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PP- Problem Solving2 (PS2) 完整詳解版
V1.0
作者: yuma168 larry.tw
Huang Hsin-Yi Penda
Engedi mauricew
pauline_chiou william0625
abc123 ruru.lu
備註：本版權內容歸 作者 和 論壇共有，嚴禁任何未經允許的商業使用。
Revised History
由於這是眾人一起完成的,難免會有疏失,希望大家可以一起修正錯誤,讓這份詳解變得更完整!版本增加規則如下: 1) 修正算式錯誤or提出更好的算法, 請把版本小數+1 (Ex: V1.0 -> V1.1)2) 增加or補齊題目,請把版本個位數+1 (Ex: V2.0 ->V3.0)
版本 修正內容 (請標題號) 作者 日期V1.0 新增全部詳解 (Q1~Q197) yuma168
larry.twHuang Hsin-Yi PendaEngedimauricewpauline_chiouwilliam0625abc123ruru.lu
2008/7/17
Practice Test #2 Problem Solving(197 Questions)
1. 246-!-item-!-187;#058&000117Tanya prepared 4 different letters to be sent to 4 different addresses. For each letter, she prepared an envelope with its correct address. If the 4 letters are to be put into the 4 envelopes at random, what is the probability that only 1 letter will be put into the envelope with its correct address?
(A) (B) (C) (D) (E)
2. 509-!-item-!-187;#058&000281For every order, a certain mail-order company charges a shipping fee of $3 plus an additional $2 if the value of the order is over $50 but not over $100 or an additional $3 if the value of the order is over $100. How much greater are the total shipping fees for 2 orders of $75 each than the total shipping fee for 1 order of $150 ?
(A) $1(B) $2(C) $3(D) $4(E) $5------------------------------------------------------------------------------------------------------------------------------------【答案】D【思路】2 orders of $75 each : 每件價值都75,所以要額外費用2元,且又兩件, 2(3+2)=101 order of $150: 1(3+3)=6依照題意相減可得4------------------------------------------------------------------------------------------------------------------------------------3. 827-!-item-!-187;#058&000411A copy service charges $0.05 per copy for the first 100 copies, $0.04 per copy for the next 100 copies, and $0.03 per copy for all copies thereafter. What would the copy service charge for 350 copies?
(A) $10.50(B) $11.50(C) $12.00(D) $13.00(E) $13.50------------------------------------------------------------------------------------------------------------------------------------【答案】E
【思路】------------------------------------------------------------------------------------------------------------------------------------
4. 1197-!-item-!-187;#058&000782If w, x, and y are consecutive odd positive integers and w < x < y, which of the following could be equal to y - x - w ?
(A) -4(B) -2(C) -1(D) 0(E) 3------------------------------------------------------------------------------------------------------------------------------------【答案】C【思路】首先判斷 奇數－奇數－奇數＝奇數,可排除答案只剩(C)(E)代數字3 5 7 7-5-3= -1 -1 1 3 3-1-(-1)=3 (可是題目說要正整數,所以-1不行)
------------------------------------------------------------------------------------------------------------------------------------5. 1353-!-item-!-187;#058&000886Working alone at its own constant rate, a machine seals k cartons in 8 hours, and working alone at its own constant rate, a second machine seals k cartons in 4 hours. If the two machines, each working at its own constant rate and for the same period of time, together sealed a certain number of cartons, what percent of the cartons were sealed by the machine working at the faster rate?
(A) 25%(B) (C) 50%(D)(E) 75%
6. 1456-!-item-!-187;#058&000991[?]
If w, x, y, and z are numbers on the number line shown, which of the following products is least?
(A) wy(B) wz(C) xy(D) xz(E) yz
7. 1502-!-item-!-187;#058&001086A certain telephone company offers two plans, A and B. Under plan A, the company charges a total of $0.60 for the first 7 minutes of each call and $0.06 per minute thereafter. Under plan B, the company charges $0.08 per minute of each call. What is the duration of a call, in minutes, for which the company charges the same amount under plan A and under plan B ?
(A) 2(B) 9(C) 15(D) 21(E) 30------------------------------------------------------------------------------------------------------------------------------------【答案】B【思路】設t為時間For A: Charges=0.6+0.06(t-7) For B: Charges=0.08t依照題意charges相同0.6+0.06(t-7)=0.08t0.02t=0.6-0.42=0.18t=0.18/0.02=9min------------------------------------------------------------------------------------------------------------------------------------8. 1608-!-item-!-187;#058&001224In the xy-plane, each point on circle K has nonnegative coordinates and the center of K is the point (4, 7). What is the maximum possible area of K ?
(A) (B) (C) (D) (E)
9. 1662-!-item-!-187;#058&002391Equal amounts of water were poured into two empty jars of different capacities, which made one jar full and the other jar full. If the water in the jar with the lesser capacity is then poured into the jar with the greater capacity, what fraction of the larger jar will be filled with
water?
(A) (B) (C) (D) (E)
10. 1708-!-item-!-187;#058&002411A pair of shoes is on sale for $60. If this price is 20 percent less than the regular price of the shoes, what is the regular price of the shoes?
(A) $72(B) $75(C) $80(D) $96(E) $108------------------------------------------------------------------------------------------------------------------------------------【答案】B【思路】60/0.8 = 75------------------------------------------------------------------------------------------------------------------------------------11. 1971-!-item-!-187;#058&002527Which of the following lists the number of points at which a circle can intersect a triangle?
(A) 2 and 6 only(B) 2, 4, and 6 only(C) 1, 2, 3, and 6 only(D) 1, 2, 3, 4, and 6 only(E) 1, 2, 3, 4, 5, and 6------------------------------------------------------------------------------------------------------------------------------------【答案】E【思路】一個圓至多可以跟三角形有幾個交點 畫畫看 6個 ==> E------------------------------------------------------------------------------------------------------------------------------------12. 2238-!-item-!-187;#058&002618[?]If the two regions above have the same area, what is the ratio t : s ?
(A) 2 : 3(B) 16 : 3(C) (D) (E)
13. 2392-!-item-!-187;#058&002762[?]: line missed
(A) A certain list of 100 data has an average (arithmetic mean) of 6 and a standard deviation of d, where d is positive. Which of the following pairs of data, when added to the list, must result in a list of 102 data with standard deviation less than d ?(B) 0 and 0(C) 0 and 6(D) 0 and 12(E) 6 and 6
14. 2546-!-item-!-187;#058&002908If Sally drives at a constant speed of 50 miles per hour, how many minutes will be required for her to drive 10 miles?
(A) 9(B) 10(C) 11(D) 12(E) 13------------------------------------------------------------------------------------------------------------------------------------【答案】D【思路】距離/速度=時間 10/50=0.2 (hr) = 12(mins)------------------------------------------------------------------------------------------------------------------------------------15. 2647-!-item-!-187;#058&002944If a = 1 and [?], which of the following is NOT a possible value of b ?
(A) -2(B) -1(C) 0(D) 1(E) 2
16. 2698-!-item-!-187;#058&002953[?] All points (x, y) that lie below the line l, shown above, satisfy which of the following inequalities?
(A) y < 2x + 3(B) y < -2x + 3(C) y < -x + 3(D)(E)
17. 2747-!-item-!-187;#058&002959[?]
On the number line above, what is the length of segment AB ?
(A) 2.2(B) 0.38(C) 0.22(D) 0.038(E) 0.022
18. 2793-!-item-!-187;#058&002984After a fisherman sold [?] of the fish he had caught and gave away [?] of the remaining fish, he had 4 fish left. What was the total number of fish he had caught?
(A) 8(B) 16(C) 20(D) 32(E) 40
19. 2896-!-item-!-187;#058&003100[?]
For each country listed in the left column of the table, the number in the right column gives the number of units of Country X currency that is equivalent to 1 unit of the country's currency. Which of the following is equivalent to the greatest number of units of Country X currency?
(A) 4 units of Country A currency(B) 25 units of Country B currency
(C) 98 units of Country C currency(D) 3 units of Country D currency(E) 7 units of Country E currency
20. 2942-!-item-!-187;#058&003104For any positive integer n, the length of n is defined as the number of prime factors whose product is n. For example, the length of 75 is 3, since 75 = 3 ?? 5 ?? 5. How many two-digit positive integers have length 6 ?
(A) None(B) One(C) Two(D) Three(E) Four
21. 2988-!-item-!-187;#058&003110A company wants to buy computers and printers for a new branch office, and the number of computers can be at most 3 times the number of printers. Computers cost $1,500 each, and printers cost $300 each. What is the greatest number of computers that the company can buy if it has a total of $9,100 to spend on computers and printers?
(A) 2(B) 3(C) 4(D) 5(E) 6------------------------------------------------------------------------------------------------------------------------------------【答案】D【思路】C=3P1500C + 300P 91001600C 9100
C 5.多 所以最多可買5台computers------------------------------------------------------------------------------------------------------------------------------------22. 3254-!-item-!-187;#058&003229If [?], then N is between
(A) 0 and (B) and (C) and (D) and (E) and 2
23. 3470-!-item-!-187;#058&003305240, 120, 60, 30, . . .
In the sequence above, each term after the first is ½ of the preceding term. What is the least term of the sequence that is greater than 1 ?
(A) (B) (C) (D) (E)
24. 3573-!-item-!-187;#058&003330A box contains 25 red blocks, 100 blue blocks, and 175 yellow blocks. What is the probability that a block picked at random from the box will be red?
(A)
(B) (C) (D) (E)
25. 3619-!-item-!-187;#058&003382A fast-food company plans to build 4 new restaurants. If there are 12 sites that satisfy the company's criteria for location of new restaurants, in how many different ways can the company select the 4 sites needed for the new restaurants if the order of selection does not matter?
(A) 48(B) 288(C) 495(D) 990(E) 11,880------------------------------------------------------------------------------------------------------------------------------------【答案】C
【思路】------------------------------------------------------------------------------------------------------------------------------------26. 3669-!-item-!-187;#058&003387If x is an even integer, which of the following must be an odd integer?
(A) (B) (C) 3x^2(D) (E)
27. 3721-!-item-!-187;#058&003433[?]
The figure shown represents a board with four rows of pegs, and at the bottom of the board are four cells numbered 1 to 4. Whenever the ball shown passes through the opening between two adjacent pegs in the same row, it will hit the peg directly beneath the opening. The ball then has probability of passing through the opening immediately to the left of that peg and probability of passing through the opening immediately to the right. What is the probability that when the ball passes through the first two pegs at the top it will end up in cell 2 ?
(A) (B) (C) (D) (E)
28. 3770-!-item-!-187;#058&003486What is the greatest possible area of a triangular region with one vertex at the center of a circle of radius 1 and the other two vertices on the circle?
(A) (B) (C) (D) 1(E)
29. 3873-!-item-!-187;#058&003594If n denotes a number to the left of 0 on the number line such that the square of n is less than 1/100, then the reciprocal of n must be
(A) less than -10
(B) between -1 and (C) between and 0(D) between 0 and (E) greater than 10
30. 4244-!-item-!-187;#058&003828An investor purchased 20 shares of a certain stock at a price of $45.75 per share. Later this investor purchased 30 more shares at a price of $46.25 per share. What was the average (arithmetic mean) price per share that this investor paid for the 50 shares?
(A) $45.80(B) $45.95(C) $46.00(D) $46.05(E) $46.20------------------------------------------------------------------------------------------------------------------------------------【答案】D
【思路】
------------------------------------------------------------------------------------------------------------------------------------31. 4295-!-item-!-187;#058&003848A certain basket contains 10 apples, 7 of which are red and 3 of which are green. If 3 different apples are to be selected at random from the basket, what is the probability that 2 of the apples selected will be red and 1 will be green?
(A) (B) (C) (D) (E)
32. 4504-!-item-!-187;#058&003922[?]
When N is divided by T, the quotient is S and the remainder is V. Which of the following expressions is equal to N ?
