(A) (1, 2) (B) (2, 1) (C) (1, 1) (D) (2, 2) (E) (1, 3)
------------------------------------------------------------------------------------------------------------------------------------ 【答案】A 【思路】1.2x2xy42y?23=> x+y=3 2.33?3 =>聯立方程式得知 (x,y)=(1,2)
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83. 9550-!-item-!-187;#058&006969
{-10, -6, -5, -4, -2.5, -1, 0, 2.5, 4, 6, 7, 10}
A number is to be selected at random from the set above. What is the probability that the number selected will be a solution of the equation (x - 5)(x + 10)(2x - 5) = 0 ?
(A) (B) (C) (D) (E)
84. 9603-!-item-!-187;#058&006986
For all numbers x such that x [?] 1, if g(x) is defined by [?], then
(A) (B) (C) (D) (E)
85. 9649-!-item-!-187;#058&007038
Of the 800 employees of Company X, 70 percent have been with the company for at least ten years. If y of these \would reduce the percent of \
(A) 200 (B) 160 (C) 112 (D) 80 (E) 56
------------------------------------------------------------------------------------------------------------------------------------ 【答案】A 【思路】設y為 老員工的離職數 => (560?y)(800?y) = 0.6 => 0.4y=80 => y=200 ------------------------------------------------------------------------------------------------------------------------------------
86. 9697-!-item-!-187;#058&007051
The ratio of the amount of Alex's fuel oil bill for the month of February to the amount of his fuel oil bill for the month of January was [?]. If the fuel oil bill for February had been $40 more, the corresponding ratio would
have been . How much was Alex's fuel oil bill for January?
(A) $240 (B) $300 (C) $360 (D) $450 (E) $540
87. 9743-!-item-!-187;#058&007054
A television manufacturer produces 600 units of a certain model each month at a cost to the manufacturer of $90 per unit and all of the produced units are sold each month. What is the minimum selling price per unit that will ensure that the monthly profit (revenue from sales minus the manufacturer's cost to produce) on the sales of these units will be at least $42,000 ?
(A) $110 (B) $120 (C) $140 (D) $160 (E) $180
------------------------------------------------------------------------------------------------------------------------------------ 【答案】D 【思路】最少的賣價以獲有$42,000 ，則單賣價為=單成本+單利潤 => 90 + 42000= 160 600------------------------------------------------------------------------------------------------------------------------------------
88. 9789-!-item-!-187;#058&007104
In May Mrs. Lee's earnings were 60 percent of the Lee family's total income. In June Mrs. Lee earned 20 percent more than in May. If the rest of the family's income was the same both months, then, in June, Mrs. Lee's earnings were approximately what percent of the Lee family's total income?
(A) 64% (B) 68% (C) 72% (D) 76% (E) 80%
------------------------------------------------------------------------------------------------------------------------------------ 【答案】A 【思路】假設Lee全家所得為x, 則五月份Lee單所得 0.6x, 其他所得為0.4x。六月份Lee單所得為: 0.72x (o.6*1.2)，所以六月份Lee所得佔全家所得的百分比為: 0.72x0.72x?0.4x=0.64 -------------------------------------------------------------------------------------------------------------
89. 9835-!-item-!-187;#058&007168
For one toss of a certain coin, the probability that the outcome is heads is 0.6. If this coin is tossed 5 times, which of the following is the probability that the outcome will be heads at least 4 times?
(A) (0.6)^5 (B) 2(0.6)^4
(C) 3(0.6)^4(0.4)
(D) 4(0.6)^4(0.4) + (0.6)^5 (E) 5(0.6)^4(0.4) + (0.6)^5
------------------------------------------------------------------------------------------------------------------------------------ 【答案】E
【思路】最少有四次的頭表示 : 四次有頭的機率(不管順序) + 五次全頭的機率 =(0.6)455+(0.6) ?0.4?C4-------------------------------------------------------------------------------------------------------------
90. 10100-!-item-!-187;#058&007272 [?]
If [?] and [?] represent single digits in the correctly worked computation above, what is the value of [?] + [?] ?
(A) 7 (B) 9 (C) 10 (D) 11 (E) 13
91. 10146-!-item-!-187;#058&007291
A certain car averages 25 miles per gallon of gasoline when driven in the city and 40 miles per gallon when driven on the highway. According to these rates, which of the following is closest to the number of miles per gallon that the car averages when it is driven 10 miles in the city and then 50 miles on the highway?
