| {{U}}Directions:{{/U}} In the following questions, choose the best answer from the five choices listed. |
单选题
The Center City Little League is divided into d divisions. Each division has t teams, and each team has p players. How many players are there in the entire league?
【正确答案】
B
【答案解析】Since d divisions each havet teams, multiply to get dt teams; and since each team has p players, multiply the number of teams (dt) by p to get the total number of players: dtp.
**Use TACTIC 2, Chapter 11. Pick three easy-to-use numbers for t, d, and p. Assume that there are 2 divisions, each consisting of 4 teams, so, there are 2 x 4 = 8 teams. Then assume that each team has 10 players, for a total of 8 × 10 = 80 players. Now check the choices. Which one is equal to 80 when d = 2, t = 4, and p = 10? Only dtp.
单选题
A number x is chosen at random from the set of positive integers less than 10. What is the probability that 
?
?
【正确答案】
B
【答案解析】There are nine positive integers less than 10: 1, 2 9. For which of them is 
? Only 1 and 2: 
When x=3, 
and for all the others 
. The probability is .
? Only 1 and 2: When x=3, and for all the others . The probability is .
单选题
【正确答案】
B
【答案解析】Solve the given equation: 
Add the fractions:
Multiply both sides by a:
3 = 12a
Divide both sides by 12: 
**You can use TACTIC 1, Chapter 11: back-solve; try Choice C 
, so the left-hand side equals 9. That's too small. Now, be careful." a fraction gets bigger when its denominator gets smaller [KEY FACT B4]. Eliminate Choices C, D, and E, and try a smaller value for a: 
works.
Add the fractions:
Multiply both sides by a:
3 = 12a
Divide both sides by 12:
**You can use TACTIC 1, Chapter 11: back-solve; try Choice C , so the left-hand side equals 9. That's too small. Now, be careful." a fraction gets bigger when its denominator gets smaller [KEY FACT B4]. Eliminate Choices C, D, and E, and try a smaller value for a: works.