(A) ST(B) S + V(C) ST + V(D) T(S - V)(E)
33. 4550-!-item-!-187;#058&003924What is the number of different committees of 4 people that can be selected from a group of 10 people?
(A) 20(B) 40(C) 80(D) 120(E) 210------------------------------------------------------------------------------------------------------------------------------------【答案】E
【思路】
------------------------------------------------------------------------------------------------------------------------------------
34. 4707-!-item-!-187;#058&003966
[?]
The table shows the numbers of greeting cards for various occasions sold at a certain store last year. According to the table, for which of the following occasions was the number of cards sold closest to [?] of the number of birthday cards sold?
(A) Valentine's Day(B) Secretary's Day(C) Mother's Day(D) Father's Day(E)
35. 4808-!-item-!-187;#058&003979If the operation @ is defined for all positive integers x and w by x @ w = [?] , then (3 @ 1) @ 3 =
(A) 2(B) 4(C) 8(D) 16(E) 32
36. 5018-!-item-!-187;#058&004104If x = kc and y = kt, then y - x =
(A) k(t - c)(B) k(c - t)(C) c(k - t)(D) t(k - c)(E) k(1 - t)---------------------------------------------------------------------------------------------------------------------------【答案】A【思路】kt-kc=k(t-c)-------------------------------------------------------------------------------------------------------------------------------
37. 5174-!-item-!-187;#058&004144The function f is defined for all positive integers n by the following rule: f(n) is the number of positive integers each of which is less than n and has no positive factor in common with n other than 1. If p is any prime number then f(p) =
(A) p - 1(B) p - 2(C) (D) (E) 2
38. 5275-!-item-!-187;#058&004179A certain business produced x rakes each month from November through February and shipped 0.5x rakes at the beginning of each month from March through October. The business paid no storage costs for the rakes from November through February, but it paid storage costs of $0.10 per rake each month from March through October for the rakes that had not been shipped. In terms of x, what was the total storage cost, in dollars, that the business paid for the rakes for the 12 months from November through October?
(A) 0.40x(B) 1.20x(C) 1.40x(D) 1.60x(E) 3.20x---------------------------------------------------------------------------------------------------------------------------
【答案】C【思路】3-10 每個月各運出 0.5x所以每個月存貨為 3 月(3.5) 4(3) 5(2.5) 6(2) 7(1.5) 8(1) 9(0.5) 10(0)
-------------------------------------------------------------------------------------------------------------------------
39. 5378-!-item-!-187;#058&004220[?]The table shows the number of calls received by each of five operators during each of 4 one-hour periods. For which operator was the standard deviation of the numbers of calls received during these 4 periods the least?
(A) Operator A(B) Operator B(C) Operator C(D) Operator D(E) Operator E
40. 5532-!-item-!-187;#058&004320A certain company sold 1,000 blenders at $100 each and 10 stoves at $1,000 each. If the company's total cost for the blenders and stoves was $50,000, what was the company's total gross profit on these items?
(A) $10,000(B) $20,000(C) $30,000(D) $50,000(E) $60,000---------------------------------------------------------------------------------------------------------------------------【答案】E
【思路】-------------------------------------------------------------------------------------------------------------------------
41. 5689-!-item-!-187;#058&004421In the infinite sequence a1, a2, a3, . . . , an, . . . , each term after the first is equal to twice the previous term. If a5 - a2 = 12, what is the value of a1 ?
(A) 4(B) (C) 2(D) (E)
42. 5737-!-item-!-187;#058&004537(-3)^(-2) =
(A) - 9(B) -6(C) (D) (E) 9
43. 5837-!-item-!-187;#058&004612A college admissions officer predicts that 20 percent of the students who are accepted will not attend the college. According to this prediction, how many students should be accepted to achieve a planned enrollment of x students?
(A) 1.05x(B) 1.1x
(C) 1.2x(D) 1.25x(E) 1.8x---------------------------------------------------------------------------------------------------------------------------【答案】D【思路】設錄取人數為 y
-------------------------------------------------------------------------------------------------------------------------
44. 5884-!-item-!-187;#058&004663The arithmetic mean and standard deviation of a certain normal distribution are 13.5 and 1.5, respectively. What value is exactly 2 standard deviations less than the mean?
(A) 10.5(B) 11.0(C) 11.5(D) 12.0(E) 12.5---------------------------------------------------------------------------------------------------------------------------【答案】A
【思路】-------------------------------------------------------------------------------------------------------------------------
45. 5933-!-item-!-187;#058&004664If a certain wheel turns at a constant rate of x revolutions per minute, how many revolutions will the wheel make in k seconds?
(A) 60kx(B) kx(C) (D) (E)
46. 5979-!-item-!-187;#058&004694If a coin has an equal probability of landing heads up or tails up each time it is flipped, what is the probability that the coin will land heads up exactly twice in 3 consecutive flips?
(A) 0.125(B) 0.25(C) 0.375(D) 0.50(E) 0.666------------------------------------------------------------------------------------------------------------------------------------【答案】C【思路】丟三次要有剛好兩次頭朝上(當作正面)所以會有三種情形:
正正反:
正反正:
反正正:
三個情形(“或”的觀念,所以相加)=
------------------------------------------------------------------------------------------------------------------------------------
47. 6025-!-item-!-187;#058&004767A certain bakery has 6 employees. It pays annual salaries of $14,000 to each of 2 employees, $16,000 to 1 employee, and $17,000 to each of the remaining 3 employees. The average (arithmetic mean) annual salary of these employees is closest to which of the following?
(A) $15,200(B) $15,500(C) $15,800(D) $16,000(E) $16,400------------------------------------------------------------------------------------------------------------------------------------【答案】C【思路】低分區,算術平均數的題目
------------------------------------------------------------------------------------------------------------------------------------
48. 6071-!-item-!-187;#058&004779If x is equal to the sum of the even integers from 40 to 60, inclusive, and y is the number of even integers from 40 to 60, inclusive, what is the value of x + y ?
(A) 550(B) 551(C) 560(D) 561(E) 572------------------------------------------------------------------------------------------------------------------------------------【答案】C【思路】X是40~60所有偶數相加 Y是40~60中所有偶數的數目(Y表示有多少個偶數) 所以 550 + 11(40,42,44,46,48,50,52,54,56,58,60) = 561------------------------------------------------------------------------------------------------------------------------------------
49. 6121-!-item-!-187;#058&004785If two of the four expressions x + y, x + 5y, x - y, and 5x - y are chosen at random, what is the probability that their product will be of the form of x^2 - (by)^2, where b is an integer?
(A) (B) (C) (D) (E)
50. 6173-!-item-!-187;#058&004786If [?], what is the value of n ?
(A) (B) (C) (D) (E)
51. 6219-!-item-!-187;#058&004789Which of the following is equal to the average (arithmetic mean) of (x + 2)^2 and (x - 2)^2 ?
(A) x^2(B) x^2 + 2(C) x^2 + 4(D) x^2 + 2x(E) x^2 + 4x------------------------------------------------------------------------------------------------------------------------------------【答案】C【思路】
------------------------------------------------------------------------------------------------------------------------------------
52. 6267-!-item-!-187;#058&004794If x < 0, then [?] is
(A) -x(B) -1(C) 1(D) x(E)
53. 6313-!-item-!-187;#058&004799During a car trip, Maria stopped to rest after she traveled [?] of the total distance to her destination. She stopped again after she traveled of the distance remaining between her first stop and her destination, and then she drove the remaining 120 miles to her destination. What was the total distance, in miles, from Maria's starting point to her destination?
(A) 280(B) 320(C) 360(D) 420(E) 480
54. 6364-!-item-!-187;#058&004806P, Q, and R are located in a flat region of a certain state. Q is x miles due east of P and y miles due north of R. Each pair of points is connected by a straight road. What is the number of hours needed to drive from Q to R and then from R to P at a constant rate of z miles per hour, in terms of x, y, and z ? (Assume x, y, and z are positive.)
(A) (B) (C) (D) (E)
55. 6410-!-item-!-187;#058&004809The 15 homes in a new development are each to be sold for one of three different prices so that the developer receives an average (arithmetic mean) of $200,000 per home. If 4 of the homes are to be sold for $170,000 each and 5 are to be sold for $200,000 each, what will be the selling price of each of the remaining 6 homes?
(A) $200,000(B) $210,000(C) $215,000(D) $220,000(E) $230,000
------------------------------------------------------------------------------------------------------------------------------------【答案】C【思路】設剩下六個,每個home賣得x元
X=220000元------------------------------------------------------------------------------------------------------------------------------------
56. 6461-!-item-!-187;#058&004810To celebrate a colleague's retirement, the T coworkers in an office agreed to share equally the cost of a catered lunch. If the lunch costs a total of x dollars and S of the coworkers fail to pay their share, which of the following represents the additional amount, in dollars, that each of the remaining coworkers would have to contribute so that the cost of the lunch is completely paid?
(A) (B) (C) (D) (E)
57. 6510-!-item-!-187;#058&004845[?]
At the end of each year, a certain credit card company pays a bonus to each of its credit card holders based on the amount, up to $10,000, that the cardholder charged throughout the year. A 0.5 percent bonus is paid on the first $1,000 charged, a 1.0 percent bonus is paid on the next $2,000 charged and so on, as indicated in the table above. What is the maximum annual bonus, in dollars?
(A) $100(B) $150(C) $200(D) $250(E) $500
58. 6618-!-item-!-187;#058&004870[?]
If p, q, r, and s are as shown on the number line above, which of the following products is greatest?
(A) (B) (C) (D) (E)
59. 6664-!-item-!-187;#058&004887The cost of picture frame M is $10.00 less than 3 times the cost of picture frame N. If the cost of frame M is $50.00, what is the cost of frame N ?
(A) $13.33(B) $16.66(C) $20.00(D) $26.66(E) $40.00------------------------------------------------------------------------------------------------------------------------------------【答案】C【思路】
按照提議列出方程式 : M = 3N - 1050 = 3N -10 可得N=20------------------------------------------------------------------------------------------------------------------------------------
60. 6711-!-item-!-187;#058&004926The value of [?] is
(A) between -9 and -10(B) between -8 and -9(C) between -4 and -5(D) between -3 and -4(E) undefined
61. 6814-!-item-!-187;#058&004969[?]
A computer chip manufacturer expects the ratio of the number of defective chips to the total number of chips in all future shipments to equal the corresponding ratio for shipments S1, S2, S3, and S4 combined, as shown in the table above. What is the expected number of defective chips in a shipment of 60,000 chips?
(A) 14(B) 20(C) 22(D) 24(E) 25
62. 7185-!-item-!-187;#058&005078In a certain furniture store, each week Nancy earns a salary of $240 plus 5 percent of the amount of her total sales that exceeds $800 for the week. If Nancy earned a total of $450 one week, what were her total sales that week?
(A) $2,200(B) $3,450(C) $4,200(D) $4,250(E) $5,000-------------------------------------------------------------------------------------------------------------------------------【答案】E【思路】設total sales 為X元, 則 240+(x-800) 0.05=450 -------------------------------------------------------------------------------------------------------------------------------
63. 7231-!-item-!-187;#058&005082The sum of the first 50 positive even integers is 2,550. What is the sum of the even integers from 102 to 200, inclusive?
(A) 5,100(B) 7,550(C) 10,100(D) 15,500(E) 20,100------------------------------------------------------------------------------------------------------------------------------【答案】B【思路】2+4+6+8+10………100=2550, 102+104+106+108+110……200=(100+2)+(100+4)+(100+6)+(100+8)…….+(100+200) =50 100+(2+4+6+8+……….100) =5000+2550=7550-------------------------------------------------------------------------------------------------------------------------------
64. 7285-!-item-!-187;#058&005104[?]
A certain bank uses the formula above to approximate the annual percentage rate R of a monthly installment loan. Which of the following is an equivalent form of the formula?
