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GWD-3 questions

我在概念上有些不太明白这些题,可否有牛牛给解答一下.感激万分!!

Q6:

The figure above shows the dimensions of a semicircular cross section of a one-way tunnel.  The single traffic lane is 12 feet wide and is equidistant from the sides of the tunnel.  If vehicles must clear the top of the tunnel by at least ½ foot when they are inside the traffic lane, what should be the limit on the height of vehicles that are allowed to use the tunnel?

A.     5½ ft

B.     7½ ft

C.     8 ½ ft

D.     9½ ft

E.      10 ft

Q26:

There are 8 books on a shelf, of which 2 are paperbacks and 6 are hardbacks.  How many possible selections of 4 books from this self include at least one paperback?

A.     40

B.     45

C.     50

D.     55

E.      60

Q31:

There are 8 magazines lying on a table; 4 are fashion magazines and the other 4 are sports magazines.  If 3 magazines are to be selected at random from the 8 magazines, what is the probability that at least one of the fashion magazines will be selected?

A.     1/2

B.     2/3

C.     32/35

D.     11/12

E.      13/14

The figure above shows the dimensions of a semicircular cross section of a one-way tunnel.  The single traffic lane is 12 feet wide and is equidistant from the sides of the tunnel.  If vehicles must clear the top of the tunnel by at least ½ foot when they are inside the traffic lane, what should be the limit on the height of vehicles that are allowed to use the tunnel?

A.     5½ ft

B.     7½ ft

C.     8 ½ ft

D.     9½ ft

E.      10 ft

Q26:

There are 8 books on a shelf, of which 2 are paperbacks and 6 are hardbacks.  How many possible selections of 4 books from this self include at least one paperback?

A.     40

B.     45

C.     50

D.     55

E.      60

Q31:

There are 8 magazines lying on a table; 4 are fashion magazines and the other 4 are sports magazines.  If 3 magazines are to be selected at random from the 8 magazines, what is the probability that at least one of the fashion magazines will be selected?

A.     1/2

B.     2/3

C.     32/35

D.     11/12

E.      13/14

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Q31:

分子 : C{3,8}- C{3,4} =52  

因為題目是問至少有一本是fashion, 所以用全部扣掉都是sports的情形 

分母 : C{3,8} =56

Ans: 52/56 = 13/14 (E)

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Q26:

解法1: C{4,8}- C{4,6} =55 (D)

 用全部扣掉都抽到hardbacks的情形

解法2: C{1,2}*C{3,6}+ C{2,2}*C{2,6} =55 (D)

 抽到一本paperback 加上 抽到二本paperbacks

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Q6 :

把它看成一個隧道

求車子的高度(要留1/2feet)

= (半徑10的平方 - 寬6的平方)開根號 - 1/2

= 8-1/2 =7+1/2 (B)

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