PP-PS1完整详解版-V2[1].0

113. 11514-!-item-!-187;#058&007740 For all positive integers m, m = 3m when m is odd and m = 1/2 m when m is even. Which of the following is equivalent to 9 x 6 ? (A) 81 (B) 54 (C) 36 (D) 27 (E) 18 114. 11561-!-item-!-187;#058&007757

If 0 < x < 1, what is the median of the values x, x-1, x2, √X, and x3 ?

(A) x (B) x-1 (C) x2 (D) √x (E) x3 115. 11608-!-item-!-187;#058&007787

A used-car dealer sold one car at a profit of 25 percent of the dealer's purchase price for that car and sold another car at a loss of 20 percent of the dealer's purchase price for that car. If the dealer sold each car for $20,000, what was the dealer's total profit or loss, in dollars, for the two transactions combined?

(A) $1,000 profit (B) $2,000 profit (C) $1,000 loss (D) $2,000 loss (E) $3,334 loss

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

【思路】 注意題意(題目是說 賺的25% 與賠的 20% 是 dealer's purchase price 而不是 $20,000) 題目是說賣兩台車分別價格都是20,000元，不同之處在於一台車讓car dealer 賺了25%的價差另外一台則賠了20%

設 purchase price 為 賺25%的為a 賠20%的為b

?1?0.25)?a?20,000 ? a= 16,000 ?賺 4000元 ?1?0.2)?b?20,000 ? b=25,000 ?賠5000元

故淨賠1000元 ?答案 C

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A certain junior class has 1,000 students and a certain senior class has 800 students. Among these

students, there are 60 sibling pairs, each consisting of 1 junior and 1 senior. If 1 student is to be selected at random from each class, what is the probability that the 2 students selected will be a sibling pair?

(A) (B) (C) (D) (E)

117. 11706-!-item-!-187;#058&007820

A certain office supply store stocks 2 sizes of self-stick notepads, each in 4 colors: blue, green, yellow, or pink. The store packs the notepads in packages that contain either 3 notepads of the same size and the same color or 3 notepads of the same size and of

3 different colors. If the order in which the colors are packed is not considered, how many different packages of the types described above are possible?

(A) 6 (B) 8 (C) 16 (D) 24 (E) 32

------------------------------------------------------------------------------------------------------------------------------------ 【答案】 C

【思路】 基本的排列組合問題

兩種package 要求 A. same size and the same color

B. same size and 3 different colors A.

C12?C34?8 ?8種組合 C12?C34?8 ?8種組合

B.

總共 8+8=16種組合 ?答案 C

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For a certain examination, a score of 58 was 2 standard deviations below the mean, and a score of 98 was 3 standard deviations above the mean. What was the mean score for the examination?

(A) 74 (B) 76 (C) 78 (D) 80 (E) 82 【答案】 A

【思路】 標準差與平均數的問題，掌握below 跟 above應該輕鬆解題 設 standard deviation為 A

Mean 為 B 可列下列聯立方程式

B?2A?58 解聯立 得 A=8 B=74

B?3A?98? 答案 A

119. 12289-!-item-!-187;#058&008361

The figure shows seven train stations and the distances, in miles, along the railways that connect these stations. Beginning at one of the stations, a train takes 25 hours to travel directly to station W at an average rate of 50 miles per hour. At which of the stations did the train begin?

(A) T (B) U (C) V (D) Y (E) Z 120.

12390-!-item-!-187;#058&008396

Which of the following is closest to the value of

(A) 10 (B) 1 (C) 0.1 (D) 0.01 (E) 0.001 121. 12439-!-item-!-187;#058&008408

A vending machine is designed to dispense 8 ounces of coffee into a cup. After a test that recorded the number of ounces of coffee in each of 1,000 cups dispensed by the vending machine, the 12 listed amounts, in ounces, were selected from the data. If the 1,000 recorded amounts have a mean of 8.1 ounces and a standard deviation of 0.3 ounce, how many of the 12 listed amounts are within 1.5 standard deviations of the mean?

(A) Four (B) Six (C) Nine (D) Ten (E) Eleven 122. 12485-!-item-!-187;#058&008472

Jill, who lives in City C, plans to visit 3 different cities, M, L, and S. She plans to visit each city exactly once and return to City C after the 3 visits. She can visit the cities in any order. In how many different orders can she visit the 3 cities?

(A) 3 (B) 6 (C) 8 (D) 9 (E) 12

------------------------------------------------------------------------------------------------------------------------------------ 【答案】 B

【思路】 排列組合問題

題目說每個城市只能造訪一次 故列式 3! = 1?2?3=6 有6種不同的走法

------------------------------------------------------------------------------------------------------------------------------------ 123. 12532-!-item-!-187;#058&008676

Of the following integers, which is the closest approximation to [?]

(A) 7 (B) 10 (C) 13

(D) 15 (E) 17 124. 12632-!-item-!-187;#058&008905

Of the 12 temporary employees in a certain company, 4 will be hired as permanent employees. If 5 of the 12 temporary employees are women, how many of the possible groups of 4 temporary employees consist of 3 women and 1 man?

(A) 22 (B) 35 (C) 56 (D) 70 (E) 105

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

【思路】排列組合問題

這題看似複雜，其實就是C幾取幾的問題

12個temporary employees裡面包含了7男 5女

題目問說 how many of the possible groups of 4 temporary employees consist of 3 women and 1 man? <在四個temporary employees裡面要有3個女人1個男人的可能為多少組> 因為是組合，每個男女都是一個獨立的個體，故

5C3?C17?70? D

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125. 12681-!-item-!-187;#058&008922

The figure shown represents a piece of land that is in the shape of a quarter circle. If the land is enclosed by a fence, which of the following is closest to the length, in feet, of the fence?

(A) 278 (B) 341 (C) 357 (D) 400 (E) 441 126. 12727-!-item-!-187;#058&008936

Which of the following is equal to the value of 2^5+ 2^5 + 3^5 + 3^5 + 3^5 ?

(A) 5^6 (B) 13^5

(C) 2^6 + 3^6 (D) 2^7 + 3^8 (E) 4^5 + 9^5

------------------------------------------------------------------------------------------------------------------------------------ 【答案】 C

【思路】很簡單的乘法問題

題目 2^5+ 2^5 + 3^5 + 3^5 + 3^5 可以簡化成 2?(2^5)+3?(3^5) ?答案C

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The total cost of a vacation was divided equally among 3 people. If the total cost of the vacation had been divided equally among 4 people, the cost per person would have been $50 less. What was the total cost of