单选题
a, b, and c are the measures of the angles
of isosceles triangle ABC
x, y, and z are the measures of the angles
of right triangle XYZ
Line k goes through (1,1) and (5,2).
Line m is perpendicular to k.
a, b, and c are the measures of the angles
of isosceles triangle ABC
x, y, and z are the measures of the angles
of right triangle XYZ
Line k goes through (1,1) and (5,2).
Line m is perpendicular to k.
【正确答案】
B
【答案解析】This can easily be solved in less than a minute by adding, but in only 5 seconds by thinking! Use TACTIC 5: don't calculate; compare. Each of the three numbers in Column B is greater than the corresponding number in Column A.
【正确答案】
D
【答案解析】Use TACTIC 1. When x = 1, the columns are equal; when x = 2, they aren't.
**Use TACTIC 3
[*]
This is a much easier comparison, x2 could equal 1, but doesn't have to. The answer is Choice D.
【正确答案】
A
【答案解析】You can easily calculate each of the times— by dividing 7 by 6 in Column A, and 6 by 7 in Column B. However, it is easier to just observe that the time in Column A is more than one hour, whereas the time in Column B is less than one hour.
【正确答案】
B
【答案解析】Use TACTIC 3
[*]
Since it is given that cd ＜ 0, so is 2cd.
**If you can't expand (c + d)2, use TACTIC 1. Replace c and d with numbers satisfying cd ＜ 0.
Both times Column B was greater: choose B.
[*]
Since it is given that cd ＜ 0, so is 2cd.
**If you can't expand (c + d)2, use TACTIC 1. Replace c and d with numbers satisfying cd ＜ 0.
| Column A | Column B | Compare | Eliminate | |
| Let c = 1 and d = -1 |
(1 +-1)2 = 0 |
12 + (-1)2 = 1+1=2 |
B is greater |
A and C |
| Let c = 3 and d = -5 |
(3 +-5)2= (-2)2 = 4 |
32 + (-5)2 = 9 + 25 = 34 |
B is greater |
|
【正确答案】
C
【答案解析】The average of 3 numbers is their sum divided by 3. Since in any triangle the sum of the measures of the 3 angles is 180° [KEY FACT J 1 ], the average in each column is equal to 180 + 3 = 60.
**Use TACTIC 1. Pick values for the measures of the angles. For example, in isosceles △ABC choose 70, 70, 40; in right △XYZ, choose 30, 60, 90. Each average is 60. Choose C.
【正确答案】
B
【答案解析】Since b ＜ 0, 6b is negative, whereas b6 is positive.
**Use TACTIC 1. Replace b with numbers satisfying b ＜ 0.
Both times Column B was greater: choose B.
**Use TACTIC 1. Replace b with numbers satisfying b ＜ 0.
| Column A | Column B | Compare | Eliminate | |
| Let b = -1 | 6(-1) = -6 | (-1)6 = 1 | B is greater | A and C |
| Let b = -2 | 6(-2) = -12 | (-2)6 = 64 | B is greater |
【正确答案】
B
【答案解析】Again, use TACTIC 5: don't calculate the two areas; compare them. The circle in Column A has a radius of 17, and so its diameter is 34. Since the circle in Column B has a larger diameter, its area is greater.
【正确答案】
A
【答案解析】Again, use TACTIC 5: don't calculate either slope. Quickly, make a rough sketch of line k, going through (1,1) and (5,2), and draw line m perpendicular to it.
[*]
Line k has a positive slope (it slopes upward), whereas line m has a negative slope (it slopes downward). Column A is greater. [Note: the slope of k is[*] and the slope of m is -4. See Section 14-N for all the facts you need to know about slopes.]
**If you don't know this fact about slopes, use TACTIC 6. The answer cannot be Choice D, and if two lines intersect, their slopes cannot be equal, so eliminate Choice C. Guess Choices A or B.
【正确答案】
D
【答案解析】Every sixth integer is a multiple of 6 and every ninth integer is a multiple of 9, so in a large interval there will be many more multiples of 6. But in a very small interval, there might be none or possibly just one of each. **Use TACTIC 1. Let x = 1. Between 100 and 101 there are no multiples of 6 and no multiples of 9. Eliminate Choices A and B. Choose a large number for x: 100, for example. Between 100 and 200 there are many more multiples of 6 than there are multiples of 9. Eliminate Choice C.