(A) (B) (C) (D) (E)
65. 7385-!-item-!-187;#058&005343A salesperson received a commission of 3 percent of the sale price for each of the first 100 machines that she sold and 4 percent of the sale price for each machine that she sold after the first 100. If the sale price of each machine was $10,000 and the salesperson received a $36,000 commission, how many machines did she sell?
(A) 90(B) 103(C) 105(D) 115(E) 120------------------------------------------------------------------------------------------------------------------------------【答案】D【思路】前100台commission-> 10000 100 0.03=30000則(10000x) 0.04=6000x=15+100=115-------------------------------------------------------------------------------------------------------------------------------
66. 7431-!-item-!-187;#058&005458From a group of 21 astronauts that includes 12 people with previous experience in space flight, a 3-person crew is to be selected so that exactly 1 person in the crew has previous experience in space flight. How many different crews of this type are possible?
(A) 432(B) 594(C) 864(D) 1,330(E) 7,980------------------------------------------------------------------------------------------------------------------------------【答案】A【思路】12-previous experience, 9-previous experience,則2個沒經驗和1個有經驗的組合?
=432
-------------------------------------------------------------------------------------------------------------------------------
67. 7481-!-item-!-187;#058&005467S represents the sum of the weights of n fish in pounds. Which of the following represents the average (arithmetic mean) of the n weights in ounces? (1 pound = 16 ounces)
(A) 16nS(B) (C) (D) (E)
68. 7638-!-item-!-187;#058&005506In a certain bathtub, both the cold-water and the hot-water fixtures leak. The cold-water leak alone would fill an empty bucket in c hours, and the hot-water leak alone would fill the same
bucket in h hours, where c < h. If both fixtures began to leak at the same time into the empty bucket at their respective constant rates and consequently it took t hours to fill the bucket, which of the following must be true? [?]
(A) I only(B) II only(C) III only(D) I and II(E) I and III
69. 8008-!-item-!-187;#058&005955If (2^x)(3^y) = 288, where x and y are positive integers, then [2^(x - 1)][3^(y - 2)] =
(A) 16(B) 24(C) 48(D) 96(E) 144-------------------------------------------------------------------------------------------------------------------------------【答案】A
【思路】 =288 x=5,y=2
則 =16-------------------------------------------------------------------------------------------------------------------------------
70. 8217-!-item-!-187;#058&006107
If - = 162, then x(x - 1) =
(A) 12(B) 16(C) 20(D) 30(E) 81-------------------------------------------------------------------------------------------------------------------------------【答案】C
【思路】 - = 162,
則 (1- )= = 2 =2
則X-1=4, X=5 5 4=20-------------------------------------------------------------------------------------------------------------------------------
71. 8372-!-item-!-187;#058&006254For which of the following values of x is [?] NOT defined as a real number?
(A) 1(B) 2(C) 3(D) 4(E) 5
72. 8421-!-item-!-187;#058&006278[?]
(A) 1(B) (C)
(D) 18(E) 20
73. 8467-!-item-!-187;#058&006379The maximum temperatures, in degrees Fahrenheit, recorded in a city on 5 consecutive days were x + 3, 95, 87, x + 7, and x. If the average (arithmetic mean) of these temperatures was 90 degrees Fahrenheit, what is the value of x ?
(A) 85(B) 86(C) 87(D) 88(E) 89---------------------------------------------------------------------------------------------------------------
【答案】B
【思路】已知平均值，求未知數 x : => 3x=258, x=86
---------------------------------------------------------------------------------------------------------------74. 8516-!-item-!-187;#058&006446There are 15 slate rocks, 20 pumice rocks, and 10 granite rocks randomly distributed in a certain field. If 2 rocks are to be chosen at random and without replacement, what is the probability that both rocks will be slate rocks?
(A) (B) (C) (D) (E)
75. 8673-!-item-!-187;#058&006582The y-intercept of a line [?] is 4. If the slope of [?] is negative, which of the following could be the x-intercept of [?] ?
(A) I only(B) II only(C) III only(D) I and II(E) I and III
76. 8721-!-item-!-187;#058&006602A hiker walking at a constant rate of 4 miles per hour is passed by a cyclist traveling in the same direction along the same path at a constant rate of 20 miles per hour. The cyclist stops to wait for the hiker 5 minutes after passing her, while the hiker continues to walk at her constant rate. How many minutes must the cyclist wait until the hiker catches up?
(A) (B) 15(C) 20(D) 25(E)
77. 8876-!-item-!-187;#058&006751A contest will consist of n questions, each of which is to be answered either "True" or "False." Anyone who answers all n questions correctly will be a winner. What is the least value of n for which the probability is less than [?] that a person who randomly guesses the answer to each
question will be a winner?
(A) 5(B) 10(C) 50(D) 100(E) 1,000
78. 9309-!-item-!-187;#058&006922If , then x =
(A) c2 + (B) c6 + (C) c9 + (D) c12 + (E) c18 +
79. 9358-!-item-!-187;#058&006924If ab is not 0, then a^(-1) + b^(-1) =
(A) a + (B) -(a + b)(C) (D) (E)
80. 9407-!-item-!-187;#058&006938If 0 < x < 1, which of the following inequalities must be true? [?]
(A) None(B) I only(C) II only(D) I and II only(E) I, II, and III
81. 9454-!-item-!-187;#058&006950If [?], what is the value of n ?
(A) -2(B) -1(C) 0(D) 1(E) 2
82. 9500-!-item-!-187;#058&006955If (2^x)(2^y) = 8 and (9^x)(3^y) = 81, then (x, y) =
(A) (1, 2)(B) (2, 1)(C) (1, 1)(D) (2, 2)(E) (1, 3)------------------------------------------------------------------------------------------------------------------------------------
【答案】A
【思路】1. => x+y=3 2. =>聯立方程式得知 (x,y)=(1,2)
------------------------------------------------------------------------------------------------------------------------------------
83. 9550-!-item-!-187;#058&006969{-10, -6, -5, -4, -2.5, -1, 0, 2.5, 4, 6, 7, 10}A number is to be selected at random from the set above. What is the probability that the number selected will be a solution of the equation (x - 5)(x + 10)(2x - 5) = 0 ?
(A) (B) (C) (D) (E)
84. 9603-!-item-!-187;#058&006986For all numbers x such that x [?] 1, if g(x) is defined by [?], then
(A) (B) (C) (D) (E)
85. 9649-!-item-!-187;#058&007038Of the 800 employees of Company X, 70 percent have been with the company for at least ten years. If y of these "long-term" members were to retire and no other employee changes were to occur, what value of y would reduce the percent of "long-term" employees in the company to 60 percent?
(A) 200(B) 160(C) 112(D) 80(E) 56------------------------------------------------------------------------------------------------------------------------------------
【答案】A
【思路】設 y 為 老員工的離職數 => = 0.6 => 0.4y=80 => y=200
------------------------------------------------------------------------------------------------------------------------------------
86. 9697-!-item-!-187;#058&007051The ratio of the amount of Alex's fuel oil bill for the month of February to the amount of his fuel oil bill for the month of January was [?]. If the fuel oil bill for February had been $40 more, the corresponding ratio would have been . How much was Alex's fuel oil bill for January?
(A) $240(B) $300(C) $360(D) $450(E) $540
87. 9743-!-item-!-187;#058&007054A television manufacturer produces 600 units of a certain model each month at a cost to the manufacturer of $90 per unit and all of the produced units are sold each month. What is the minimum selling price per unit that will ensure that the monthly profit (revenue from sales minus the manufacturer's cost to produce) on the sales of these units will be at least $42,000 ?
(A) $110(B) $120(C) $140(D) $160(E) $180------------------------------------------------------------------------------------------------------------------------------------
【答案】D
【思路】最少的賣價以獲有$42,000 ，則單賣價為=單成本+單利潤 => 90 + = 160
------------------------------------------------------------------------------------------------------------------------------------
88. 9789-!-item-!-187;#058&007104In May Mrs. Lee's earnings were 60 percent of the Lee family's total income. In June Mrs. Lee earned 20 percent more than in May. If the rest of the family's income was the same both months, then, in June, Mrs. Lee's earnings were approximately what percent of the Lee family's total income?
(A) 64%(B) 68%(C) 72%(D) 76%(E) 80%------------------------------------------------------------------------------------------------------------------------------------
【答案】A
【思路】假設 Lee 全家所得為 x, 則五月份 Lee 單所得 0.6x, 其他所得為 0.4x。六月份 Lee 單所得為: 0.72x
(o.6*1.2)，所以六月份 Lee 所得佔全家所得的百分比為: =0.64
-------------------------------------------------------------------------------------------------------------
89. 9835-!-item-!-187;#058&007168For one toss of a certain coin, the probability that the outcome is heads is 0.6. If this coin is tossed 5 times, which of the following is the probability that the outcome will be heads at least 4 times?
(A) (0.6)^5(B) 2(0.6)^4(C) 3(0.6)^4(0.4)(D) 4(0.6)^4(0.4) + (0.6)^5(E) 5(0.6)^4(0.4) + (0.6)^5------------------------------------------------------------------------------------------------------------------------------------
【答案】E
【思路】最少有四次的頭表示 : 四次有頭的機率(不管順序) + 五次全頭的機率 = +
-------------------------------------------------------------------------------------------------------------
90. 10100-!-item-!-187;#058&007272[?]If [?] and [?] represent single digits in the correctly worked computation above, what is the value of [?] + [?] ?
(A) 7(B) 9(C) 10(D) 11(E) 13
91. 10146-!-item-!-187;#058&007291A certain car averages 25 miles per gallon of gasoline when driven in the city and 40 miles per gallon when driven on the highway. According to these rates, which of the following is closest to the number of miles per gallon that the car averages when it is driven 10 miles in the city and then 50 miles on the highway?
(A) 28(B) 30(C) 33(D) 36(E) 38---------------------------------------------------------------------------------------------------------------------------------【答案】D
【思路】在city每開25mile要耗1gallon的油 開10mile要耗 gallon的油
在highway每開40mile要耗1gallon的油 開50mile要耗 gallon的油
由此可知平均為 ---------------------------------------------------------------------------------------------------------------------------------
92. 10192-!-item-!-187;#058&007298On his drive to work, Leo listens to one of three radio stations, A, B, or C. He first turns to A. If A is playing a song he likes, he listens to it; if not, he turns to B. If B is playing a song he likes, he listens to it; if not, he turns to C. If C is playing a song he likes, he listens to it; if not, he turns off the radio. For each station, the probability is 0.30 that at any given moment the station is playing a song Leo likes. On his drive to work, what is the probability that Leo will hear a song he likes?
(A) 0.027(B) 0.090(C) 0.417(D) 0.657(E) 0.900---------------------------------------------------------------------------------------------------------------------------------【答案】D【思路】Pr(Leo聽到喜歡的歌) = 1 – Pr(ABC三台都沒有Leo喜歡的歌) = 1 – (0.73)3 = 0.657---------------------------------------------------------------------------------------------------------------------------------
93. 10238-!-item-!-187;#058&007360If $1,000 was invested at an annual interest rate of 5.6 percent compounded annually, which of the following represents the amount the investment was worth after 3 years?
(A) $1,000(1.056)(3)(B) $1,000(3 + 1.056)
(C) $1,000[1 + 3(0.056)](D) $1,000[1 + (0.056)^3](E) $1,000(1.056)^3---------------------------------------------------------------------------------------------------------------------------------【答案】E【思路】複利計息時，本利和 = 本金 x (1 + 利率)期數
= 1,000 x (1.056)3 ---------------------------------------------------------------------------------------------------------------------------------
94. 10284-!-item-!-187;#058&007376A certain candy manufacturer reduced the weight of Candy Bar M by 20 percent but left the price unchanged. What was the resulting percent increase in the price per ounce of Candy Bar M ?
