Practice Set 1

• Problem #1: Boxes A, B, C, D, and E represent underground chambers, and the arrows represent tunnels between them. You start in Chamber A and crawl through the tunnels, eventually ending up either in Chamber D or Chamber E. If you end up in Chamber D, you will be eaten by a cave bear. If you end up in Chamber E, you will be attacked by vampire bats. You can only move in the direction in which the arrows are pointing. When leaving a chamber, you are equally likely to use any of the available exit tunnels. What is the probability that you will end up in Chamber D and therefore get eaten by a cave bear?
  
• Problem #2: The arithmetic mean of the numbers in the set {1, 7, 9, 20, x} is 11 less than x. What is the arithmetic mean of the set?
• Problem #3: What perfect-square integer is closest to 240?
• Problem #4: The sequence 12, x, y, z, 15 is an arithmetic sequence. What is the value of y? Express your answer as a decimal to the nearest tenth.
• Problem #5: Two complementary angles, A and B, have measures in the ratio 9:21, respectively. In degrees, what is the measure of angle B minus the measure of angle A?
• Problem #6: You are kidnapped by an evil zombie. The zombie says, "I will let you go if you guess the positive three-digit number I am thinking of. The sum of the three digits is 12. The sum of the hundreds and tens digit is 5 times the ones digit. The tens digit is 1." What number is the zombie thinking of?
• Problem #7: A palindrome is a number that reads the same forward and backward, such as 717 or 3003. What is the smallest palindrome greater than 12345?
• Problem #8: On Mondays, Tuesdays, Wednesdays, and Thursdays, Johnny spends 9 hours of each day sleeping. On Fridays, Saturdays, and Sundays, Johnny spends 10 hours of each day sleeping. If you choose a random day of the week and then choose a random time of that day, what is the probability that Johnny is asleep at that time on that day? Express your answer as a common fraction.
• Problem #9: M and N are positive integers that satisfy the equation M(M-N)=31. What is the value of N?
• Problem #10: A certain ninja clan first came together on January 1, 2002, with an unknown number of members. Throughout the rest of 2002, 3 more members joined. During 2003, the number of members doubled. During 2004, 54 members joined. There were a total of 90 ninjas in the clan at the end of 2004. Assuming that no ninjas left the clan (that's against ninja rules), how many members were there to start with on January 1, 2002?

Solutions