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题目： A certain online form requires a 2-digit code for the day of the month to be entered into one of its fields, such as 04 for the 4th day of the month. The code is valid if it is 01, 02, 03, …, 31 and not valid otherwise. The transpose of a code xy is yx. For example, 40 is the transpose of 04. If N is the number of valid codes having a transpose that is not valid, what is the value of N ?

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题目： If x < y < z and y − x > 5, where x is an even integer and y and z are odd integers, what is the least possible value of z − x ?

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题目： Five integers between 10 and 99, inclusive, are to be formed by using each of the ten digits exactly once in such a way that the sum of the five integers is as small as possible. What is the greatest possible integer that could be among these five numbers?

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题目： When the integer n is divided by 17, the quotient is x and the remainder is 5. When n is divided by 23, the quotient is y and the remainder is 14. Which of the following is true?

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题目： Of the following, which is greatest?

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题目： If n = p² and p is a prime number greater than 5, what is the units digit of n² ?

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题目： A computer can perform 1,000,000 calculations per second. At this rate, how many hours will it take this computer to perform the 3.6 × 10¹¹ calculations required to solve a certain problem?

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题目： In an auditorium, 360 chairs are to be set up in a rectangular arrangement with x rows of exactly y chairs each. If the only other restriction is that 10 < x < 25, how many different rectangular arrangements are possible?

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题目： If the product of the integers w, x, y, and z is 770, and if 1 < w < x < y < z, what is the value of w + z ?

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题目：
The addition problem above shows four of the 24 different integers that can be formed by using each of the digits 1, 2, 3, and 4 exactly once in each integer. What is the sum of these 24 integers?

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题目： A country's per capita national debt is its national debt divided by its population. Is the per capita national debt of Country G within $5 of $500 ?

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题目： The cardinality of a finite set is the number of elements in the set. What is the cardinality of set A ?

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题目： For each positive integer k, let a _k = . Is the product a₁a₂ … a_n an integer?

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题目： Let S be a set of outcomes and let A and B be events with outcomes in S. Let ∼B denote the set of all outcomes in S that are not in B and let P(A) denote the probability that event A occurs. What is the value of P(A) ?

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题目： What is the number of integers that are common to both set S and set T ?