GWD9 3道数学难题求助

Q20:

The table above shows the results of a survey of 100 voters each responded “favorable” or “unfavorable” or “not sure” when asked about their impressions of candidate M and of candidate N.  What was the number of voters who responded “favorable” for both candidates?

(1)    The number of voters who did not respond “favorable” for either candidate was 40.

(2)    The number of voters who responded “unfavorable” for both candidates was 10.

A. Statement (1) ALONE is sufficient, but statement (2) alone is not sufficient.

B. Statement (2) ALONE is sufficient, but statement (1) alone is not sufficient.

C. BOTH statements TOGETHER are sufficient, but NEITHER statement ALONE is sufficient.

D. EACH statement ALONE is sufficient.

If the sequence x₁, x_2, x_{3, …,} x_n, … is such that x₁  = 3 and x_n+1
                = 2x_n – 1 for n ≥ 1, then x₂₀ – x₁₉ =

A.       2¹⁹

B.       2²⁰

C.      2²¹

D.      2²⁰ - 1

E.       2²¹ - 1

Answer:

Q8:

The points R, T, and U lie on a circle that has radius 4.  If the length of arc RTU is , what is the length of line segment RU?

A.  3/4    

B.  8/3    

C.      3

D.      4

E.       6

Answer:
                

第二道

答案A：可先求出 x₂=5 

             又根据已知可得x₂₀ – x₁₉= 2（x₁₉
                            – x₁₈）

              同理                   x₁₉ – x₁₈=
                                        2¹（x₁₈
                                            – x₁₇）

              所以                   x₂₀ – x₁₉ =2²（x₁₈
                                                    – x₁₇）

              。。。。           x₂₀ – x₁₉ =2¹⁸（x₂
                                                                – x₁）=  2¹⁹

这样啊，谢谢！

第三道

答案：D   已知弧长求弦长解法：先求弦或弧对应的圆心角：360*弧长/圆周长

          本题为360*4/3/8=60度 因此
                 RUO是个等边三角形

第一道：

答案是：A        由1条件可知欢迎两个候选人的人集合是60人 ，是由分别欢迎两人的40和30人

                 的集合的并集，因此可得出都欢迎VOTERS是10人

                 由2则无法推出来