PP-PS1完整详解版-V2[1].0

PP-Problem Solving1 (PS1)

完整詳解版 V2.0

作者: pauline_chiou william0625

gman

yuma168

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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~Q196) 作者 pauline_chiou william0625 gman yuma168 larry.tw edas9101 iamsmall 日期 2008-07-01 V1.1 V2.0 Update Q36,Q51,Q57,Q139,Q142,Q143 5,6,11,13,14,15,17,18,25,28,29,31,37,38,46,47,50,55,56,59,61,62,63,67,72,78,80,83, 87,91,92,93,97,102,103,107,112,113,114,119,120,121,125,128,129,131,133,150,158,162,168,173,176,177,179,182,187,191,190,193, 2008-08-29 2008-11-09

Practice Test #1 Problem Solving

(196 Questions)

1. 409-!-item-!-187;#058&000306

A grocery store purchased crates of 40 oranges each for $5.00 per crate and then sold each orange for $0.20. What was the store's gross profit on each crate of oranges?

(A) $3.00 (B) $6.00 (C) $8.00 (D) $10.00 (E) $13.00

------------------------------------------------------------------------------------------------------------------------------------ 【答案】A

【思路】revenue=cost+profit,

假設X為 the store's gross profit on each crate of oranges 0.2x40 (sold each orange for $0.20)=5( per crate)+X 8=5+X, X=3

------------------------------------------------------------------------------------------------------------------------------------ 2. 455-!-item-!-187;#058&000316

The product P of two prime numbers is between 9 and 55. If one of the prime numbers is greater than 2 but less than 6 and the other is greater than 13 but less than 25, then P =

(A) 15 (B) 33 (C) 34 (D) 46 (E) 51

------------------------------------------------------------------------------------------------------------------------------------ 【答案】E

【思路】前提是p是兩個”質數”的乘積

one of the prime numbers is greater than 2 but less than 6 包含3,5

the other is greater than 13 but less than 25 包含 17,19,23 p 可能為51,57,69,85,95,115 (又9

------------------------------------------------------------------------------------------------------------------------------------ 3. 664-!-item-!-187;#058&000504

A certain taxi company charges $3.10 for the first [?] of a mile plus $0.40 for each additional of a mile. What would this company charge for a taxi ride that was 8 miles long?

(A) $15.60 (B) $16.00 (C) $17.50 (D) $18.70 (E) $19.10 4. 765-!-item-!-187;#058&000550

In a stack of boards at a lumber yard, the 20th board counting from the top of the stack is immediately below the 16th board counting from the bottom of the stack. How many boards are in the stack?

(A) 38 (B) 36 (C) 35 (D) 34 (E) 32

------------------------------------------------------------------------------------------------------------------------------------ 【答案】D

【思路】上面數下來第20個剛好在由下往上數第16個的下面→上面數下來第20個是下面數來第15個 （下面

有14個,上面有19個,在加上中心點那一個 19+14+1＝34

------------------------------------------------------------------------------------------------------------------------------------ 5. 812-!-item-!-187;#058&000553 If , then m =

(A) 17 (B) 18 (C) 34 (D) 35 (E) 36 6. 859-!-item-!-187;#058&000568

The value of is closest to which of the following?

(A) 1 (B) 10 (C) 102 (D) 103 (E) 104 7. 905-!-item-!-187;#058&000575

For every positive even integer n, the function h(n) is defined to be the product of all the even integers from 2 to n, inclusive. If p is the smallest prime factor of h(100) + 1, then p is

(A) between 2 and 10 (B) between 10 and 20 (C) between 20 and 30 (D) between 30 and 40 (E) greater than 40

------------------------------------------------------------------------------------------------------------------------------------ 【答案】E 【思路】h(100)?1?(2?4?6?...?100)?1?250?50!?1 假設h(100)+1最小因數是 n , n<50 例如47好了, 既然47是因數, 他就能整除h(100)+1 可是發現h(100)裡面有47的因數,可以整除 那h(100)+1被47除的餘數為1,表示47不是h(100)+1的因數 同理去想 小於50的其它因式 也是會一樣的結果 所以h(100)+1的因式是在 大於50外 重點在那50!, 假如 小於50的質數是h(100)的factor,那就不會是h(100)+1的factor ,因為餘數會是1 ------------------------------------------------------------------------------------------------------------------------------------ 8. 1221-!-item-!-187;#058&000650

A flower arrangement consists of 30 roses, each of which is either white or red. If a rose is to be selected at random from the flower arrangement, the probability that the rose selected will be white is twice the probability that it will be red. How many white roses are in the flower arrangement?

(A) 5 (B) 10 (C) 15 (D) 20