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1、难题集锦难题集锦 A 1. If j and k are even integers and j , then what is the value of 234? A. 1024 B. 2048 C. 8624 D. 22528 E. cannot be determined by the condition given 13. If 1 100, and 678 $ is a multiple of 4 but not a multiple of 3, then which of the following could be true? Indicate all possible value
2、s. A. n is even B. n is odd C. n is prime D. n is a multiple of 3 E. n is a multiple of 4 14. f, g, h are consecutive prime numbers such that f g h Quantity A Quantity B f + g + h 3g 15. k is a positive integer and 225 and 216 are both divisors of k. If k = 2&3(5* , where a, b and c are positive int
3、egers, what is the least possible value of a + b + c ? A. 4 B. 5 C. 6 D. 7 E. 8 16. x is an integer greater than 3. Quantity A the number of even factors of 2x Quantity B the number of odd factors of 3x 17. In how many ways can 16 different gifts be divided among four children such that each child r
4、eceives exactly four gifts? A. 16= B. (4!)= C. 16!/ (4!)= D. 16!/4! E. 4BC 18. If 867B+ 86= 36, then n = A. 1/3 B. 1/2 C. 3/5 D. 2/3 E. 4/5 19. If 55 percent of a group of people have brown hair and 80 percent of the same group do not have red hair, whats the fraction of those who do not have brown
5、hair have red hair? A. 1/4 B. 4/11 C. 4/9 D. 5/9 E. 4/5 20. Last year Melania had a total of $20000 invested in two mutual funds, Capital Growth Fund and Venture Index Fund. At the end of the year, she analyzed her investments and found that her earnings on her shares of Capital Growth Fund were thr
6、ee times half of her earnings on her investment in Venture Index Fund. If she earned a total of $1250 on her investments in the two funds, and had three times as much money invested in Capital Growth Fund as in Venture Index Fund, what percent interest did Melania earn on her investment in Venture I
7、ndex Fund? A. 0.075 B. 0.01 C. 7.5 D. 10 E. 500 21. The function f is defined by f(27$ $ )=3$-x+5 Quantity A: f (4) Quantity B: 75 22. Quantity A: 180+a Quantity B: b+c 23. The average of three different positive integers is 6. Quantity A The product of the three integers Quantity B 25 24. List K co
8、nsists of 16 positive numbers. List M is obtained from list K by multiplying each number in list K by -1 Quantity A The standard deviation of K Quantity B The standard deviation of M 25-26 are based on the graph given. 25. How many of the age-groups each accounted for more than 15 percent of the tot
9、al number of occupational injuries in State X in 1998? A. One B. Two C. Three D. Four E. Five 26. In 1998, if one-half of the occupational injuries in the combined 34-and under age-groups were incurred by men, what was the number of occupational injuries incurred by men in the combined 35-and-over a
10、ge-groups? A. 33,500 B. 31,900 C. 30,500 D. 25,400 E. 21,700 27. For the 55-64 age-group in 1998, the average (arithmetic mean) number of work-hours lost per occupational injury was 48.5. If a workweek is 40 work-hours, which of the following is closest to the total number of workweeks lost due to o
11、ccupational injuries in the 55-64 age-group in 1998? A. 4500 B. 5200 C. 5500 D. 5900 E. 6300 28. In a graduating class of 236 students, 142 took algebra and 121 took chemistry. What is the greatest possible number of students that could have taken both algebra and chemistry? 29. P, Q, and R are thre
12、e points in a plane, and R does not lie on line PQ. Which of the following is true about the set of all points in the plane that are the same distance from all three points? A. It contains no points. B. It contains one point. C. It contains two points. D. It is a line. E. It is a circle. 30. The ran
13、dom variable X is normally distributed. The values 650 and 850 are at the 60th and 90th percentiles of the distribution of X, respectively. Quantity A The value at the 75th percentile of the distribution of X Quantity B 750 31. In a probability experiment, G and H are independent events. The probabi
14、lity that G will occur is r, and the probability that H will occur is s, where both r and s are greater than 0. Quantity A the probability that either G will occur or H will occur, but not both Quantity B r+s rs 32. Quantity A The number of primes that are divisible by 9 Quantity B The number of pri
15、mes that are divisible by 19 33. What is the sum of all possible solutions of the equation |x + 4|2 10|x+4|=24 A. -16 B. -14 C. -12 D. -8 E. -6 34. Quantity A AB Quantity B BC 35. If k is the greatest positive integer such that 3E is a divisor of 15! then k = A. 3 B. 4 C. 5 D. 6 E. 7 36. Sid intende
16、d to type a seven-digit number, but the two “3” he meant to type did not appear. What appeared instead was the five-digit number 52115. How many different seven-digit numbers could Sid have meant to type? A. 10 B. 16 C. 21 D. 24 E. 27 37. How many integers between 1 and 10$B are such that the sum of their digits is 2? A. 190 B. 210 C. 211 D. 230 E. 231 38. At a certain university, 60% of the professors are women, and 70% of the professors are tenu