(A) 28 (B) 30 (C) 33 (D) 36 (E) 38
--------------------------------------------------------------------------------------------------------------------------------- 【答案】D
10【思路】在city每開25mile要耗1gallon的油 ? 開10mile要耗25gallon的油 50 在highway每開40mile要耗1gallon的油 ? 開50mile要耗40gallon的油
(50?10)?36.5....1050(?) 由此可知平均為 2540
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92. 10192-!-item-!-187;#058&007298
On his drive to work, Leo listens to one of three radio stations, A, B, or C. He first turns to A. If A is playing a song he likes, he listens to it; if not, he turns to B. If B is playing a song he likes, he listens to it; if not, he turns to C. If C is playing a song he likes, he listens to it; if not, he turns off the radio. For each station, the probability is 0.30 that at any given moment the station is playing a song Leo likes. On his drive to work, what is the probability that Leo will hear a song he likes?
(A) 0.027 (B) 0.090 (C) 0.417 (D) 0.657
(E) 0.900
--------------------------------------------------------------------------------------------------------------------------------- 【答案】D
【思路】Pr(Leo聽到喜歡的歌) = 1 – Pr(ABC三台都沒有Leo喜歡的歌) = 1 – (0.73)3 = 0.657
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93. 10238-!-item-!-187;#058&007360
If $1,000 was invested at an annual interest rate of 5.6 percent compounded annually, which of the following represents the amount the investment was worth after 3 years?
(A) $1,000(1.056)(3) (B) $1,000(3 + 1.056) (C) $1,000[1 + 3(0.056)] (D) $1,000[1 + (0.056)^3] (E) $1,000(1.056)^3
--------------------------------------------------------------------------------------------------------------------------------- 【答案】E
期數
【思路】複利計息時，本利和 = 本金 x (1 + 利率) = 1,000 x (1.056)3
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94. 10284-!-item-!-187;#058&007376
A certain candy manufacturer reduced the weight of Candy Bar M by 20 percent but left the price unchanged. What was the resulting percent increase in the price per ounce of Candy Bar M ?
(A) 5% (B) 10% (C) 15% (D) 20% (E) 25%
--------------------------------------------------------------------------------------------------------------------------------- 【答案】E
【思路】價格不變，商品重量卻減為原來的80%，可知價格變成1 / 0.8 = 1.25，漲了25%
P (正式解法：若設商品價格為x元，原來的商品重量為M盎司，則每盎司的價錢就是M。
PP?1.25M，可知每盎司價格漲了25%。) 減重為80%後，每盎司的價錢就成了0.8M---------------------------------------------------------------------------------------------------------------------------------
95. 10331-!-item-!-187;#058&007378
The total of Company C's assets in 1994 was 300 percent greater than the total in 1993, which in turn was 400 percent greater than the total in 1992. If the total of Company C's assets in 1992 was N dollars, which of the following represents the total of Company C's assets, in dollars, in 1994 ?
(A) 7N (B) 8N (C) 9N (D) 12N (E) 20N
--------------------------------------------------------------------------------------------------------------------------------- 【答案】E
【思路】文字題，注意文字敘述上的陷阱。
“assets in 1994 was 300 percent greater than the total in 1993” 意指前者「超過」後者三倍，所以1994年的資產是1993年的4倍，不是3倍。同理1993年的資產則是1992年的5倍(不是4倍)。因此1994年的資產是1992年的 4 x 5 = 20倍。
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96. 10378-!-item-!-187;#058&007391
The contents of a certain box consist of 14 apples and 23 oranges. How many oranges must be removed from the box so that 70 percent of the pieces of fruit in the box will be apples?
(A) 3 (B) 6 (C) 14 (D) 17 (E) 20
--------------------------------------------------------------------------------------------------------------------------------- 【答案】D
【思路】最初盒中的水果一共有14 + 23 = 37個，
14設應該取走的橘子是x個，可知取走橘子以後蘋果占盒中水果的比例是37?X，需為70%。
14?0.7因此37?X ，解得 x = 17。
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97. 10424-!-item-!-187;#058&007444
Each unit of a certain product costs a manufacturer $9 to produce. The manufacturer sells the product in boxes of 50 units for $560 per box. How many boxes of the product does the manufacturer need to sell to yield a profit of $110,000 ?
(A) 90 (B) 100 (C) 900 (D) 1,000 (E) 1,100
------------------------------------------------------------------------------------------------------------------------------------ 【答案】D 【思路】
the cost of every box is 9×50=450,
therefore the profit of every box is 560-450=110 560-9×50=110000/110=1000(box)
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98. 10475-!-item-!-187;#058&007489
An athlete runs R miles in H hours, then rides a bicycle Q miles in the same number of hours. Which of the following represents the athlete's average speed, in miles per hour, for these two activities combined?
(A) (B) (C) (D) (E)
99. 10524-!-item-!-187;#058&007561 [?]
For the numbers on the number line above, which of the following statements is true?
(A) x + y > y (B) xz > xy (C) tz < z (D) mu < 0 (E) tm > 0