(A) 5%(B) 10%(C) 15%(D) 20%(E) 25%---------------------------------------------------------------------------------------------------------------------------------【答案】E【思路】價格不變，商品重量卻減為原來的80%，可知價格變成1 / 0.8 = 1.25，漲了25%
(正式解法：若設商品價格為x元，原來的商品重量為M盎司，則每盎司的價錢就是 。
減重為80%後，每盎司的價錢就成了 ，可知每盎司價格漲了25%。)---------------------------------------------------------------------------------------------------------------------------------
95. 10331-!-item-!-187;#058&007378The total of Company C's assets in 1994 was 300 percent greater than the total in 1993, which in turn was 400 percent greater than the total in 1992. If the total of Company C's assets in 1992 was N dollars, which of the following represents the total of Company C's assets, in dollars, in 1994 ?
(A) 7N(B) 8N(C) 9N(D) 12N(E) 20N---------------------------------------------------------------------------------------------------------------------------------【答案】E【思路】文字題，注意文字敘述上的陷阱。 “assets in 1994 was 300 percent greater than the total in 1993” 意指前者「超過」後者三倍，所以1994年的資產是1993年的4倍，不是3倍。同理1993年的資產則是1992年的5倍(不是4倍)。因此1994年的資產是1992年的 4 x 5 = 20倍。---------------------------------------------------------------------------------------------------------------------------------
96. 10378-!-item-!-187;#058&007391The contents of a certain box consist of 14 apples and 23 oranges. How many oranges must be removed from the box so that 70 percent of the pieces of fruit in the box will be apples?
(A) 3(B) 6(C) 14(D) 17(E) 20---------------------------------------------------------------------------------------------------------------------------------【答案】D
【思路】最初盒中的水果一共有14 + 23 = 37個，
設應該取走的橘子是x個，可知取走橘子以後蘋果占盒中水果的比例是 ，需為70%。
因此 ，解得 x = 17。---------------------------------------------------------------------------------------------------------------------------------
97. 10424-!-item-!-187;#058&007444Each unit of a certain product costs a manufacturer $9 to produce. The manufacturer sells the product in boxes of 50 units for $560 per box. How many boxes of the product does the manufacturer need to sell to yield a profit of $110,000 ?
(A) 90(B) 100(C) 900(D) 1,000(E) 1,100------------------------------------------------------------------------------------------------------------------------------------【答案】D【思路】the cost of every box is 9×50=450,therefore the profit of every box is 560-450=110 560-9×50=110000/110=1000(box)------------------------------------------------------------------------------------------------------------------------------------
98. 10475-!-item-!-187;#058&007489An athlete runs R miles in H hours, then rides a bicycle Q miles in the same number of hours. Which of the following represents the athlete's average speed, in miles per hour, for these two activities combined?
(A) (B) (C) (D) (E)
99. 10524-!-item-!-187;#058&007561[?]
For the numbers on the number line above, which of the following statements is true?
(A) x + y > y(B) xz > xy(C) tz < z(D) mu < 0(E) tm > 0
100.10681-!-item-!-187;#058&0076192 + 2 + 2^2 + 2^3 + 2^4 + 2^5 + 2^6 + 2^7 + 2^8 =
(A) 2^9(B) 2^10(C) 2^16(D) 2^35(E) 2^37------------------------------------------------------------------------------------------------------------------------------------【答案】A【思路】
此題最快的方式背等比級數求合 sum of geometric progression 的公式 等比級數求合公式: a0, a1, ... , anwhere a0 × r = a1, a1 × r = a2, .....then
Sn = if r<1
or
Sn = if r>1
所以：
a 首項 r 公比
=
=
= 2 +
=
=
= 此題商喀還有一個比較不正統的解法，可參考有一點等比的概念 2+2+2^2+2^3+2^4+2^5+2^6+2^7+2^8=2^9 2+2=2^2 原式= 2^2+2^2+2^3+2^4+2^5+2^6+2^7+2^8=2^9 (2^2+2^2=2^3) 原式= 2^3+2^3+2^4+2^5+2^6+2^7+2^8=2^9 (2^3+2^3=2^4) ..依此類推 第N項=N-1項的總和 所以 2+2+2^2+2^3+2^4+2^5+2^6+2^7+2^8=2^9
------------------------------------------------------------------------------------------------------------------------------------
101.10730-!-item-!-187;#058&007650[?]The table above shows the amount of waste material, in tons, recycled by each of five counties in a single year and the amount of waste material, also in tons, that was disposed of in landfills by the five counties in that year. Which county had the lowest ratio of waste material disposed of to waste material recycled in the year reported in the table?
(A) A(B) B(C) C
(D) D(E) E
102.10776-!-item-!-187;#058&007653A certain store found that last year the average (arithmetic mean) monthly sales from January through October was $120,000. In November and December, the monthly sales were 3 and 5 times, respectively, the average for the other 10 months. What was the store's average monthly sales last year?
(A) $180,000(B) $216,000(C) $252,000(D) $318,000(E) $360,000------------------------------------------------------------------------------------------------------------------------------------【答案】A
【思路】
------------------------------------------------------------------------------------------------------------------------------------
103.10822-!-item-!-187;#058&007696A certain meter records voltage between 0 volts and 10 volts, inclusive. If the average (arithmetic mean) value of 3 recordings on the meter was 8 volts, what was the smallest possible recording, in volts?
(A) 2(B) 3(C) 4(D) 5(E) 6------------------------------------------------------------------------------------------------------------------------------------【答案】C【思路】total: 8x3=24 取最小的話, 另外兩個都要是最大的. 24-10-10=4------------------------------------------------------------------------------------------------------------------------------------
104.10868-!-item-!-187;#058&007697The temperatures in degrees Celsius recorded at 6 in the morning in various parts of a certain country were 10, 5, -2, -1, -5, and 15. What is the median of these temperatures?
(A) -2(B) -1(C) 2(D) 3(E) 5------------------------------------------------------------------------------------------------------------------------------------【答案】C【思路】
從小到大排列-5, -2, -1, 5, 10 15
------------------------------------------------------------------------------------------------------------------------------------
105.10917-!-item-!-187;#058&007716[?]
In the figure above, what is the value of x ?
(A) 55(B) 60(C) 65(D) 70(E) 75
106.10964-!-item-!-187;#058&007770Joshua and Jose work at an auto repair center with 4 other workers. For a survey on healthcare insurance, 2 of the 6 workers will be randomly chosen to be interviewed. What is the probability that Joshua and Jose will both be chosen?
(A) (B) (C) (D) (E)
107.11013-!-item-!-187;#058&007796[?] The table above shows the total sales recorded in July for the 5 salespeople at Acme Truck Sales. It was discovered that one of Cal's sales was incorrectly recorded as one of Ann's sales. After this error was corrected, Ann's total sales were still higher than Cal's total sales, and the median of the 5 sales totals was $330,000. What was the value of the incorrectly recorded sale?
(A) $30,000(B) $48,000(C) $90,000(D)(E)
108.11175-!-item-!-187;#058&007894[?]
On the number line above, the segment from 0 to 1 has been divided into fifths, as indicated by the large tick marks, and also into sevenths, as indicated by the small tick marks. What is the least possible distance between any two of the tick marks?
(A) (B) (C) (D) (E)
109.11276-!-item-!-187;#058&008007What is the value of [?], to the nearest whole number?
(A) 8
(B) 11(C) 12(D) 15(E) 32
110.11325-!-item-!-187;#058&008034During a trip on an expressway, Don drove a total of x miles. His average speed on a certain 5-mile section of the expressway was 30 miles per hour, and his average speed for the remainder of the trip was 60 miles per hour. His travel time for the x-mile trip was what percent greater than it would have been if he had traveled at a constant rate of 60 miles per hour for the entire trip?
(A) 8.5%(B) 50%(C) (D) (E)
111.11378-!-item-!-187;#058&008123[?]
In the figures above, if the area of the triangle on the right is twice the area of the triangle on the left, then in terms of s, S =
(A) (B) (C) (D) (E) 2s
112.11750-!-item-!-187;#058&008431For a certain race, 3 teams were allowed to enter 3 members each. A team earned 6 - n points whenever one of its members finished in nth place, where 1 <= n <= 5. There were no ties, disqualifications, or withdrawals. If no team earned more than 6 points, what is the least possible score a team could have earned?
(A) 0(B) 1(C) 2(D) 3(E) 4------------------------------------------------------------------------------------------------------------------------------------【答案】D【思路】There are 9 individual members in total.
There were no ties, disqualifications or withdrawls, therefore all 9 members finished the race, and each one finished in a different place.
1st place = 5 points.2nd place = 4 points.3rd place = 3 points.4th place = 2 points. 5th place = 1 point.6th place = 0 points.7th place = 0 points.8th place = 0 points.9th place = 0 points.
There are a total of 5 + 4 + 3 + 2 + 1 = 15 points to be awarded.; those points must be distributed in one way or another among the three teams.
None of the team earned more than 6 points, therefore when maximizing two of the teams in order to minimize the third, we cannot go over 6 points per team.
I gave one team 6 points and the other team 5 points since I took the "no ties" to mean that there were no ties among individual members and no ties among the total score of each of the teams.(However, "no ties" probably applies to individual members only, in that case, each of the two teams will get 6 points).
If one team gets 5 + 1 = 6 points, and another team gets 4 + 2 = 6 points, they can get 6+6 =12. .third team got the the least possible 15-12 =3 pts. with the minimum.------------------------------------------------------------------------------------------------------------------------------------
113.11853-!-item-!-187;#058&008463[?]
For the inequalities above, what is the maximum possible value of P + Q + R + S ?
(A) -2(B) 0(C) 2(D) 4(E) 6
114.11899-!-item-!-187;#058&008467If xy + k = k and x is not 0, which of the following must be true?
(A) x > y(B) x + y = 0(C) y = 0(D) |x - y | = 0(E) xy = 1------------------------------------------------------------------------------------------------------------------------------------
【答案】C
【思路】(A) 且 x>y, 假設 x=3,y=2,
(B) X+Y=0, 且 ,假設 x=3, y=-3,
(D) |x - y | = 0 且 ,假設 x=3,y=3,
(E) xy = 1 且 ,假設 x=3,y= ,
(C)y=0, 且 ,則 xy=0,thus xy + k = k must be true------------------------------------------------------------------------------------------------------------------------------------115.12001-!-item-!-187;#058&008506A certain roller coaster has 3 cars, and a passenger is equally likely to ride in any 1 of the 3 cars each time that passenger rides the roller coaster. If a certain passenger is to ride the roller coaster 3 times, what is the probability that the passenger will ride in each of the 3 cars?
(A) 0(B) (C) (D) (E) 1
116.12050-!-item-!-187;#058&008561A certain manufacturer of cake, muffin, and bread mixes has 100 buyers, of whom 50 purchase cake mix, 40 purchase muffin mix, and 20 purchase both cake mix and muffin mix. If a buyer is to be selected at random from the 100 buyers, what is the probability that the buyer selected will be one who purchases neither cake mix nor muffin mix?
(A) (B) (C) (D) (E)
117.12100-!-item-!-187;#058&008590There 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) (B) (C) (D) (E)
118.12146-!-item-!-187;#058&008756For each hour of production, a certain factory requires 1 assembly line worker for every 25 units to be produced in that hour. The factory also requires 12 managers regardless of the number of units to be produced. Which of the following expressions represents the total number of assembly line workers and managers that this factory requires to produce 50N units in one hour, where N is a positive integer?
