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各位，本人在做PREP数学的时候汇总了一些难题，现发出来请大家一起讨论一下，正确答案在每题的边上都可以找到！ 请各位高手对自己感兴趣的题目进行分析求解，大家彼此交流一下解题思路！ 55. 4687-!-item-!-187;#058&004202 C Malik's recipe for 4 servings of a certain dish requires 1 cups of pasta. According to this recipe, what is the number of cups of pasta that Malik will use the next time he prepares this dish?
(1) The next time he prepares this dish, Malik will make half as many servings as he did the last time he prepared the dish.
(2) Malik used 6 cups of pasta the last time he prepared this dish.
86. 7767-!-item-!-187;#058&005660 E Each of the students in a certain class received a single grade of P, F, or I. What percent of the students in the class were females?
(1) Of those who received a P, 40 percent were females.
(2) Of those who received either an F or I, 80 percent were males.
90. 8266-!-item-!-187;#058&005947 D On Jane's credit card account, the average daily balance for a 30-day billing cycle is the average (arithmetic mean) of the daily balances at the end of each of the 30 days. At the beginning of a certain 30-day billing cycle, Jane's credit card account had a balance of $600. Jane made a payment of $300 on the account during the billing cycle. If no other amounts were added to or subtracted from the account during the billing cycle, what was the average daily balance on Jane's account for the billing cycle?
(1) Jane's payment was credited on the 21st day of the billing cycle.
(2) The average daily balance through the 25th day of the billing cycle was $540.
137. 14062-!-item-!-187;#058&009802 D If x is an integer, is (x ^2+ 1)(x + 5) an even number?
(1) x is an odd number.
(2) Each prime factor of x ^2is greater than 7.
147. 14800-!-item-!-187;#058&010134 C Each employee on a certain task force is either a manager or a director. What percent of the employees on the task force are directors?
(1) The average (arithmetic mean) salary of the managers on the task force is $5,000 less than the average salary of all employees on the task force.
(2) The average (arithmetic mean) salary of the directors on the task force is $15,000 greater than the average salary of all employees on the task force.
159. 15957-!-item-!-187;#058&010660 C If n is a positive integer and r is the remainder when (n - 1)(n + 1) is divided by 24, what is the value of r ?
(1) n is not divisible by 2.
(2) n is not divisible by 3.
170. 16927-!-item-!-187;#058&010946 B If n and t are positive integers, what is the greatest prime factor of the product nt ?
(1) The greatest common factor of n and t is 5.
(2) The least common multiple of n and t is 105.
196. 19155-!-item-!-187;#058&012165 B How many odd integers are greater than the integer x and less than the integer y ?
(1) There are 12 even integers greater than x and less than y.
(2) There are 24 integers greater than x and less than y.
202. 19528-!-item-!-187;#058&012279 D Each employee of Company Z is an employee of either Division X or Division Y, but not both. If each division has some part-time employees, is the ratio of the number of full-time employees to the number of part-time employees greater for Division X than for Company Z ?
(1) The ratio of the number of full-time employees to the number of part-time employees is less for Division Y than for Company Z.
(2) More than half of the full-time employees of Company Z are employees of Division X, and more than half of the part-time employees of Company Z are employees of Division Y.
214. 20789-!-item-!-187;#058&013258 D The cost of a square slab is proportional to its thickness and also proportional to the square of its length. What is the cost of a square slab that is 3 meters long and 0.1 meter thick?
(1) The cost of a square slab that is 2 meters long and 0.2 meter thick is $160 more than the cost of a square slab that is 2 meters long and 0.1 meter thick.
(2) The cost of a square slab that is 3 meters long and 0.1 meter thick is $200 more than the cost of a square slab that is 2 meters long and 0.1 meter thick.
217. 21093-!-item-!-187;#058&013542 B
a1, a2, a3,……, a15
In the sequence shown, a n= a n-1 + k, where 2 ≤ n ≤15 and k is a nonzero constant. How many of the terms in the sequence are greater than 10 ?
(1) a1 = 24
(2) a8 = 10
7. 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 E
43. A committee of three people is to be chosen from four married couples. What is the number of different committees that can be chosen if two people who are married to each other cannot both serve on the committee? (A) 16 (B) 24 (C) 26 (D) 30 (E) 32 E
48. A certain city with a population of 132,000 is to be divided into 11 voting districts, and no district is to have a population that is more than 10 percent greater than the population of any other district. What is the minimum possible population that the least populated district could have? (A) 10,700 (B) 10,800 (C) 10,900 (D) 11,000 (E) 11,100 D
59. In the figure above, points P and Q lie on the circle with center O. What is the value of s? (A) 1/2 (B) 1 (C)√2 (D)√3 (E)√2/2 B
68. The number 75 can be written as the sum of the squares of 3 different positive integers. What is the sum of these 3 integers? (A) 17 (B) 16 (C) 15 (D) 14 (E) 13 E
77. At a dinner party, 5 people are to be seated around a circular table. Two seating arrangements are considered different only when the positions of the people are different relative to each other. What is the total number of different possible seating arrangements for the group? (A) 5 (B) 10 (C) 24 (D) 32 (E) 120 C
106. If a certain sample of data has a mean of 20.0 and a standard deviation of 3.0, which of the following values is more than 2.5 standard deviations from the mean? (A) 12.0 (B) 13.5 (C) 17.0 (D) 23.5 (E) 26.5 A
110. The residents of Town X participated in a survey to determine the number of hours per week each resident spent watching television. The distribution of the results of the survey had a mean of 21 hours and a standard deviation of 6 hours. The number of hours that Pat, a resident of Town X, watched television last week was between 1 and 2 standard deviations below the mean. Which of the following could be the number of hours that Pat watched television last week? (A) 30 (B) 20 (C) 18 (D) 12 (E) 6 D
117. 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 C
118. 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 A
7.51 8.22 7.86 8.36 8.09 7.83 8.30 8.01 7.73 8.25 7.96 8.53 121. 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 E
127. 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 the vacation? (A) $200 (B) $300 (C) $400 (D) $500 (E) $600 E
139. A set of 15 different integers has a median of 25 and a range of 25. What is the greatest possible integer that could be in this set? (A) 32 (B) 37 (C) 40 (D) 43 (E) 50 D
143. In a survey of students, each student selected from a list of 12 songs the 2 songs that the student liked best. If each song was selected 4 times, how many students were surveyed? (A) 96 (B) 48 (C) 32 (D) 24 (E) 18 D
175. Before being simplified, the instructions for computing income tax in Country R were to add 2 percent of one's annual income to the average (arithmetic mean) of 100 units of Country R's currency and 1 percent of one's annual income. Which of the following represents the simplified formula for computing the income tax, in Country R's currency, for a person in that country whose annual income is I? (A) 50 + I/200 (B) 50 + 3I/100 (C) 50 + I/40 (D) 100 + I/50 (E) 100 + 3I/100 C
193. A basket contains 5 apples, of which 1 is spoiled and the rest are good. If Henry is to select 2 apples from the basket simultaneously and at random, what is the probability that the 2 apples selected will include the spoiled apple? (A) 1/5 (B) 3/10 (C) 2/5 (D) 1/2 (E) 3/5 C
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