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台北四戰 Q51 V2x 失敗...
AA: The following appeared in a memorandum from the development director of the
Largo Piano Company.
“The Largo Piano Company has long been known for producing carefully
handcrafted, expensive pianos used by leading concert pianists. During the past
few years, however, our revenues have declined; meanwhile, the Allegro Musical
Instrument Company introduced a line of inexpensive digital pianos and then saw
its revenues increase. In order to increase Largo’s sales and in fact outsell Allegro, we
should introduce a line of digital pianos in a variety of price ranges. Our
digital pianos would be likely to find instant acceptance with customers, since
they would be associated with the prestigious Largo
name.” AI: “Businesses and other
organizations have overemphasized the importance of working as a team. Clearly,
in any human group, it is the strong individual, the person with the most
commitment and energy, who gets things done.”
原數學JJ補充&糾正: 46. (PS) known that a&b are integers, a-b and a/b are both evens, ask which of following must be odd? (A) a/2 (B) b/2 (C) (a+b)/2 (D) (a+2)/2 (E) (b+2)/2 解: 這題花了我最久時間, 最後選錯了. 正確答案應該是 (a+2)/2 先看a/b=even=2n, 得a=2nb, 可知a為偶數, b可偶可奇 再看a-b=even, 可知a, b同偶或同奇, 結合上述條件, 得a, b皆為偶數, 設b=2m 得出a=2nb=4nm, 表示a為4的倍數 答: (a+2)/2=(4nm+2)/2=2nm+1, 一個偶數+1必為奇數.
62. (DS) a, b為非負整數(nonnegative), 問√(a+b)=√a+√b是否成立? (1) (a+b)^2=a^2+b^2 (2) (a+b)^3=a^3+b^3 答: 選D
72. (DS)拋硬幣試驗possibility of toss，正反兩面head and tail的概率不相等，問拋兩次each of two tosses都是head的概率？
(1) 拋一次, 是head的概率是出現tail機率的2倍 (2) 拋兩次，一次head且一次tail的概率是4/9 解：設每次toss中head的概率為p, 題中問的是能否知道p2。
條件1 sufficient 條件2的機率是2*p*(1-p)=4/9, 解出p=1/3 or
2/3, 無法得知是head or tail的機率. Insufficient
答: 選A
90. (DS) 某公司招聘管理人員，應徵者有Business Administration學位的人, 也有會西班牙語的，請問會西班牙語的人總共有多少? (1) 有Business Administration學位的人佔全部的4/5 (2) 擁有Business Administration學位的人裡面, 1/4會西班牙語 答: 選E (因為不知道non-MBA的人裡面多少人會西班牙語)
92. 定義Terminating decimal為有限小數. 問c/d是terminating decimal嗎? (忘記題目是否有限定c, d的範圍) (1) c is a factor of 60 (2) d is a factor of 250 答: 當時選的是B (因為分母沒有9, 不會產生無限循環小數) 請再多注意c, d的屬性範圍, 可以確定的是題目”沒有”提到有理數, 無理數之類的字眼 (rational, irrational numbers)
NEW JJ: 1. (DS) 某個數x有n-digits, 問能否知道x^2的digits數? (1) n=2 (2) 2x有3 digits 答: 選C
2. (PS) 某公司1984年的獲利為1994年獲利的83又1/3%, 問從1984年到1994年獲利增加了多少%? 答: 20%
3. (PS) 某公司在1990年的profits為3 millions, 2000年時profits為6 millions. 此外, 2000年的revenues比1990年多了20%, 2000年的expenses比1990年少了10%, 問1990年的expenses為多少? (A) 7 millions (B) 7.5 millions (C) 8 millions (D) 8.5 millions (E) 9 millions 答: 8 millions
4. (PS) List S包含了integers consist of 1 to 103, 問List S裡的數median為多少? 答: 52
5. (PS) x^4可以被81整除, 問x被9除可能的餘數為? (A) 1 (B) 2 (C) 4 (D) 6 (E) 8 答: 6
6. (PS) 某物體行進的速度是14.3km per hour, 問它的速度為多少miles per second (rounded to the nearest tenths)? (題目附註1 km
= 0.6 miles) (A) 0.002 (B) 0.004 (C) 0.152 (D) 0.254 (E) 0.368 [數字不確定] 答: 0.002
7. (PS) 某機器R製造chips的速度為3 chips/per 2 minutes, 機器S製造chips的速度為9 chips/per 5 minutes, 假設兩台機器速度維持constant, 各製造了450 chips, how many more hours or how many less hours did R take than S? (A) 20 minutes less (B) 50 minutes less (C) 70 minutes less (D)50 minutes more (E) 70 minutes more 答: 50 minutes “more” 注意別選錯了! 8. (PS) 某水果站(fruit stand)賣apple一個50 cents, 也賣orange一個60 cents, 某人買了apple與orange總共10個, 這10個水果價錢的arithmetic average是56, 問某人需要放回多少個orange, 才能使得arithmetic average為52? 答: 5個
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