(A) 12 + 50N(B) 12 + 2N(C) 62N(D) 37N(E) 25N------------------------------------------------------------------------------------------------------------------------------------
【答案】B
【思路】這題其實不難,但被閱讀卡住 主要問有多少 assembly line worker and managers that factory requires to produce50N units
in one hour
The factory also requires 12 managers regardless of the number of units to be produced.---
不管工廠生產的產品數量有多少, 工廠經理的編制都需要 12 人 一條線一小時生產25 unit所以生產50N需要2N workers thus, total number=12+2N------------------------------------------------------------------------------------------------------------------------------------
119.12192-!-item-!-187;#058&008830A certain farmer pays $30 per acre per month to rent farmland. How much does the farmer pay per month to rent a rectangular plot of farmland that is 360 feet by 605 feet? (43,560 square feet = 1 acre)
(A) $5,330(B) $3,630(C) $1,350(D) $360(E) $150------------------------------------------------------------------------------------------------------------------------------------
【答案】E
【思路】360x605=217,800
=5 (acres), the farmer pay5x30=$150 per month to rent a rectangular plot of
farmland that is 360
feet by 605 feet------------------------------------------------------------------------------------------------------------------------------------
120.12241-!-item-!-187;#058&008920The diameter of circle S is equal in length to a side of a certain square. The diameter of circle T is equal in length to a diagonal of the same square. The area of circle T is how many times the area of circle S ?
(A) (B) (C) 2(D) (E)
121.12343-!-item-!-187;#058&009002Pat, Kate, and Mark charged a total of 162 hours to a certain project. If Pat charged twice as much time to the project as Kate and [?] as much time as Mark, how many more hours did Mark charge to the project than Kate?
(A) 18(B) 36(C) 72(D) 90(E) 108
122.12443-!-item-!-187;#058&009133If n is a positive integer, which of the following must be an even integer?
(A) n + 1(B) n + 2(C) n^2 + 2(D) n^2 + n(E) n^2 + 2n------------------------------------------------------------------------------------------------------------------------------------
【答案】D
【思路】positive integer 包含奇數,偶數, and o (A)n + 1,假設n=2, n+1=3≠even integer(B)n + 2,假設n=1,n+2=3≠even integer
(C) ,假設n=3, =9+2=11≠even integer
(E) ,假設n=3, =9+6=15≠even integer
(D) ,假設n=3, =9+3=12=even integer;假設n=2, =4+2=6=even integer;
假設n=0, =0=even integer, must be an even integer.------------------------------------------------------------------------------------------------------------------------------------
123.12489-!-item-!-187;#058&009157Of the 100 passengers who entered a railroad station, 10 passengers had 4 pieces of luggage each, 20 had 5 pieces of luggage each, 50 had 2 pieces of luggage each, and the rest had no luggage. What was the average (arithmetic mean) number of pieces of luggage per passenger?
(A) 1(B) 1.4
(C) 2(D) 2.4(E) 3------------------------------------------------------------------------------------------------------------------------------------
【答案】D
【思路】沒有 luggage 的有:100-10-20-50=20
total luggage=10x4+20x5+50x2+20x0=240
the average (arithmetic mean) number of pieces of luggage per passenger=
------------------------------------------------------------------------------------------------------------------------------------
124.12535-!-item-!-187;#058&009197A rectangular region has a fence along three sides and a wall along the fourth side. The fenced side opposite the wall is twice the length of each of the other two fenced sides. If the area of the rectangular region is 128 square feet, what is the total length of the fence, in feet?
(A) 4(B) 8(C) 16(D) 32(E) 64------------------------------------------------------------------------------------------------------------------------------------
【答案】D
【思路】一個長方形有個 fence,這個 fence 有三邊組成,另一邊是靠牆(表示沒有 fence)
牆壁對面的 length 是其他兩邊的兩倍,假設其他兩邊 length=x, thus 牆壁對面的 length=2x
the area= =128,x=8 thus牆壁對面的length=16 the total length of the fence=8+8+16=32(小心!有一邊是靠牆)------------------------------------------------------------------------------------------------------------------------------------
125.12583-!-item-!-187;#058&009318Of the following, which is greatest?
[?]
(A) (B) (C) 3^(-2)(D) 5^(-2)(E) 2^3
126.12631-!-item-!-187;#058&0093809.4 9.9 9.9 9.9 10.0 10.2 10.2 10.5The mean and the standard deviation of the 8 numbers shown are 10.0 and 0.3, respectively. What percent of the 8 numbers are within 1 standard deviation of the mean?
(A) 90%(B) 85%(C) 80%(D) 75%(E) 70%------------------------------------------------------------------------------------------------------------------------------------
【答案】D
【思路】
1 standard deviation of the mean
表示 10-0.3<number<10+0.3
9.7＜9.9 9.9 9.9 10.0 10.2 10.2＜10.3
有六個數在之中 9.7 和 10.3之間, =75%
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127.12731-!-item-!-187;#058&009562In May, Xiang sold 15 used cars. For these 15 cars, the range of the selling prices was $15,000 and the lowest selling price was $4,500. In June, Xiang sold 10 used cars. For these 10 cars, the range of the selling prices was $16,500 and the lowest selling price was $6,100. What was the range of the selling prices of the 25 used cars sold by Xiang in May and June?
(A) $15,600(B) $15,750(C) $16,820(D) $18,100(E) $19,200------------------------------------------------------------------------------------------------------------------------------------
【答案】D
【思路】
the range of the selling prices was $15,000, the lowest selling price was $4,500 可得五月最大值15000+4500=19500
the range of the selling prices was $16,500 and the lowest selling price was $6,100 可得六月最大值 16500+6100=22600
22600-4500=18100
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128.12783-!-item-!-187;#058&009601[?]
In the figure shown, the length of line segment QS is . What is the perimeter of equilateral triangle PQR ?
(A) 12(B) (C) 24(D) (E) 48
129.12829-!-item-!-187;#058&009608A television network sells advertising time on a certain program at the rate of $10,000 per minute. If the program is shown once a day for 5 days a week, what is the cost of advertising on this program for 3 weeks at 30 seconds per day?
(A) $15,000(B) $25,000(C) $75,000(D) $90,000(E) $150,000------------------------------------------------------------------------------------------------------------------------------------
【答案】C
【思路】
30秒 等於 0.5 分
5×3×0.5×10000=75000
------------------------------------------------------------------------------------------------------------------------------------
130.12875-!-item-!-187;#058&009671If (400)(6,000) = (240)(100^x), what is the value of x ?
(A) 5(B) 4(C) 3(D) 2(E) 1------------------------------------------------------------------------------------------------------------------------------------
【答案】D
【思路】
(400)(6,000)=(2400)(1000)=(240)(10000)=(240)( )
X=2
------------------------------------------------------------------------------------------------------------------------------------
131.12921-!-item-!-187;#058&009694If x is an even integer and y is an odd integer, which of the following is even?
(A) 3x + 4y - 1(B) 3x + 3y - 2(C) 4x + 4y + 1(D) 4x + 3y + 2(E) 4x + 3y + 1------------------------------------------------------------------------------------------------------------------------------------
【答案】E
【思路】
x is an even,x乘以偶數還是偶數, 4x 為偶數
y is an odd,y乘以奇數結果為奇數, 3y 為奇數,可得 3y+1 為偶數
故 4x + 3y + 1 為偶數
------------------------------------------------------------------------------------------------------------------------------------
132.13076-!-item-!-187;#058&009801[?]
(A) 3^(-6)(B) 3^(-5)(C) 3^(-1)(D) 3^5(E) 3^6
133.13123-!-item-!-187;#058&009850The lunch menu at a certain restaurant contains 4 different entrees and 5 different side dishes. If a meal consists of 1 entree and 2 different side dishes, how many different meal combinations could be chosen from this menu?
(A) 10(B) 20(C) 40(D) 80(E) 100------------------------------------------------------------------------------------------------------------------------------------
【答案】C
【思路】
=40
------------------------------------------------------------------------------------------------------------------------------------
134.13169-!-item-!-187;#058&009883[?]
If x is an integer, which of the following must be an odd integer?
(A) 2x + 2(B) 4x + 3(C) 13x(D) 14x(E)
135.13220-!-item-!-187;#058&009935Machine A produces pencils at a constant rate of 9,000 pencils per hour, and machine B produces pencils at a constant rate of 7,000 pencils per hour. If the two machines together must produce 100,000 pencils and if each machine can operate for at most 8 hours, what is the least amount of time, in hours, that machine B must operate?
(A) 4(B) (C) (D) 6(E)
136.13320-!-item-!-187;#058&009993A school purchased 2 computers whose prices were $1,000 and $2,000, respectively. The school is to purchase 2 more computers from a list of computers whose prices range from $1,000 to $2,000, inclusive. The greatest possible average (arithmetic mean) price of the 4 computers is how much greater than the least possible average price of the 4 computers?
(A) $250(B) $500(C) $750(D) $1,000(E) $1,250------------------------------------------------------------------------------------------------------------------------------------【答案】B【思路】其餘的兩台電腦以最大值（2000）和最小值（1000）代入算平均值。(1000+2000+2000+2000)/4 – (1000+2000+1000+1000)/4 = 500------------------------------------------------------------------------------------------------------------------------------------
137.13366-!-item-!-187;#058&010014Connie paid a sales tax of 8 percent on her purchase. If the sales tax had been only 5 percent, she would have paid $12 less in sales tax on her purchase. What was the total amount that Connie paid for her purchase including sales tax?
(A) $368(B) $380(C) $400(D) $420(E) $432------------------------------------------------------------------------------------------------------------------------------------【答案】E【思路】設 x 為原價。1.08x = 1.05x+12X = 12/0.03 = 4001.08x = 432------------------------------------------------------------------------------------------------------------------------------------
138.13412-!-item-!-187;#058&010022A grocer stacked oranges in a pile. The bottom layer was rectangular with 3 rows of 5 oranges each. In the second layer from the bottom, each orange rested on 4 oranges from the bottom layer, and in the third layer, each orange rested on 4 oranges from the second layer. Which of the following is the maximum number of oranges that could have been in the third layer?
(A) 5(B) 4(C) 3(D) 2(E) 1------------------------------------------------------------------------------------------------------------------------------------【答案】C【思路】以這題簡單的程度來看，畫圖最快。也可以想成是五個位子選兩個一起的位子有幾個？直向 x橫向。
------------------------------------------------------------------------------------------------------------------------------------
139.13466-!-item-!-187;#058&010025[?]
The figure shows the top side of a circular medallion made of a circular piece of colored glass surrounded by a metal frame, represented by the shaded region. If the radius of the medallion is r centimeters and the width of the metal frame is s centimeters, then in terms of s and r, what is the area of the metal frame, in square centimeters?
(A) (B) (C) (D) (E)
140.13512-!-item-!-187;#058&010037A farm used two harvesting machines, H and K, to harvest 100 acres of wheat. Harvesting machine H, working alone at its constant rate, harvested 40 acres of wheat in 8 hours. Then harvesting machine K was brought in, and harvesting machines H and K, working together at their respective constant rates, harvested the remaining acres of wheat in 5 hours. Harvesting machine K harvested how many acres of wheat per hour?
(A) 7(B) 8(C) 12(D) 13(E) 15------------------------------------------------------------------------------------------------------------------------------------【答案】A【思路】H 每小時作 40/8=5 acres. 60 acres要花12小時。
K= 60/7 (K作60 acres所花的時間)60/(60/7)=7 (每小時收成的acres)------------------------------------------------------------------------------------------------------------------------------------
141.13558-!-item-!-187;#058&010099A charitable organization has a goal of raising $300,000 in 100 days. If it raised $200,000 in the first 60 days, what is the average (arithmetic mean) number of dollars per day that it must raise for the last 40 days in order to achieve its goal?
(A) $2,500(B) $3,000(C) $5,000(D) $6,000(E) $7,500------------------------------------------------------------------------------------------------------------------------------------【答案】A
【思路】300,000-20,000=10,000 必須在40天完成10,000的目標10,000/40 = 2,500------------------------------------------------------------------------------------------------------------------------------------
142.13607-!-item-!-187;#058&010106[?]
On the number line shown, the tick marks are equally spaced. What is the value of y - x ?
(A) 4(B) 6(C) 8(D) 9(E) 10
143.13707-!-item-!-187;#058&010123Of the 50 employees of a certain company, 30 earn an average (arithmetic mean) salary of $30,000, 15 earn an average salary of $40,000, and 5 earn an average salary of $60,000. What is the average salary earned by the employees of this company?
