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730以上   题数：15
S is a set of points in the plane. How many distinct triangles can be drawn that have three of the points in S as vertices?(1) The number of distinct points in S is 5.(2) No three of the points in S are collinear.
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) 2 is not a factor of n.(2) 3 is not a factor of n.
If x and y are integers, is y an even integer?(1) 2y – x = x2 – y2(2) x is an odd integer.
Is the integer n odd?(1) n is divisible by 3.(2) 2n is divisible by twice as many positive integers as n.
A school administrator will assign each student in a group of n students to one of m classrooms. If 3 < m < 13 < n, is it possible to assign each of the n students to one of the m classrooms so that each classroom has the same number of students assigned to it?(1) It is possible to assign each of 3n students to one of m classrooms so that each classroom has the same number of students assigned to it.(2) It is possible to assign each of 13n students to one of m classrooms so that each classroom has the same number of students assigned to it.
The integers m and p are such that 2 < m < p and m is not a factor of p. If r is the remainder when p is divided by m, isr > 1 ?(1) The greatest common factor of m and p is 2.(2) The least common multiple of m and p is 30.
The table above shows the distance, in kilometers, by the most direct route, between any two of the four cities, R, S, T, and U. For example, the distance between City R and City Uis 62 kilometers. What isthe value of x ?(1) By the most direct route, the distance between S and T is twice the distance between S and R.(2) By the most direct route, the distance between T and U is 1.5 times the distance between R and T.
If there are more than two numbers in a certain list, is each of the numbers in the list equal to 0 ?(1) The product of any two numbers in the list is equal to 0. (2) The sum of any two numbers in the list is equal to 0.
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.
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.
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