Practice Set 5
- Problem #1: You have 7 different Harry Potter books to arrange in a row on one shelf. You want to keep the 3 books Harry Potter and the Sorceror's Stone, Harry Potter and the Chamber of Secrets, and Harry Potter and the Prisoner of Azkaban next to each other, not necessarily in that order. In how many different orders can you arrange the 7 books on the shelf?
- Problem #2: How many prime numbers between 1 and 200 end in the digit 5?
- Problem #3: There are 4 candidates running for class president in Mrs. Schorgenheimer's class: John, Barack, Hillary, and you. On average, each candidate received 7 votes. If each candidate received at least one vote, what is the greatest number of votes that you could have received?
- Problem #4: A and B are complementary angles. In degrees, what is the sum of the measures of the supplements of A and B?
- Problem #5: How many numbers between 1 and 1,000,000, inclusive, are both perfect squares and perfect cubes?
- Problem #6: There are three types of monsters that live under my bed: Bervokens, VonMergles, and Guzzalles. A Bervloken has 16 tentacles, 3 nostrils, and 5 horns. A VonMergle has 8 tentacles, 2 nostrils, and 14 horns. A Guzzalle has 20 tentacles, 1 nostril, and 3 horns. Last night, under my bed, there were 112 tentacles, 11 nostrils, and 45 horns. How many monsters were under my bed in all?
- Problem #7: In the following alphanumeric, each letter represents a different digit. What digit does L stand for?
- Problem #8: Chuck, who is by now a compulsive dice-rolling gambler, rolls a die three times. What is the probability that the sum of his rolls is 6?
- Problem #9: Three circles, centered at points A, B, and C, are externally tangent to one another. The perimeter of triangle ABC is 32. What is the sum of the radii of the three circles?
- Problem #10: What is the length of line segment AB? Express your answer in simplified radical form.
Solutions