(A) $30,000(B) $36,000(C) $40,000(D) $45,000(E) $50,000------------------------------------------------------------------------------------------------------------------------------------【答案】B【思路】
= =36K
------------------------------------------------------------------------------------------------------------------------------------
144.13921-!-item-!-187;#058&010164[?]
The table shows the quantities of eggs, flour, and sugar used by a certain baker to make one cake of each of the three different types. If the baker had 24 eggs, 30 cups of flour, and 10 cups of sugar available and had to make 2 angel food cakes and 1 devil's food cake, what is the maximum number of pound cakes that the baker could make with the remaining ingredients?
(A) 3(B) 4(C) 5(D) 6(E) 8
145.13967-!-item-!-187;#058&010235At 12:00 noon, the temperature in a certain storage room was 64. If the temperature in the storage room decreased at a constant rate of 2 per hour for the next 8 hours, what was the temperature in the storage room at 8:00 in the evening?
(A) 2(B) 8(C) 16(D) 48(E) 54------------------------------------------------------------------------------------------------------------------------------------
【答案】D【思路】64-(8*2)=48------------------------------------------------------------------------------------------------------------------------------------
146.14067-!-item-!-187;#058&010315In a certain group of 10 members, 4 members teach only French and the rest teach only Spanish or German. If the group is to choose a 3-member committee, which must have at least 1 member who teaches French, how many different committees can be chosen?
(A) 40(B) 50(C) 64(D) 80(E) 100------------------------------------------------------------------------------------------------------------------------------------【答案】E【思路】at least 1 member who teaches French 表示有可能只有一位法文老師，也有可能是兩位或三位三位中，一位是法文老師 C4取1 * C6取2 =(四位法文老師選一位) * (剩下六位老師選兩位)=60三位中，兩位是法文老師 C4取2 * C6取1 =(四位法文老師選兩位) * (剩下六位老師選一位)=36三位全是法文老師 C4取3 * C6取0 =(四位法文老師選三位) * (剩下六位老師選零位)=4P=60+36+1=100------------------------------------------------------------------------------------------------------------------------------------
147.14926-!-item-!-187;#058&010459Last semester an assistant was paid a total of $800 for grading papers in a class of 37 students. If each student handed in 7 papers and the assistant graded all of these papers, then, to the nearest whole dollar, the assistant's pay per paper graded was
(A) $5(B) $4(C) $3(D) $2(E) $1------------------------------------------------------------------------------------------------------------------------------------【答案】C【思路】Total papers reviewed: 37*7=259Pay per paper=800/259=3.0888030888… to the nearest whole dollar3------------------------------------------------------------------------------------------------------------------------------------
148.15080-!-item-!-187;#058&010499Amy's grade was the 90th percentile of the 80 grades for her class. Of the 100 grades from another class, 19 were higher than Amy's, and the rest were lower. If no other grade was the same as Amy's grade, then Amy's grade was what percentile of the grades of the two classes combined?
(A) 72nd(B) 80th(C) 81st(D) 85th(E) 92nd------------------------------------------------------------------------------------------------------------------------------------【答案】D【思路】80*(1-90%) =8 There are 8 people ahead of Amy in her class Combined with another class, there are 19+8=27 people’s grades ahead of Amy’s.# of people whose grades below Amy’s / total people of twp class (100+80-
27)/(100+80)=85%------------------------------------------------------------------------------------------------------------------------------------
149.15127-!-item-!-187;#058&010506To determine her state income tax last year, Elena computed 5 percent of her gross income, rounded the resulting figure down to the nearest $100, and subtracted $50 for each dependent that she claimed. If Elena's gross income was $34,500 and she claimed 2 dependents, how much did she determine her state income tax to be?
(A) $1,600(B) $1,625(C) $1,650(D) $1,675(E) $1,700------------------------------------------------------------------------------------------------------------------------------------【答案】A【思路】Down to the nearest $100 $34,500*5%=$1,725 (the nearest $100 will be $1,700)$1,700-50*2=$1,600------------------------------------------------------------------------------------------------------------------------------------
150.15173-!-item-!-187;#058&010507The area of a square garden is A square feet and the perimeter is P feet. If A = 2P + 9, what is the perimeter of the garden, in feet?
(A) 28(B) 36(C) 40(D) 56(E) 64------------------------------------------------------------------------------------------------------------------------------------【答案】B【思路】A=(P/4)^2 A=P^2/16A = 2P + 9 (given) P^2/16=2P+9 P^2-32P-144=0 (P-36)(P+4)=0 P=36------------------------------------------------------------------------------------------------------------------------------------
151.15220-!-item-!-187;#058&010594Which of the following is closest to [?]
(A) 4(B) 7(C) 9(D) 12(E) 16
152.15432-!-item-!-187;#058&010733Square S is inscribed in circle T. If the perimeter of S is 24, what is the circumference of T ?
(A) 6 (B) 12 (C) (D) (E)
153.15587-!-item-!-187;#058&010762At a certain supplier, a machine of type A costs $20,000 and a machine of type B costs $50,000. Each machine can be purchased by making a 20 percent down payment and repaying the remainder of the cost and the finance charges over a period of time. If the finance charges are equal to 40 percent of the remainder of the cost, how much less would 2
machines of type A cost than 1 machine of type B under this arrangement?
(A) $10,000(B) $11,200(C) $12,000(D) $12,800(E) $13,200------------------------------------------------------------------------------------------------------------------------------------【答案】E
【思路】Machine A: down payment: remainder:40000-8000=32000 finance charge: total:40000+12800=52800
Machine B:50000 down payment: remainder:50000-10000=40000 finance charge: total:50000+16000=66000difference between two arrangement:66000-52800=13200------------------------------------------------------------------------------------------------------------------------------------
154.15633-!-item-!-187;#058&010772Bobby bought two shares of stock, which he sold for $96 each. If he had a profit of 20 percent on the sale of one of the shares but a loss of 20 percent on the sale of the other share, then on the sale of both shares combined Bobby had
(A) a profit of $10(B) a profit of $8(C) a loss of $8(D) a loss of $10(E) neither a profit nor a loss------------------------------------------------------------------------------------------------------------------------------------【答案】C【思路】設賺的股票原本價格X 賠的股票原本價格Y 1.2X=96 X=80 原本價格 96-8-=16賺 0.8Y=120 Y=120原本價格 120-96=24 賠 24-16=8…LOSS------------------------------------------------------------------------------------------------------------------------------------
155.16166-!-item-!-187;#058&010984A certain brand of gasoline costs $1.25 per gallon. Using this gasoline, if a car averages 30 miles to the gallon, what is the cost of the gasoline needed for the car to travel 120 miles?
(A) $4.50(B) $5.00(C) $5.50(D) $6.00(E) $6.50------------------------------------------------------------------------------------------------------------------------------------【答案】B
【思路】
------------------------------------------------------------------------------------------------------------------------------------
156.16266-!-item-!-187;#058&011027A certain restaurant offers 6 kinds of cheese and 2 kinds of fruit for its dessert platter. If each dessert platter contains an equal number of kinds of cheese and kinds of fruit, how many different dessert platters could the restaurant offer?
(A) 8(B) 12(C) 15(D) 21(E) 27------------------------------------------------------------------------------------------------------------------------------------【答案】E【思路】因為Equal number 表示可以一個或兩個
------------------------------------------------------------------------------------------------------------------------------------
157.16315-!-item-!-187;#058&011053If k and t are integers and k2 - t2 is an odd integer, which of the following must be an even integer? [?]
(A) None(B) I only(C) II only(D) III only(E) I, II, and III
158.16365-!-item-!-187;#058&011058If x and y are positive, which of the following must be greater than [?]
[?]
(A) (B) None(C) I only(D) II only(E) I and III
159.16573-!-item-!-187;#058&011089What is the greatest prime factor of 417 - 228 ?
(A) 2(B) 3(C) 5(D) 7(E) 11------------------------------------------------------------------------------------------------------------------------------------【答案】D【思路】找最大質因數 189 = 3的三次方與7的一次方, 最大質因數7------------------------------------------------------------------------------------------------------------------------------------
160.16619-!-item-!-187;#058&011092An automobile manufacturer offers a station wagon with either a 6-cylinder engine or a 4-cylinder engine and with either a manual transmission or an automatic transmission. A trailer hitch is also offered, but only on a station wagon with a 6-cylinder engine. How many combinations of the five options listed does the manufacturer offer for its station wagon?
(A) 3(B) 4(C) 5(D) 6(E) 8------------------------------------------------------------------------------------------------------------------------------------
【答案】D【思路】2 (4與6-cyline) 2 (MANUL OR automatic) + 1(6-cyline with hitch) 2 (manul or automatic) 4+2=6------------------------------------------------------------------------------------------------------------------------------------
161.16989-!-item-!-187;#058&011313The temperature of a certain cup of coffee 10 minutes after it was poured was 120 degrees Fahrenheit. If the temperature F of the coffee t minutes after it was poured can be determined by the formula F = 120[2^(-at)] + 60, where F is in degrees Fahrenheit and a is a constant, then the temperature of the coffee 30 minutes after it was poured was how many degrees Fahrenheit?
(A) 65(B) 75(C) 80(D) 85(E) 90------------------------------------------------------------------------------------------------------------------------------------【答案】B【思路】先將10帶入方程式t得位置 求出a 再將30帶入方程式 求出解
------------------------------------------------------------------------------------------------------------------------------------
162.17416-!-item-!-187;#058&011441If x is an odd integer, which of the following is also an odd integer?
(A) 2x(B) 4x + 2(C) x2 + 3(D) x2 + x + 3(E) x2 + 2x + 1------------------------------------------------------------------------------------------------------------------------------------【答案】D【思路】A. 2乘以任何數=偶數 B..偶數+偶數=偶數 C. 奇數+奇數=偶數 D. 奇數+奇數+奇數=奇數 E. 奇數+偶數+1=偶數------------------------------------------------------------------------------------------------------------------------------------
163.17463-!-item-!-187;#058&011464The mass of 1 cubic meter of a substance is 800 kilograms under certain conditions. What is the volume, in cubic centimeters, of 1 gram of this substance under these conditions? (1 kilogram = 1,000 grams and 1 cubic meter = 1,000,000 cubic centimeters)
(A) 0.80(B) 1.25(C) 8.00(D) 12.50(E) 80.00
------------------------------------------------------------------------------------------------------------------------------------【答案】B
【思路】
------------------------------------------------------------------------------------------------------------------------------------
164.17509-!-item-!-187;#058&011499Lisa bought a house for $70,000 and paid closing costs equal to 2 percent of the purchase price. Later Lisa sold the house for $82,000 and paid a broker's commission equal to 10 percent of the selling price. What was Lisa's profit from the two transactions?
(A) $2,160(B) $2,400(C) $3,600(D) $3,800(E) $12,000------------------------------------------------------------------------------------------------------------------------------------【答案】B
【思路】
------------------------------------------------------------------------------------------------------------------------------------
165.17668-!-item-!-187;#058&011589A circular cloth with a diameter of 20 inches is placed on a circular tray with a diameter of 24 inches. What fraction of the tray's surface is not covered by the cloth?
(A) (B) (C) (D) (E)
166.17879-!-item-!-187;#058&01163470, 75, 80, 85, 90, 105, 105, 130, 130, 130The list shown consists of the times, in seconds, that it took each of 10 schoolchildren to run a distance of 400 meters. If the standard deviation of the 10 running times is 22.4 seconds, rounded to the nearest tenth of a second, how many of the 10 running times are more than 1 standard deviation below the mean of the 10 running times?
