[求助]GWD31套数学讨论:第九，十套

各位战友，小弟在网上找了许久也没有看到GWD31套数学的讨论，很多都是讨论VERBAL的，但数学里很多题目知道答案却还是不知道怎么做，（过程！！）想在此向给位高手求救！！谢谢了~~

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.

E. Statements (1) and (2) TOGETHER are NOT sufficient.

Answer: A

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9-Q26:

In the decimal representation of x, where 0 < x < 1, is the tenths digit if x nonzero?

(1)    16x is an integer.

(2)    8x is an integer.

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.

E. Statements (1) and (2) TOGETHER are NOT sufficient.

Answer: B

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10-Q4:

If S is the sum of the reciprocals of the consecutive integers from 91 to 100, inclusive, which of the following is less than S?

  I.  1/8

        II.  1/9

       III.  1/10

A.   None

B.   I only

C.   III only

D.   II and III only

E.    I, II, and III

  Answer: C

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10-Q8:

An equilateral triangle that has an area of  9倍根号3is inscribed in a circle.  What is the area of the circle?

Answer: C （12派）

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Q10:

A certain quantity is measured on two different scales, the R-scale and the S-scale, that are related linearly.  Measurements on the R-scale of 6 and 24 correspond to measurements on the S-scale of 30 and 60, respectively.  What measurement on the R-scale corresponds to a measurement of 100 on the S-scale?

A.    20

B.    36

C.    48

D.    60

E.     84

Answer: C

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9-Q20:

condition 1: if 40 ppl didn't respond favorable to either candidate, then those 40 ppl would have responded "unfavorable" or "unsure" to either candidate or both candidates. Then the remaining 60 ppl would be those who either support one of the candidates or both candidates. Therefore, with condition 1, we would know that there were 10 ppl who responded favorable to both candidates 40(favM)+30(favN)-60=10

condition 2: with the info given in this condition, we could only know that the number of ppl who responded unfavorable to either one or both of the candidates. No info is given concerning the number of ppl who responded unsure. As a result, we couldn't determine exactly how many ppl responded favorable to both candidates.

9 Q26:

16X要是整數,那麼X就得是X的因數,那麼X有可能是 1/16(0.0625)==>這個的小數點後十分位就不是0,所以A不行

8X的話,從最小的x=1/8看起,1/8等於0.125,那麼他不管乘以2,3.....小數點後十分位數都不會是0,因此選B

10-Q4:

1/91+1/92....+1/100,這串數字最大的是1/91,其他1/92到1/100每一個數都小於他,所以假設1/91+...+1/100的答案是X,那麼X一定小於10/91,這樣可得到 X<10/91<1/9<1/8,至於X是否大於1/10呢?我的想法是1/10等於10/100,既然1/91,1/92...到1/99都大於1/100,那麼X必定大於10/100,因此X的值可以約略估計是1/10<X<1/9<1/8,因此選C(這題這樣想其實有點慢..所以想請問是否各位有更好的想法?)

10-Q8:

這題可先把圖大概畫出來,三角形面積是9倍根號3,可設此三角形的底的一半是X,把全等三角形垂直切成一半,裡面的兩個三角形內角關係必是30, 60, 90,那麼邊長關係就是1:2:根號3,透過這關係可以找到三角形的高,再將兩個小三角形其中一個切成一個直角三角形(這個也是30,60,90度的關係)+鈍角三角形,就可以求出圓的半徑和面積

10-Q10:

在R這個scale上,18個極距等於s上30個極距,s上的100和60差40,所以假設這在r上相當於x的極距的話,那麼

18:30=x:40, x=24, 24+24=48