constitute a different code, how many different stocks is it possible to uniquely designate with these codes?
(A) 2,951 (B) 8,125 (C) 15,600 (D) 16,302 (E) 18,278
------------------------------------------------------------------------------------------------------------------------------------ 【答案】E
【思路】題目有前提If the letters may be repeated and if the same letters used in a different order
constitute a different code,
所以one letter-26種
two letters-26x26種
three letters-26x26x26種
total=18,278
------------------------------------------------------------------------------------------------------------------------------------ 40. 5629-!-item-!-187;#058&004684
Six machines, each working at the same constant rate, together can complete a certain job in 12 days. How many additional machines, each working at the same constant rate, will be needed to complete the job in 8 days?
(A) 2 (B) 3 (C) 4 (D) 6 (E) 8
------------------------------------------------------------------------------------------------------------------------------------ 【答案】B
【思路】速率x時間=工作量(距離)
11 Sx12(days)=1,S= 12(six machines),表示一台的速率72(這個地方要小心！！)
假設x台機器complete the job in 8 days
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All of the stocks on the over-the-counter market are designated by either a 4-letter or a 5-letter code that is created by using the 26 letters of the alphabet. Which of the following gives the maximum number of different stocks that can be designated with these codes?
(A) 2(26^5) (B) 26(26^4) (C) 27(26^4) (D) 26(26^5) (E) 27(26^5)
------------------------------------------------------------------------------------------------------------------------------------ 【答案】C
【思路】either a 4-letter or a 5-letter
1?X?8＝172,X=9,所以必須增加3台機器complete the job in 8 days
264?265?264?26?264?264(1?26)?27?264
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42. 5722-!-item-!-187;#058&004704
Mark bought a set of 6 flower pots of different sizes at a total cost of $8.25. Each pot cost $0.25 more than the next one below it in size. What was the cost, in dollars, of the largest pot?
(A) $1.75 (B) $1.85 (C) $2.00 (D) $2.15 (E) $2.30
------------------------------------------------------------------------------------------------------------------------------------ 【答案】C
【思路】假設最小size cost X
比X大一個size=X+0.25,大兩個size=x+0.5….依序
8.25＝X+(X+0.25)+(X+0.5)+(X+0.75)+(X+1)+(X+1.25),X=0.75 so, the largest pot costs 0.75+1.25=$2.00
------------------------------------------------------------------------------------------------------------------------------------ 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
------------------------------------------------------------------------------------------------------------------------------------ 【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>
cab 是同一種組合）
------------------------------------------------------------------------------------------------------------------------------------ 44. 5871-!-item-!-187;#058&004763
A certain company employs 6 senior officers and 4 junior officers. If a committee is to be created that is made up of 3 senior officers and 1 junior officer, how many different committees are possible?
(A) 8 (B) 24 (C) 58 (D) 80 (E) 210
------------------------------------------------------------------------------------------------------------------------------------ 【答案】D
【思路】C(6,3)XC(4,1) =20X4=80
------------------------------------------------------------------------------------------------------------------------------------ 45. 5918-!-item-!-187;#058&004778
While working alone at their respective constant rates, computer X processes 240 files in 4 hours and computer Y processes 240 files in 8 hours. If all files processed by these computers are the same size, how long would it take the two computers, working at the same time and at their respective constant rates, to process a total of 240 files?
(A) 2 hr
(B) 2 hr 20 min (C) 2 hr 40 min
8?6?4?32 OOO → 一個蘿蔔一個坑，求組合!!（3!是因為 abc acb bac bca cba 3!(D) 6 hr
(E) 6 hr 20 min
------------------------------------------------------------------------------------------------------------------------------------ 【答案】C
【思路】computer X processes 60 files in1 hour, and computer Y processes 30 files in 1 hour so, X和Y一起做可以完成90 files in 1 hour 若一起完成240files, 需花費 T=
------------------------------------------------------------------------------------------------------------------------------------ 46. 5966-!-item-!-187;#058&004795
2402＝2hours(2 hr 40 min) 903If x ≠0, then
(A) -1 (B) 0 (C) 1 (D) x
(E) |x| / x 47. 6013-!-item-!-187;#058&004836
(A) 300 and 400 (B) 400 and 500 (C) 500 and 600 (D) 600 and 700 (E) 700 and 800 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
------------------------------------------------------------------------------------------------------------------------------------ 【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
------------------------------------------------------------------------------------------------------------------------------------ 49. 6490-!-item-!-187;#058&005075 [?]
The table above shows the distribution of scores on a geography quiz given to a class of 25 students. Which of the following is closest to the average (arithmetic mean) quiz score for the class?
(A) 8.6 (B) 8.5 (C) 8.4 (D) 8.3
is between
(E) 8.0 50. 6541-!-item-!-187;#058&005092 Which of the following is an integer?
(A) I only (B) II only (C) III only
(D) I and II only (E) I, II, and III 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
------------------------------------------------------------------------------------------------------------------------------------ 【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
------------------------------------------------------------------------------------------------------------------------------------ 52. 6641-!-item-!-187;#058&005112 [?]
In the circle above, PQ is parallel to diameter OR, and OR has length 18. What is the length of minor arc PQ ?
(A) (B) (C) (D) (E) 53. 6687-!-item-!-187;#058&005122
Mary purchased 3 theater tickets with an average (arithmetic mean) price of $8. If Mary also purchases a fourth theater ticket with a price of $16, what is the average price of all 4 theater tickets? (A) $4 (B) $6 (C) $8