(A) One(B) Two(C) Three(D) Four(E) Five------------------------------------------------------------------------------------------------------------------------------------【答案】B
【思路】Mean=
more than 1 standard deviation below the mean 表示要超過一個標準差100-22.4=77.6 以下
只有 70 75 2個數------------------------------------------------------------------------------------------------------------------------------------
167.18146-!-item-!-187;#058&011731In a survey of 248 people, 156 are married, 70 are self-employed, and 25 percent of those who
are married are self-employed. If a person is to be randomly selected from those surveyed, what is the probability that the person selected will be self-employed but not married?
(A) (B) (C) (D) (E)
168.18192-!-item-!-187;#058&011758A stamping machine produces 100 gaskets per hour. When this machine works with a newer machine, the two machines, working simultaneously and independently at their respective constant rates, produce a total of 2,000 gaskets in 8 hours. How many gaskets does the newer machine produce per hour?
(A) 125(B) 150(C) 160(D) 175(E) 200------------------------------------------------------------------------------------------------------------------------------------【答案】B
【思路】
------------------------------------------------------------------------------------------------------------------------------------
169.18239-!-item-!-187;#058&011831If [?] and n = 40, then S =
(A) 121(B) 162(C) 420(D) 780(E) 820
170.18339-!-item-!-187;#058&011871For any triangle T in the xy-coordinate plane, the center of T is defined to be the point whose x-coordinate is the average (arithmetic mean) of the x-coordinates of the vertices of T and whose y-coordinate is the average of the y-coordinates of the vertices of T. If a certain triangle has vertices at the points (0,0) and (6,0) and center at the point (3,2), what are the coordinates of the remaining vertex?
(A) (3,4)(B) (3,6)(C) (4,9)(D) (6,4)(E) (9,6)------------------------------------------------------------------------------------------------------------------------------------【答案】C
【思路】就是說 XY 作表面上的任何一個三角形的中點的座標(x, y), 都是它三個頂點的 x,y 的坐
標平均值. 一個三角形,給出了其中兩個定點座標和三角形中點座標,
求另一個頂點座標..9-6-0=3
6-0-0=6
------------------------------------------------------------------------------------------------------------------------------------
171.18385-!-item-!-187;#058&011883Lynn lent Robert $10,000 at 6 percent simple annual interest to be repaid at the end of 3 years. What was the total amount that Robert had to pay to Lynn?
(A) $10,180(B) $10,190(C) $10,600(D) $11,800(E) $11,910------------------------------------------------------------------------------------------------------------------------------------【答案】D
【思路】------------------------------------------------------------------------------------------------------------------------------------
172.18647-!-item-!-187;#058&012110Nathan took out a student loan for $1,200 at 10 percent annual interest, compounded annually. If he did not repay any of the loan or interest during the first 3 years, which of the following is closest to the amount of interest that he owed for the 3 years?
(A) $360(B) $390(C) $400(D) $410(E) $420------------------------------------------------------------------------------------------------------------------------------------【答案】C
【思路】 最接近400
------------------------------------------------------------------------------------------------------------------------------------
173.18801-!-item-!-187;#058&012255If 0 < m < 1, which of the following expressions has the least value?
(A) m(B) m^2(C) m^3(D) 2 - m(E) (m + 1)^2------------------------------------------------------------------------------------------------------------------------------------【答案】C【思路】小數次方越乘越小------------------------------------------------------------------------------------------------------------------------------------
174.18908-!-item-!-187;#058&012310[?]
If the tick marks on the number line shown are equally spaced, what is the value of ?
(A) 9(B) 6(C) 4(D) 3(E) 2
175.19062-!-item-!-187;#058&012458Five pieces of wood have an average (arithmetic mean) length of 124 centimeters and a median length of 140 centimeters. What is the maximum possible length, in centimeters, of
the shortest piece of wood?
(A) 90(B) 100(C) 110(D) 130(E) 140------------------------------------------------------------------------------------------------------------------------------------【答案】B 【思路】假設五根木頭由低到高依序為A,B,C,D,E
A+B+C+D+E=124*5=620
C=140 所以 A+B+D+E=620-140=480
又C是中數，所以D+E>=140*2=280
故A+B<=480-280=200
所以A最大的可能為A=B=100------------------------------------------------------------------------------------------------------------------------------------
176.19324-!-item-!-187;#058&012548In the xy-plane, line k has positive slope and x-intercept 4. If the area of the triangle formed by line k and the two axes is 12, what is the y-intercept of line k ?
(A) -6(B) -4(C) -3(D) 3(E) 6------------------------------------------------------------------------------------------------------------------------------------【答案】A
【思路】面積為12 由於是正斜率 所以應在第四象限 -6
------------------------------------------------------------------------------------------------------------------------------------
177.19424-!-item-!-187;#058&012637Machines X and Y produce bottles at their respective constant rates. Machine X produces k bottles in 6 hours and machine Y produces k bottles in 2 hours. How many hours does it take machines X and Y, working simultaneously, to produce 12k bottles?
(A) 8(B) 12(C) 15(D) 18(E) 24------------------------------------------------------------------------------------------------------------------------------------【答案】D
【思路】設花N小時
------------------------------------------------------------------------------------------------------------------------------------
178.19473-!-item-!-187;#058&012640[?]
Isaac can purchase a certain item in four different ways, as shown in the table. What is the lowest price for which he can purchase this item?
(A) $88.10(B) $89.00(C) $89.10(D) $89.50(E) $90.00
179.19627-!-item-!-187;#058&012670The number of years of service of the eight employees in a production department are 15, 10, 9, 17, 6, 4, 14, and 16. What is the range in the number of years of service of the eight employees?
(A) 10(B) 11(C) 12(D) 13(E) 14------------------------------------------------------------------------------------------------------------------------------------【答案】D【思路】RANGE=最大減最小=17-4=13------------------------------------------------------------------------------------------------------------------------------------
180.19674-!-item-!-187;#058&012673Bob invested $2,000 in fund A and $1,000 in fund B. Over the next two years, the money in fund A earned a total interest of 12 percent for the two years combined and the money in fund B earned 30 percent annual interest compounded annually. Two years after Bob made these investments, Bob's investment in fund A was worth how much more than his investment in fund B ?
(A) $500(B) $550(C) $600(D) $650(E) $700------------------------------------------------------------------------------------------------------------------------------------【答案】B
【思路】------------------------------------------------------------------------------------------------------------------------------------
181.19721-!-item-!-187;#058&012675The distributor of cases of a certain beverage charges $60 per case for orders of 1 to 5 cases, $50 per case for orders of 6 to 20 cases, and $45 per case for orders of more than 20 cases. If the distributor filled three orders, one for 3 cases of the beverage, one for 11 cases of the beverage, and one for 30 cases of the beverage, what was the total amount the distributor charged for the orders?
(A) $1,960(B) $2,000(C) $2,040(D) $2,080(E) $2,120------------------------------------------------------------------------------------------------------------------------------------【答案】D
【思路】------------------------------------------------------------------------------------------------------------------------------------
182.19767-!-item-!-187;#058&012676Two members of a club are to be selected to represent the club at a national meeting. If there are 190 different possible selections of the 2 members, how many members does the club have?
(A) 20(B) 27(C) 40(D) 57(E) 95------------------------------------------------------------------------------------------------------------------------------------【答案】A
【思路】 設N個member
------------------------------------------------------------------------------------------------------------------------------------
183.19813-!-item-!-187;#058&012836A certain company had an annual profit of $15 million in 1998 and an annual profit of $20 million in 1999. In 2000 the company had an annual loss of $5 million. What was the company's average (arithmetic mean) annual profit for the 3 years?
(A) $5 million(B) $10 million(C) $13 million(D) $20 million(E) $25 million------------------------------------------------------------------------------------------------------------------------------------【答案】B
【思路】
------------------------------------------------------------------------------------------------------------------------------------
184.19859-!-item-!-187;#058&012871For each hour at his part-time job, Jack is paid $0.05 per box for the first 100 boxes of apples packed and $0.07 for each additional box of apples packed. If Jack packed 125 boxes of apples in one hour, how much was he paid for that hour?
(A) $6.25(B) $6.75(C) $7.00(D) $7.50
(E) $8.75------------------------------------------------------------------------------------------------------------------------------------【答案】B
【思路】------------------------------------------------------------------------------------------------------------------------------------
185.19906-!-item-!-187;#058&012893If the probability that event S will not occur is 1 - y, then the probability that event S will occur is
(A) y^2 - 1(B) y^2(C) y/2 (D) y - 1(E) y------------------------------------------------------------------------------------------------------------------------------------【答案】E【思路】不會發生機率1-Y 會發生機率=1-不會發生機率=1-(1-Y)=Y------------------------------------------------------------------------------------------------------------------------------------
186.20012-!-item-!-187;#058&012968[?]
The table shows the number of residents in a certain development who are willing to contribute to build a swimming pool, provided the required contribution does not exceed the amount indicated by the resident. The following three amounts are being considered as the required contribution. Which would ensure that more than half of the residents contribute to build the pool? (A) None(B) I only(C) II only(D) I and II only(E) I, II, and III
187.20058-!-item-!-187;#058&012969According to a financial analyst, if Company C sets the unit selling price of its product at x dollars, then its monthly profit P, in dollars, is given by the formula P = 1,000(4x - x^2 - 2). According to this formula, at what amount should Company C set the unit selling price of its product so that its monthly profit is $2,000 ?
(A) $1(B) $2(C) $3(D) $4(E) $6------------------------------------------------------------------------------------------------------------------------------------【答案】B
【思路】
------------------------------------------------------------------------------------------------------------------------------------
188.20105-!-item-!-187;#058&012975Helen, Jim, and Ivan each purchased some books at a bookstore. Helen purchased 4 books and Jim purchased 1 book. If the 3 people purchased an average (arithmetic mean) of 2 books
per person, how many books did Ivan purchase?
(A) 1(B) 2(C) 3(D) 4(E) 5------------------------------------------------------------------------------------------------------------------------------------【答案】A
【思路】設買N本
------------------------------------------------------------------------------------------------------------------------------------
189.20151-!-item-!-187;#058&012976Denise made 9 sales calls on Monday, 6 sales calls on Tuesday, 7 sales calls on Wednesday, 9 sales calls on Thursday, and 11 sales calls on Friday. What was the average (arithmetic mean) number of sales calls that Denise made for these 5 days?
(A) 8.4(B) 8.6(C) 8.8(D) 9.0(E) 9.2------------------------------------------------------------------------------------------------------------------------------------【答案】A
【思路】
------------------------------------------------------------------------------------------------------------------------------------
190.20197-!-item-!-187;#058&013023Each day Linda spends 6 hours at her baby-sitting job, for which she is paid $15.00 per hour. In addition, Linda spends a total of 1.5 hours each day, for which she is not paid, traveling to and from the job. What is Linda's hourly rate of pay for the total amount of time that she spends each day at her baby-sitting job and traveling to and from that job?
(A) $7.50(B) $9.00(C) $10.00(D) $10.75(E) $12.00------------------------------------------------------------------------------------------------------------------------------------【答案】E
【思路】
------------------------------------------------------------------------------------------------------------------------------------
191.20243-!-item-!-187;#058&013091A certain class, consisting of a lecture and a question-and-answer session, lasted from 2:45 to 4:30 one afternoon. If the lecture lasted from 2:45 to 4:15, then the question-and-answer session was what fraction of the total class time?
(A) (B) (C) (D) (E)
192.20560-!-item-!-187;#058&013287
[?]
(A) 10(B) 20(C) 40(D) 80(E) 100
193.20876-!-item-!-187;#058&013435In a class of 30 students, 2 students did not borrow any books from the library, 12 students each borrowed 1 book, 10 students each borrowed 2 books, and the rest of the students each borrowed at least 3 books. If the average (arithmetic mean) number of books borrowed per student was 2, what is the maximum number of books that any single student could have borrowed?
