SiLi

77.        9031-!-item-!-187;#058&006222
At a dinner party, 5 people are to be seated around a circular table.  Two seating arrangements are considered different only when the positions of the people are different relative to each other.  What is the total number of different possible seating arrangements for the group?
(A) 5
(B) 10
(C) 24
(D) 32
(E) 120
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【答案】C
【思路】
若為一直線排法 為5！
但此題目為圓形
五個人排圈圈...
ABCDE
BCDEA
CDEAB
DEABC
EABCD
都是一樣
故排圈圈時就是5!/5=4!
除以五是為了消除每次相鄰位置改變時都會有重複的情況

SiLi

68.        8012-!-item-!-187;#058&005726
The number 75 can be written as the sum of the squares of 3 different positive integers.  What is the sum of these 3 integers?
(A) 17
(B) 16
(C) 15
(D) 14
(E) 13
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【答案】E
【思路】
75為the sum of the squares of 3 different positive integers
=81 ＞75
故3 different positive integers需小於9

7＋5＋1=13

SiLi

58.        7090-!-item-!-187;#058&005463
In the graduating class of a certain college, 48 percent of the students are male and 52 percent are female.  In this class 40 percent of the male and 20 percent of the female students are 25 years old or older.  If one student in the graduating class is randomly selected, approximately what is the probability that he or she will be less than 25 years old?
(A) 0.90
(B) 0.70
(C) 0.45
(D) 0.30
(E) 0.25
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【答案】B
【思路】
設the graduating class 共有x位學生
Male 有 人
Female有 人
Male且25 years old or older有  ＝0.192x
Female且25 years old or older有  =0.104x
求少於25歲的人數比例，
1-0.296=0.704

SiLi

51.        6587-!-item-!-187;#058&005111
Circular gears P and Q start rotating at the same time at constant speeds.  Gear P makes 10 revolutions per minute, and gear Q makes 40 revolutions per minute.  How many seconds after the gears start rotating will gear Q have made exactly 6 more revolutions than gear P ?

(A) 6
(B) 8
(C) 10
(D) 12
(E) 15
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【答案】D
【思路】
P每1分鐘轉10次 => 60/10=6秒/次
Q每1分鐘轉40次 => 60/40=1.5秒/次
假設在T秒之後，Q比P多轉了6圈
(T/6) = (T/1.5) - 6
T=12

SiLi

48.        6225-!-item-!-187;#058&004914
A certain city with a population of 132,000 is to be divided into 11 voting districts, and no district is to have a population that is more than 10 percent greater than the population of any other district.  What is the minimum possible population that the least populated district could have?

(A) 10,700
(B) 10,800
(C) 10,900
(D) 11,000
(E) 11,100
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【答案】D
【思路】假設the minimum possible population that the least population district could have=x
        且假設其他10個voting district的人口 more than10percent
        x+(x+0.1x)x10=132,000  
        x=11,000

SiLi

43.        5768-!-item-!-187;#058&004705
A committee of three people is to be chosen from four married couples.  What is the number of different committees that can be chosen if two people who are married to each other cannot both serve on the committee?

(A)  16
(B)  24
(C)  26
(D)  30
(E)  32
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【答案】E
【思路】<作法1>committe中不能有couple的組合即 "全部的組合-committe中有couple的組合"
C(8,3)-4*6
=56-24
=32
(4*6代表將couple視為一個人，有4個coule，另外一個committe則為其他六個人選一個)
<作法2>    OOO → 一個蘿蔔一個坑，求組合!!（3!是因為 abc acb bac bca cba cab 是同一種組合）

SiLi

27.        3330-!-item-!-187;#058&003295
38, 69, 22, 73, 31, 47, 13, 82
Which of the following numbers is greater than three-fourths of the numbers but less than one-fourth of the numbers in the list above?

(A) 56
(B) 68
(C) 69
(D) 71
(E) 73
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【答案】D
【思路】將上述的sequence由小到大重新排列 13,22,31,38,47,69,73,82
        假設題目要求的number為X,X大於數列的 ,小於數列的
      數列共有8個數,  X8=6,  X8=2
        so, 69<X<73, 答案為71(D)

SiLi

13.        1898-!-item-!-187;#058&002486


If m lies between the integers p and s on the number line shown, which of the following is a possible value for m ?

(A) √17
(B) √4
(C) 2.9
(D) 20/4
(E) 10/3
15.        2160-!-item-!-187;#058&002594
At a speed of 50 miles per hour, a certain car uses 1 gallon of gasoline every 30 miles.  If the car starts with a full 12 gallon tank of gasoline and travels for 5 hours at 50 miles per hour, the amount of gasoline used would be what fraction of a full tank?

(A)  3/25
(B)  11/36
(C)  7/12
(D)  2/3
(E)  25/36

SiLi

9.        1700-!-item-!-187;#058&001066
Last year the range of the annual salaries of the 100 employees at Company X was $30,000.  If the annual salary of each of the 100 employees this year is 10 percent greater than it was last year, what is the range of the annual salaries of the 100 employees this year?

(A) $27,000
(B) $30,000
(C) $33,000
(D) $36,000
(E) $63,000
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【答案】C
【思路】Last year the range of the annual salaries of the 100 employees at Company X＝30,000（假設最大annual salaries=50,000,最小annual salaries=20,000）
        又今年比去年annual salary漲10％ 表示the range of the annual salaries of the 100 employees this year=50,000x(1.1)-20,000x(1.1)=33,000

SiLi

6.        859-!-item-!-187;#058&000568
The value of  is closest to which of the following?

(A) 1
(B) 10
(C) 102
(D) 103
(E) 104

7.        905-!-item-!-187;#058&000575
For every positive even integer n, the function h(n) is defined to be the product of all the even integers from 2 to n, inclusive.  If p is the smallest prime factor of h(100) + 1, then p is

(A) between 2 and 10
(B) between 10 and 20
(C) between 20 and 30
(D) between 30 and 40
(E) greater than 40
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【答案】E
【思路】
      假設h(100)+1最小因數是 n , n<50
例如47好了, 既然47是因數, 他就能整除h(100)+1
可是發現h(100)裡面有47的因數,可以整除 那h(100)+1被47除的餘數為1,表示47不是h(100)+1的因數
同理去想 小於50的其它因式 也是會一樣的結果
所以h(100)+1的因式是在 大於50外
重點在那50!, 假如 小於50的質數是h(100)的factor,那就不會是h(100)+1的factor ,因為餘數會是1