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A certain team has fewer than 50 members. If all the members are divided into groups of 3 members each.
there will be 2 members left over. If all the members are divided into groups of 5 members each, there will
also be 2 members left over. If all the members are divided into groups of 4 members each, there will be
no members left over. If 3 of the members are unavailable and the remaining members are divided into
groups of 5 members each, how many members will be left over?
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In a random 5-digit positive integer KLMNP, what is the probability that KLM and KNP are the same?
Give your answer as a fraction.
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A cube has its faces numbered from 1 to 6. The cube is weighted in such a way that when it is rolled, the probability that X will appear on the top face is equal to $$\frac{k}{X}$$, where k is a constant. What is the value of k?
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A dice has its faces numbered from 1 to 6, while a coin has its faces numbered 1 and 2. When randomly the dice and the coin together once, what is the probability that the number that appears on the top face is the same?
Give your answer as a fraction.
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In the rectangular coordinate plane above, how many points (x, y), where both x and y are integers, lie on the circle with center (0, 0) and radius 5?
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What is the units digit of ($$4^{32}$$ - $$3^{32}$$)?
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If S is the set of positive integers that are multiples of 6, and T is the set of positive integers that are multiples of 8, how many integers between 1 and 100 are in both sets S and T?
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The top surface of a certain 1-inch-thick oak board is 8 inches wide and has an area of 960 square inches. What is the price of this board? (1 foot=12 inches)
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For the 6-inch-wide boards listed, which of the following is closest to the ratio of the price per linear foot of the least expensive type of board to the price per linear foot of the most expensive type of board?
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The price of one maple board that is 8 inches wide and n feet long is $1.50 less than the price of 2 maple boards that are each 4 inches wide and n feet long. What is the value of n?
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A set consists of all three-digit positive integers with the following properties. Each integer is of the form JKL, where J, K, and L are digits; all the digits are nonzero; and the two-digit integers JK and KL are each divisible by 9. How many integers are in the set?
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Set D consists of the numbers of the form $$\frac{1}{2^{n}}$$ , where n is an integer from 1 to 10. What is the hundredths digit in the decimal representation of the product of 8,000 and the sum of the numbers in D?
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When the positive integer w is divided by 13, the remainder is 1, and when w is divided by 15, the remainder is 14. Which of the following is a possible value for w?
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A campaign director can divide the campaign workers into 10 or 11 teams. When the workers are divided into 11 teams, each of 10 of the teams has x workers and 1 team has 6 workers. When the workers are divided into 10 teams, each of 9 of the teams has x+1 workers and 1 team has 5 workers. How many campaign workers are there?
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During archery practice, Kyle made 50 attempts to hit a target. After each attempt, his success rate was calculated as the number of successful attempts to hit the target as a percent of the number of attempts up to that time. After the 20th attempt, his success rate was 45 percent. After the 40th attempt, his success rate was 55 percent. Which of the following statements must be true?
Indicate all such statements.
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The odds against the occurrence of an event are defined to be the ratio of the probability that the event will not occur to the probability that the event will occur. An integer is to be selected at random from the set of integers from k to n, where k < n. The odds against the event that the integer selected will be an even integer are 1 to 0.95. Which of the following could be the integers k and n, respectively?
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The standard deviation of n numbers $$x_{1}$$, $$x_{2}$$, $$x_{3}$$,......, $$x_{n}$$, with mean $$\overline{x}$$ is equal to $$\sqrt{\frac{s}{n}}$$, where S is the sum of the squared differences $$(x_{i} - \overline{x})^{2}$$ for 1 ≤ i ≤ n.
For what value of x is the standard deviation of the numbers 6, 14, 16, and x least?
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When a certain stock exchange closed on Tuesdays, $$\frac{1}{5}$$ of the stocks closed at the same price as on the previous day. Of the remaining stocks, 3 stocks closed at a higher price for every 4 stocks that closed at a lower price. What fraction of all the stocks on this exchange closed at a higher price than on the previous day?
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