B. 95 C. 155 D. 215 E. 275
4. One-Pile Nim is a two-person game. Pattie and Malik take turns. There is one pile of chips. On each turn, a player takes 1, 2, 3, 4, or 5 chips from the pile. The player to take the last chip wins. At one point of the game, it is Pattie’s turn and there are 1,000 chips remaining in the pile. If both players make their best plays, there is only one winning play for Pattie. What is it?
A. Take 1 chip B. Take 2 chips C. Take 3 chips D. Take 4 chips E. Take 5 chips
5. Alicia, Ben, and Camellia are each bicycling at a constant speed.
- At 3:00, Alicia is 100 m behind Ben and Ben is 200 m behind Camellia.
- At 3:08, Alicia passes Ben.
- At 3:12, Alicia passes Camellia.
As Ben passes Camellia, how many meters are they behind Alicia?
A. 100 m B. 150 m C. 200 m D. 300 m E. 400 m
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