※ 引述《hankboy ( 身體健康)》之銘言： : 作OG2題目發現了一些問題，但是怎麼想也想不出解答，懇請大大們指導，謝謝 : 1. List l consists of the numbers 1, 根號2, x and x平方, where x> 0, and the : range of the numbers in list L is 4. 求大小。 : Quantity A Quantity B : X 2 : Ans: A : 想請教，x不是應該是>0, 平方最大值為4的任何數皆可能嗎？ 為什麼X 會大於2 range指的是全距(最大值-最小值) because x > 0, if x is the greast number, then 0 < x < 1, contradicting to the fact that the range of the numbers in list L is 4. Hence, x^2 must be the greast number, and so x^2-1 = 4 => x=√5 (∵ x > 0) ∴ x > 2 : 2. 10,10,10,10,8,8,8,8,12,12,11,y. The twelve numbers shown represent the : ages, in years, of the twelve hourses on a certain city block. What is the : median age, in years, of the twelve houses on the block? : Ans 10 按順序 8,8,8,8,10,10,10,10,11,12,12 還有y 中位數位在 (12+1)/2=6.5 即四個10中間 if y=10, 沒什麼好討論的 if y > 10 or y < 10, 很清楚的一樣不影響中位數的位置 所以 median = (10+10)/2 = 10. : 3. The quantities S and T are positive and are related by the equation S = : K/T, where K is a constant. If the value of S increases by 50 percent, then : the value of T decreases by what percent? : (A) 25% : (B) 33 1/3% : (C) 50% : (D) 66 2/3% : (E) 75% : Ans: B S=K/T => K=ST ...(*) ∵ K is constant if S increases by 50 percent, then (*) becomes K= (1.5 S) (T/1.5) =: S' T', where S'=(1.5 S), T'= T/1.5 = (2/3)T = (0.666...) T ≒ (1-33 1/3%)T. Hence we choose (B). : 4. The probality that both events E and F will occur is 0.42. : Quantity A Quantity B : The probability that event E will occur 0.58 : Ans: D不一定 By the formula, P(E∪F) = P(E) + P(F) - P(E∩F) Without loss of generality, we may assume that P(E∪F) = 1, (Of course, the assumption is not strict) then P(E) + P(F) = 1 - 0.42 = 0.58. So, we may have P(F)=0 and P(E)=0.58, P(F) = 0.58 and P(E) = 0, and so on. Hence we choose (D) : 5. If a is the smallest prime number greater than 21 and b is the largest : prime number less than 16, than ab = : (A) 299 : (B) 323 : (C) 330 : (D) 345 : (E) 351 : Ans: A a is the smallest prime number(質數) greater than 21 => a = 23 b is the largest prime number less than 16 => b = 13 ab=299 ... : 6. For the 3 numbers in a list, the average (arithmetic mean) and the median : are equal to 8. if the greast number in the list is 10 greater than the least : number, what is the greast number in the list? : 此題沒找到解答，想請問該如何解？ Assume the three numbers are x , 8 , x+10. Then (x+8+x+10)/3 = 8 => x = 3 Hence the greast number in the list is x+10=13 --

※ 發信站: 批踢踢實業坊(ptt.cc) ◆ From: 111.248.237.12 ※ 編輯: victor0410 來自: 111.248.237.12 (08/19 22:48) ※ 編輯: victor0410 來自: 111.248.237.12 (08/19 22:48)