单选题
Directions: In the following of the questions,choose the best answer from the five choicew listed.
单选题
What is the measure of the angle formed by the minute and hour hands of a clock at 1:50?
(1) 90° (B) 95° (C)105° (D) 115° (E) 120°
(1) 90° (B) 95° (C)105° (D) 115° (E) 120°
【正确答案】
D
【答案解析】For problems such as this, always draw a diagram.
The measure of each of the 12 central angles from one number to the next on the clock is 30°. At 1:50 the minute hand is pointing at 10, and the hour hand has gone [*] of the way from 1 to 2. Then, from 10 to 1 on the clock is 90°, and from 1 to the hour hand is [*](30)°= 25°, a + 25° = 115°.
[*]
The measure of each of the 12 central angles from one number to the next on the clock is 30°. At 1:50 the minute hand is pointing at 10, and the hour hand has gone [*] of the way from 1 to 2. Then, from 10 to 1 on the clock is 90°, and from 1 to the hour hand is [*](30)°= 25°, a + 25° = 115°.
[*]
单选题
Which of the following CANNOT be expressed as the sum of three consecutive integers?
【正确答案】
C
【答案解析】The sum of three consecutive integers can be expressed as
n+(n+1)+(n+2)=3n+3=3(n+1),
and so must be a multiple of 3. Only 28, Choice C, is not a multiple of 3.
**Quickly add up sets of three consecutive integers: 4 + 5 + 6 = 15, 5 + 6 + 7 = 18, 6 + 7 + 8 = 21, and so on, and see the pattern (they're all multiples of 3); or cross off the choices as you come to them.
n+(n+1)+(n+2)=3n+3=3(n+1),
and so must be a multiple of 3. Only 28, Choice C, is not a multiple of 3.
**Quickly add up sets of three consecutive integers: 4 + 5 + 6 = 15, 5 + 6 + 7 = 18, 6 + 7 + 8 = 21, and so on, and see the pattern (they're all multiples of 3); or cross off the choices as you come to them.
单选题
Sandrine is now 5 times as old as Nicholas, but 7 years from now, she will be 3 times as old as he will be then. How old is Sandrine now?
【正确答案】
E
【答案解析】Set up a table./r/n
Then
5x + 7 = 3(x + 7)[*] 5x + 7 = 3x + 21[*] 2x=14[*]x=7.
Sandrine, therefore, is 35.
**Use TACTIC 1, Chapter 11, but since Sandrine is 5 times as old as Nicholas, avoid Choice C, the only answer that is not a multi-ple of 5. Try Choice B, 20. Then Nicholas is 4. In 7 years, he'll be 11 and Sandrine will be 27, which is less than 3 times as old. Try a larger number: 25 or 35.
Time | /r/n Nicholas | /r/n Sandrine | /r/n
Now | /r/n x | /r/n 5x | /r/n
In 7 years | /r/n x+7 | /r/n 5x+7 | /r/n
5x + 7 = 3(x + 7)[*] 5x + 7 = 3x + 21[*] 2x=14[*]x=7.
Sandrine, therefore, is 35.
**Use TACTIC 1, Chapter 11, but since Sandrine is 5 times as old as Nicholas, avoid Choice C, the only answer that is not a multi-ple of 5. Try Choice B, 20. Then Nicholas is 4. In 7 years, he'll be 11 and Sandrine will be 27, which is less than 3 times as old. Try a larger number: 25 or 35.