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

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

85.        9735-!-item-!-187;#058&006716
At the end of the first quarter, the share price of a certain mutual fund was 20 percent higher than it was at the beginning of the year.  At the end of the second quarter, the share price was 50 percent higher than it was at the beginning of the year. What was the percent increase in the share price from the end of the first quarter to the end of the second quarter?
(A) 20%
(B) 25%
(C) 30%
(D) 33%
(E) 40%
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【答案】B
【思路】
設年初價格為X 故第一季為120%X 第二季為150%X
故 ＝25%

SiLi

116.        11659-!-item-!-187;#058&007807
A certain junior class has 1,000 students and a certain senior class has 800 students.  Among these students, there are 60 sibling pairs, each consisting of 1 junior and 1 senior.  If 1 student is to be selected at random from each class, what is the probability that the 2 students selected will be a sibling pair?

(A)  
(B)  
(C)  
(D)  
(E)  
139.        14108-!-item-!-187;#058&009811
A set of 15 different integers has a median of 25 and a range of 25.  What is the greatest possible integer that could be in this set?

(A) 32
(B) 37
(C) 40
(D) 43
(E) 50
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【答案】 D
【思路】
Range定義=最大值-最小值

題目問說哪個最有可能是最大值,所以從最大的先推推看
E)Max:50,range25代表Min=50-25=25 ==>可是25又是中位數,所以不可能!!
D)Max:43,range25代表Min=43-25=18
列舉驗證一下: 18 19 20 21 22 23 24 25 ........43
總共15個,所以中位數左邊應該有7個
剛好25也是中位數,所以成立!!
[另解]
因為range25,各選項間距為
=>(7~32)(12~37)(15~40)(18~43)(25~50)
由於15個不同的數字,此外,中位數為25=>只有D選項符合

SiLi

142.        14580-!-item-!-187;#058&010013
The rate of a certain chemical reaction is directly proportional to the square of the concentration of chemical A present and inversely proportional to the concentration of chemical B present.  If the concentration of chemical B is increased by 100 percent, which of the following is closest to the percent change in the concentration of chemical A required to keep the reaction rate unchanged?

(A) 100% decrease
(B) 50% decrease
(C) 40% decrease
(D) 40% increase
(E) 50% increase
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【答案】D
【思路】
題目意思是說 化學物A的平方與此化學反應速率成正比
化學物B 與此化學反應速率成反比
所以B增加100% 換句話說B變成了兩倍 所以反應速率變成1/2
要讓原本的速率不變 所以A勢必要增加 能讓速度變成兩倍去抵銷那1/2倍
得到算式會是2*1/2=1
A的平方與速率成正比 所以A平方就等於2 A就等於根號2=1.41...

換句話說 增加了40%左右

SiLi

149.        15609-!-item-!-187;#058&010412
A certain library assesses fines for overdue books as follows.  On the first day that a book is overdue, the total fine is $0.10.  For each additional day that the book is overdue, the total fine is either increased by $0.30 or doubled, whichever results in the lesser amount.  What is the total fine for a book on the fourth day it is overdue?

(A) $0.60
(B) $0.70
(C) $0.80
(D) $0.90
(E) $1.00
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【答案】B
【思路】這題非常的tricky，注意關鍵字whichever results in the lesser amount，所以兩種方法都可以使用，只要是最便宜的即可，詳解見樓下。
1st : $0.1
2nd: min{0.1+0.3, 0.1*2} = 0.2
3rd: min{0.2+0.3, 0.2*2} = 0.4
4th: min{0.4+0.3, 0.4*2} = 0.7
所以答案是(B)

SiLi

150.        15710-!-item-!-187;#058&010468


(A) less than 3
(B) equal to 3
(C) between 3 and 4
(D) equal to 4
(E) greater than 4
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154.        16003-!-item-!-187;#058&010661
If n is a positive integer and the product of all the integers from 1 to n, inclusive, is a multiple of 990, what is the least possible value of n ?

(A) 10
(B) 11
(C) 12
(D) 13
(E) 14
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【答案】 B
【思路】990=2*3*5*3*11  題目問the least possible 可知 至少要乘到11才能夠是990的倍數
故答案為B

SiLi

183.        19877-!-item-!-187;#058&012576
A certain company charges $6 per package to ship packages weighing less than 2 pounds each.  For a package weighing 2 pounds or more, the company charges an initial fee of $6 plus $2 per pound.  If the company charged $38 to ship a certain package, which of the following was the weight of the package, in pounds?

(A) 16
(B) 17
(C) 19
(D) 20
(E) 22
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【答案】A
【思路】
187.        20334-!-item-!-187;#058&012770
If 0 < r < 1 < s < 2, which of the following must be less than 1 ?
   
I.        r/s
II.        rs
III.        s - r


(A) I only
(B) II only
(C) III only
(D) I and II
(E) I and III
33.        4484-!-item-!-187;#058&004004
If x^4 + y^4 = 100, then the greatest possible value of x is between

(A) 0 and 3
(B) 3 and 6
(C) 6 and 9
(D) 9 and 12
(E) 12 and 15
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【答案】B
【思路】
,所以 the greatest possible value of x is between3 and 6

SiLi

62.        7564-!-item-!-187;#058&005577
Alice's take-home pay last year was the same each month, and she saved the same fraction of her take-home pay each month.  The total amount of money that she had saved at the end of the year was 3 times the amount of that portion of her monthly take-home pay that she did not save.  If all the money that she saved last year was from her take-home pay, what fraction of her take-home pay did she save each month?

(A) 1/2
(B) 1/3
(C) 1/4
(D) 1/5
(E) 1/6
87.        9993-!-item-!-187;#058&007019

In the addition table shown above, what is the value of m + n ?

(A) -19
(B)  4
(C)  5
(D)  6
(E)  22

93.        10285-!-item-!-187;#058&007154

In the figure above, a square is inscribed in a circle.  If the area of the square region is 16, what is the area of the circular region?

(A)  2π
(B)  4π
(C)  6π
(D)  12π
(E)  16π
106.        11122-!-item-!-187;#058&007588
If a certain sample of data has a mean of 20.0 and a standard deviation of 3.0, which of the following values is more than
2.5 standard deviations from the mean?

(A) 12.0
(B) 13.5
(C) 17.0
(D) 23.5
(E) 26.5
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【答案】 A
【思路】 more than 2.5 standard deviations from the mean   
20-(2.5*3)大於所求的value  or  所求的value 大於 20+(2.5*3) 
A~E答案中只有A符合 答案A

SiLi

131.        13459-!-item-!-187;#058&009437
If the speed of x meters per second is equivalent to the speed of y kilometers per hour, what is y in terms of x ?

(1 kilometer = 1,000 meters)

(A) 5x/18
(B) 6x/5
(C) 18x/5
(D) 60x
(E) 3,600,000x
47.        6013-!-item-!-187;#058&004836
  is between

(A) 300 and 400
(B) 400 and 500
(C) 500 and 600
(D) 600 and 700
(E) 700 and 800
83.        9589-!-item-!-187;#058&006669

The table above shows the distribution of test scores for a group of management trainees.  Which score interval contains the median of the 73 scores?

(A) 60-69
(B) 70-79
(C) 80-89
(D) 90-99
(E) It cannot be determined from the information given.