Practice Set 4
- Problem #1: If a<b, b<c, c<a, and a=1, what is the sum of a, b, and c?
- Problem #2: Given an unlimited number of quarters, dimes, nickels, and pennies, in how many ways can you make 25 cents?
- Problem #3: The sum of the first N counting numbers is 2628. What is the sum of the first N positive even numbers?
- Problem #4: You are designing a running track in the shape of a rectangle connected to two semicircles, as shown in the diagram below. If you would like the perimeter of the entire shape to be 375 meters, what should x be? Use 3.14 as an approximation for π.
- Problem #5: 1 out of 6 Yummy Cereal boxes has a bobblehead of Zac Efron inside. If Katie buys 3 Yummy Cereal boxes, what is the probability that at least one will have a Zac Efron bobblehead inside? Express your answer as a common fraction.
- Problem #6: A star is formed by extending the sides of a regular pentagon, as shown. What is the measure of angle A, in degrees?
- Problem #7: A test tube was 1/8 full of hydrochloric acid. After I added 15 mL of hydrochloric acid, the test tube was 7/8 full. I then added a little more hydrochloric acid, filling the test tube completely. How many total mL of hydrochloric acid were in the test tube now?
- Problem #8: What is the smallest number with exactly 6 factors?
- Problem #9: Here's a question from a chemistry test at my school: "You live in a country where the system of time has unusual units. According to your country's system of time, if 20 gits equal 1 erb, and 1 futz equals 2 hews, and 10 erbs equal 1 futz, how many gits equal 10 hews?"
- Problem #10: In the arithmetic sequence 9, a, b, c, d, ..., y, z, 90, there are are 26 unknown numbers between 9 and 90. What is the value of z?
Solutions
