单选题
【正确答案】
D
【答案解析】Let r, C, and A represent the radius, circum-ference, and area of the circle.
[*]
Similarly,
[*]
The value of Column A is 2r, and the value of Column B is r2. Which is greater? Dividing each by r, yields 2 in Column A and r in Column B. Since there are no restrictions, r could be greater than, less than, or equal to 2.
Neither column is always greater, and the two columns are not always equal (D).
**Use TACTIC 1, Chapter 12. Let r = 1. Then, C = 2π and A = π; so a = 2 and b = 1.
Column B is greater: eliminate A and C. Try r = 2. Now, C = 4π and A = 4π; a = b and the columns are equal. Eliminate Choice B. The answer is D.
[*]
Similarly,
[*]
The value of Column A is 2r, and the value of Column B is r2. Which is greater? Dividing each by r, yields 2 in Column A and r in Column B. Since there are no restrictions, r could be greater than, less than, or equal to 2.
Neither column is always greater, and the two columns are not always equal (D).
**Use TACTIC 1, Chapter 12. Let r = 1. Then, C = 2π and A = π; so a = 2 and b = 1.
Column B is greater: eliminate A and C. Try r = 2. Now, C = 4π and A = 4π; a = b and the columns are equal. Eliminate Choice B. The answer is D.
【正确答案】
C
【答案解析】If r is the radius of the white circle, 2r is the radius of the shaded semicircle. The area of the white circle is πr2. The area of the semi-circle is [*], so the area of the shaded region is [*] The columns are equal (C).
[*]
**The solution is even easier if you use TACTIC 1, Chapter 12. Let the radius of the circle be I instead of r, and proceed as above.
The area of each region is π.
[*]
**The solution is even easier if you use TACTIC 1, Chapter 12. Let the radius of the circle be I instead of r, and proceed as above.
The area of each region is π.
【正确答案】
C
【答案解析】If there are x seats on each bus, then the group is using [*] seats. After a of them get oft, [*] of them, or [*] remain.
What fraction of the 2x seats on the two buses are now being used?[*]
**To avoid the algebra, assume there are 20 seats on each bus. At the beginning, the group is using 48 of the 60 seats on the three buses. When 12 people left, the 36 remaining people used [*] of the 40 seats on two buses.
What fraction of the 2x seats on the two buses are now being used?[*]
**To avoid the algebra, assume there are 20 seats on each bus. At the beginning, the group is using 48 of the 60 seats on the three buses. When 12 people left, the 36 remaining people used [*] of the 40 seats on two buses.