2. You pick two different integers at random from 1 to 10. What is the chance that they are consecutive?
8. Find numbers (a, b) so that 4, a, b is a geometric progression, whereas a, b, -1/2 is an arithmetic progression.
7. Suppose that triangle ABC has sides of length 5, 5, and 6. What is the area of ABC?
1. If x is 15% of 5000 and y is 300% of x, what is the value of the sum of x + y?
3. When the integers 1 to 100 are written, which digit is written the fewest number of times? Which digit is written the greatest number of times?
4. Suppose that you have three numbers a, b, c, and you know the following:
a + b = 21
a + c = 16
b + c = 23
Find a + b + c
5. In one middle school, 150 students play sports and 100 students are on the Honor Role. If 60 of the students on the Honor Roll also play sports, what is the probability that a randomly chosen students who plays a sport is also on the Honor Roll?
6. Suppose you have 5 midsized dogs. The mean weight of the4 dogs is 20 pounds (lb.); the median weight is 21 lb.; and the mode weight is 17 lb. There is only 1 pair of dogs that share the same weight. Find the weight of each dog, if each dog's weight is a positive integer.