(A) 3(B) 5(C) 8(D) 13(E) 15------------------------------------------------------------------------------------------------------------------------------------【答案】D
【思路】
剩10可買 有可能是同一個人買 10+3=13------------------------------------------------------------------------------------------------------------------------------------
194.21030-!-item-!-187;#058&013558One morning Emily recorded the time that it took to read each of her e-mail messages. The times, in seconds, were 32, 18, 20, 29, and 21. How many seconds greater was the average (arithmetic mean) time than the median time?
(A) 1(B) 1.5(C) 2.2(D) 2.5(E) 3------------------------------------------------------------------------------------------------------------------------------------【答案】E
【思路】 中位數為21 24-21=3
------------------------------------------------------------------------------------------------------------------------------------
195.21076-!-item-!-187;#058&013587For all numbers a and b, the operation # is defined by a # b = 2a + 2b + 1. What is the value of 6 # 1 ?
(A) 6(B) 7(C) 13(D) 14(E) 15------------------------------------------------------------------------------------------------------------------------------------【答案】E【思路】a代6 b代1 12+2+1=15------------------------------------------------------------------------------------------------------------------------------------
196.21176-!-item-!-187;#058&013593Company P's cost c, in dollars, of producing n units of a certain product is c = 2.5n + 25,000.
What is the greatest number of units that Company P can produce if the cost of producing these units cannot exceed $200,000 ?
(A) 55,000(B) 60,000(C) 65,000(D) 70,000(E) 75,000------------------------------------------------------------------------------------------------------------------------------------【答案】D
【思路】設N
------------------------------------------------------------------------------------------------------------------------------------
197.21223-!-item-!-187;#058&013681Working at their respective constant rates, machine A makes 100 copies in 12 minutes and machine B makes 150 copies in 10 minutes. If these machines work simultaneously at their respective rates for 30 minutes, what is the total number of copies that they will produce?
(A) 250(B) 425(C) 675(D) 700(E) 750------------------------------------------------------------------------------------------------------------------------------------【答案】D
【思路】
------------------------------------------------------------------------------------------------------------------------------------
Practice Test 2 Problem Solving Keys
1. D 246-!-item-!-187;#058&000117 2. D 509-!-item-!-187;#058&000281 3. E 827-!-item-!-187;#058&000411 4. C 1197-!-item-!-187;#058&000782 5. D 1353-!-item-!-187;#058&000886
6. B 1456-!-item-!-187;#058&000991 7. B 1502-!-item-!-187;#058&001086 8. C 1608-!-item-!-187;#058&001224 9. C 1662-!-item-!-187;#058&002391 10. B 1708-!-item-!-187;#058&002411
11. E 1971-!-item-!-187;#058&002527 12. D 2238-!-item-!-187;#058&002618 13. E 2392-!-item-!-187;#058&002762 14. D 2546-!-item-!-187;#058&002908 15. D 2647-!-item-!-187;#058&002944
16. E 2698-!-item-!-187;#058&002953 17. E 2747-!-item-!-187;#058&002959 18. B 2793-!-item-!-187;#058&002984 19. B 2896-!-item-!-187;#058&003100 20. C 2942-!-item-!-187;#058&003104
21. D 2988-!-item-!-187;#058&003110 22. C 3254-!-item-!-187;#058&003229 23. C 3470-!-item-!-187;#058&003305 24. B 3573-!-item-!-187;#058&003330 25. C 3619-!-item-!-187;#058&003382
26. E 3669-!-item-!-187;#058&003387 27. D 3721-!-item-!-187;#058&003433 28. B 3770-!-item-!-187;#058&003486 29. A 3873-!-item-!-187;#058&003594 30. D 4244-!-item-!-187;#058&003828
31. D 4295-!-item-!-187;#058&003848 32. C 4504-!-item-!-187;#058&003922 33. E 4550-!-item-!-187;#058&003924 34. B 4707-!-item-!-187;#058&003966 35. A 4808-!-item-!-187;#058&003979
36. A 5018-!-item-!-187;#058&004104 37. A 5174-!-item-!-187;#058&004144 38. C 5275-!-item-!-187;#058&004179 39. B 5378-!-item-!-187;#058&004220 40. E 5532-!-item-!-187;#058&004320
41. E 5689-!-item-!-187;#058&004421 42. D 5737-!-item-!-187;#058&004537 43. D 5837-!-item-!-187;#058&004612 44. A 5884-!-item-!-187;#058&004663 45. E 5933-!-item-!-187;#058&004664
46. C 5979-!-item-!-187;#058&004694 47. C 6025-!-item-!-187;#058&004767 48. D 6071-!-item-!-187;#058&004779 49. E 6121-!-item-!-187;#058&004785 50. C 6173-!-item-!-187;#058&004786
51. C 6219-!-item-!-187;#058&004789 52. A 6267-!-item-!-187;#058&004794 53. B 6313-!-item-!-187;#058&004799 54. C 6364-!-item-!-187;#058&004806 55. D 6410-!-item-!-187;#058&004809
56. D 6461-!-item-!-187;#058&004810 57. B 6510-!-item-!-187;#058&004845 58. A 6618-!-item-!-187;#058&004870 59. C 6664-!-item-!-187;#058&004887 60. C 6711-!-item-!-187;#058&004926
61. B 6814-!-item-!-187;#058&004969 62. E 7185-!-item-!-187;#058&005078 63. B 7231-!-item-!-187;#058&005082 64. E 7285-!-item-!-187;#058&005104 65. D 7385-!-item-!-187;#058&005343
66. A 7431-!-item-!-187;#058&005458 67. B 7481-!-item-!-187;#058&005467 68. E 7638-!-item-!-187;#058&005506 69. A 8008-!-item-!-187;#058&005955 70. C 8217-!-item-!-187;#058&006107
71. E 8372-!-item-!-187;#058&006254 72. E 8421-!-item-!-187;#058&006278 73. B 8467-!-item-!-187;#058&006379 74. D 8516-!-item-!-187;#058&006446 75. C 8673-!-item-!-187;#058&006582
76. C 8721-!-item-!-187;#058&006602 77. B 8876-!-item-!-187;#058&006751 78. E 9309-!-item-!-187;#058&006922 79. E 9358-!-item-!-187;#058&006924 80. E 9407-!-item-!-187;#058&006938
81. A 9454-!-item-!-187;#058&006950 82. A 9500-!-item-!-187;#058&006955 83. B 9550-!-item-!-187;#058&006969 84. D 9603-!-item-!-187;#058&006986 85. A 9649-!-item-!-187;#058&007038
86. A 9697-!-item-!-187;#058&007051 87. D 9743-!-item-!-187;#058&007054 88. A 9789-!-item-!-187;#058&007104 89. E 9835-!-item-!-187;#058&007168 90. B 10100-!-item-!-187;#058&007272
91. D 10146-!-item-!-187;#058&007291 92. D 10192-!-item-!-187;#058&007298 93. E 10238-!-item-!-187;#058&007360 94. E 10284-!-item-!-187;#058&007376 95. E 10331-!-item-!-187;#058&007378
96. D 10378-!-item-!-187;#058&007391 97. D 10424-!-item-!-187;#058&007444 98. E 10475-!-item-!-187;#058&007489 99. E 10524-!-item-!-187;#058&007561100. A 10681-!-item-!-187;#058&007619
101. C 10730-!-item-!-187;#058&007650102. A 10776-!-item-!-187;#058&007653103. C 10822-!-item-!-187;#058&007696104. C 10868-!-item-!-187;#058&007697105. D 10917-!-item-!-187;#058&007716
106. A 10964-!-item-!-187;#058&007770107. D 11013-!-item-!-187;#058&007796108. B 11175-!-item-!-187;#058&007894109. B 11276-!-item-!-187;#058&008007110. E 11325-!-item-!-187;#058&008034
111. C 11378-!-item-!-187;#058&008123112. D 11750-!-item-!-187;#058&008431113. C 11853-!-item-!-187;#058&008463114. C 11899-!-item-!-187;#058&008467115. C 12001-!-item-!-187;#058&008506
116. B 12050-!-item-!-187;#058&008561117. E 12100-!-item-!-187;#058&008590118. B 12146-!-item-!-187;#058&008756119. E 12192-!-item-!-187;#058&008830120. C 12241-!-item-!-187;#058&008920
121. D 12343-!-item-!-187;#058&009002122. D 12443-!-item-!-187;#058&009133123. D 12489-!-item-!-187;#058&009157124. D 12535-!-item-!-187;#058&009197125. A 12583-!-item-!-187;#058&009318
126. D 12631-!-item-!-187;#058&009380127. D 12731-!-item-!-187;#058&009562128. C 12783-!-item-!-187;#058&009601129. C 12829-!-item-!-187;#058&009608130. D 12875-!-item-!-187;#058&009671
131. E 12921-!-item-!-187;#058&009694132. E 13076-!-item-!-187;#058&009801133. C 13123-!-item-!-187;#058&009850134. B 13169-!-item-!-187;#058&009883135. A 13220-!-item-!-187;#058&009935
136. B 13320-!-item-!-187;#058&009993137. E 13366-!-item-!-187;#058&010014138. C 13412-!-item-!-187;#058&010022139. E 13466-!-item-!-187;#058&010025140. A 13512-!-item-!-187;#058&010037
141. A 13558-!-item-!-187;#058&010099142. C 13607-!-item-!-187;#058&010106143. B 13707-!-item-!-187;#058&010123144. B 13921-!-item-!-187;#058&010164145. D 13967-!-item-!-187;#058&010235
146. E 14067-!-item-!-187;#058&010315147. C 14926-!-item-!-187;#058&010459148. D 15080-!-item-!-187;#058&010499149. A 15127-!-item-!-187;#058&010506150. B 15173-!-item-!-187;#058&010507
151. B 15220-!-item-!-187;#058&010594
152. D 15432-!-item-!-187;#058&010733153. E 15587-!-item-!-187;#058&010762154. C 15633-!-item-!-187;#058&010772155. B 16166-!-item-!-187;#058&010984
156. E 16266-!-item-!-187;#058&011027157. A 16315-!-item-!-187;#058&011053158. C 16365-!-item-!-187;#058&011058159. D 16573-!-item-!-187;#058&011089160. D 16619-!-item-!-187;#058&011092
161. B 16989-!-item-!-187;#058&011313162. D 17416-!-item-!-187;#058&011441163. B 17463-!-item-!-187;#058&011464164. B 17509-!-item-!-187;#058&011499165. C 17668-!-item-!-187;#058&011589
166. B 17879-!-item-!-187;#058&011634167. A 18146-!-item-!-187;#058&011731168. B 18192-!-item-!-187;#058&011758169. E 18239-!-item-!-187;#058&011831170. B 18339-!-item-!-187;#058&011871
171. D 18385-!-item-!-187;#058&011883172. C 18647-!-item-!-187;#058&012110173. C 18801-!-item-!-187;#058&012255174. C 18908-!-item-!-187;#058&012310175. B 19062-!-item-!-187;#058&012458
176. A 19324-!-item-!-187;#058&012548177. D 19424-!-item-!-187;#058&012637178. B 19473-!-item-!-187;#058&012640179. D 19627-!-item-!-187;#058&012670180. B 19674-!-item-!-187;#058&012673
181. D 19721-!-item-!-187;#058&012675182. A 19767-!-item-!-187;#058&012676183. B 19813-!-item-!-187;#058&012836184. B 19859-!-item-!-187;#058&012871185. E 19906-!-item-!-187;#058&012893
186. D 20012-!-item-!-187;#058&012968187. B 20058-!-item-!-187;#058&012969188. A 20105-!-item-!-187;#058&012975189. A 20151-!-item-!-187;#058&012976190. E 20197-!-item-!-187;#058&013023
191. A 20243-!-item-!-187;#058&013091192. A 20560-!-item-!-187;#058&013287193. D 20876-!-item-!-187;#058&013435194. E 21030-!-item-!-187;#058&013558195. E 21076-!-item-!-187;#058&013587
196. D 21176-!-item-!-187;#058&013593197. D 21223-!-item-!-187;#058&013681