【正文】 PP Problem Solving1 (PS1) 完整詳解版 Practice Test 1 Problem Solving (196 Questions) 1. 409!item!187。058amp。000306 A grocery store purchased crates of 40 oranges each for $ per crate and then sold each orange for $. What was the store39。s gross profit on each crate of oranges? (A) $ (B) $ (C) $ (D) $ (E) $ 【答案】 A 【思路】 revenue=cost+profit, 假設 X為 the store39。s gross profit on each crate of oranges (sold each orange for $)=5( per crate)+X 8=5+X, X=3 2. 455!item!187。058amp。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(shù) ”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 9p55),故答案 E 3. 664!item!187。058amp。000504 A certain taxi pany charges $ for the first [?] of a mile plus $ for each additional of a mile. What would this pany charge for a taxi ride that was 8 miles long? (A) $ (B) $ (C) $ (D) $ (E) $ 4. 765!item!187。058amp。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(shù)下來第 20個剛好在由下往上數(shù)第 16個的下面 → 上面數(shù)下來第 20個是下面數(shù)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。058amp。000553 If , then m = (A) 17 (B) 18 (C) 34 (D) 35 (E) 36 6. 859!item!187。058amp。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。058amp。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】 50( 100 ) 1 ( 2 4 6 .. . 100 ) 1 2 50 ! 1h ? ? ? ? ? ? ? ? ? ? 假設 h(100)+1最小因數(shù)是 n , n50 例如 47好了 , 既然 47是因數(shù) , 他就能整除 h(100)+1 可是發(fā)現(xiàn) h(100)裡面有 47的因數(shù) ,可以整除 那 h(100)+1被 47除的餘數(shù)為 1,表示 47不是 h(100)+1的因數(shù) 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(shù)是 h(100)的 factor,那就不會是 h(100)+1的 factor ,因為餘數(shù)會是 1 8. 1221!item!187。058amp。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 (E) 25 【答案】 D 【思路】假設 w=the probability of white rose, r= the probability of red rose 230 30wr?? 又 w+r=30,得 w=20 9. 1700!item!187。058amp。001066 Last year the range of the annual salaries of the 100 employees at Company X was $30,000. If the annual salary of each of the 100 employees this year is 10 percent greater than it was last year, what is the range of the annual salaries of the 100 employees this year? (A) $27,000 (B) $30,000 (C) $33,000 (D) $36,000 (E) $63,000 【答案】 C 【思路】 Last year the range of the annual salaries of the 100 employees at Company X＝ 30,000（假設最大 annual salaries=50,000,最小 annual salaries=20,000） 又今年比去年 annual salary漲 10％ 表示 the range of the annual salaries of the 100 employees this year=50,000x()20,000x()=33,000 10. 1746!item!187。058amp。002343 If a = 7 and b = 7, what is the value of 2a 2b + b^2 ? (A) 49 (B) 21 (C) 49 (D) 63 (E) 77 【答案】 E 【思路】代入法 , 222a b b?? 22 7 2 ( 7 ) ( 7 )? ? ? ? ? ? ? =14+14+49=77 11. 1799