1、Individual Questions (Grade 6)(Unofficial version, for reference only)Note: Please enter your answer as a fraction if your answer is not an integer, unless otherwise specified.1.Which of the following is divisible by 6 when n is any integer?A) (2n + 3)(3n + 2)B) n(n + 1)(n + 2)C) (2n + 3)(3n 2)D) n(
2、n + 2)(3n + 6)Answer: B2.There are eight numbers which can be written with four 2s and no other symbols. These eight numbers are: 12222, 2222, 2222, 2222,2222 , 2222 , 2222 , and 2222 . Of these, which one represents the largest number? Note: These 8 numbers are numbered from 1 to 8, reading from le
3、ft to right. Write the index of the largest number, i.e. your answer should be an integer from 1 to 8, inclusive.Answer: 73.How many ways are there to seat four of a group of ten people around a circular table where two seatings are considered the same when everyone has the same immediate left and i
4、mmediate right neighbor?Answer: 12604.The sum of two positive numbers equals the sum of the reciprocals of the same two numbers. What is the product of these two numbers?Answer:15.On the planet Oberon, there are as many days in a week as there are weeks in a month. The number of months in an Oberon
5、year is twice the number of days in a month. If there are 1250 days in an Oberon year, how many months are there in an Oberonyear? Answer:506.The product of the first n positive integers is n!. For example, 3! = 3 2 1 = 6. The2value of k for which is the value of t?Answer:10002000! = k(1 3 5 7 . 199
6、7 1999)1000!is true is k = 2t. What7.In the diagram, AB and CD are congruent radii, and BC is a common tangent. Ifthe two shaded regions have equal areas, and if AB = 1, what is the area of quadrilateral ABCD?Note:(1) Use 3.14 for .(2) Please enter the value of (1000 the area of quadrilateral ABCD)
7、as your answer.Answer: 15708.Ten girls and five boys are in a room. At random, two of the fifteen leave the room. What is the most likely ratio of girls remaining to boys remaining?Note: Please enter your answer as a fraction, if it is not an integer.Answer: 949.How many cubes composed of unit cubes
8、 are there in a 3D chess cube shown below?Hint: There are 512 unit cubes. There is one cube of 8 8 8 (its dimensions). There are cubes of other sizes as well.Answer: 129610.A scientist, back from a field trip, was invited to a party with her husband. Always the scientist, she decided to observe and
9、to make measurements of the curious ritual of handshaking. Four other married couples attended the party. (There were five married couples attending the party in total.) Whenever two people shook hands, she recorded that each of the two people shook hands one time. In that way, for all of them (incl
10、uding herself and her husband), she obtained the total number of times that each person shook hands. First, she noted two obvious facts. One didnt shake hands with3ones own spouse, and one didnt shake the same persons hand more than once. Thenshe looked at her list and observed an interesting fact. If she didnt count herself, each of the other nine people shook hands a different number of times, i.e., no two of the other nine people shook hands the same number of times.(1) How many times did her husband shake hands?Answer: 4(2) How many times did she shake hands? Answer: 44
