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
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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 V1.0 修正內容 (請標題號) 新增全部詳解 (Q1~Q197) 作者 yuma168 larry.tw Huang Hsin-Yi Penda Engedi mauricew pauline_chiou william0625 abc123 ruru.lu 日期 2008/7/17
Practice Test #2 Problem Solving
(197 Questions)
1. 246-!-item-!-187;#058&000117
Tanya 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&000281
For 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)=10 1 order of $150: 1(3+3)=6 依照題意相減可得4
------------------------------------------------------------------------------------------------------------------------------------ 3. 827-!-item-!-187;#058&000411
A 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】(0.05?100)?(0.04?100)?(0.03?150)?13.5
------------------------------------------------------------------------------------------------------------------------------------
4. 1197-!-item-!-187;#058&000782
If 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&000886
Working 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&001086
A 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)=0.08t ?0.02t=0.6-0.42=0.18 ?t=0.18/0.02=9min
------------------------------------------------------------------------------------------------------------------------------------ 8. 1608-!-item-!-187;#058&001224
In 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&002391
Equal 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&002411
A 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&002527
Which 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&002908