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题目： A box contains red and blue balls only. If there are 8 balls in total, how many red balls are in the box?(1) If two balls are randomly selected without replacement, the probability that both balls are red is $$\frac{5}{14}$$(2) If two balls are randomly selected without replacement, the probability is $$\frac{15}{56}$$ that the first ball is red and the second ball is blue.

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题目： If A is an integer, what is the value of A?Statement #1: 1,000,000 < $$23^A$$ < 10,000,000Statement #2:$${7^{A+2}-7^A\over{48}}=7^A$$

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题目： One number, k , is selected at random from a set of 11 consecutive even integers. What is the probability that k = 10?(1) The average (arithmetic mean) of the set is zero.(2) The probability that k = 10 is the same as the probability that k = -10.

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题目： Mark has fewer than 9 coins. Each coin is either a quarter (worth $0.25) or a dime (worth $0.10). How many dimes does Mark have?(1) The total value of Mark's coins is $1.70(2) Mark has three times as many quarters as he has dimes.

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题目： When 900 is divided by positive integer F, the remainder is M. For some integer N > 5000, when N is divided by positive integer D, the remainder is R. Is R > F?Statement #1: M = 1Statement #2: D = 23

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题目： In a card game named Allemande, each of four players has a hand of 8 cards from a standard deck of 52. Through the play of the game, players try to maximize the point value of their final hand. Suits are irrelevant. Cards Ace through 10 have a point value equal to the number of their card: for example, the five of any suit would be worth 5 points. Face cards (Jack, Queen, and King) are worth 20 points each. Does Charles have the highest value final hand?Statement #1: Charles' final hand is worth 117 pointsStatement #2: No other player besides Charles has more than four face cards in his final hand.

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题目： If F is a factor of 105, is F is a prime number?Statement #1: F is not divisible by 3Statement #2: F < 10

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题目： If n is a positive integer, does n have four or more distinct positive factors?Statement #1: n is not primetatement #2: 900 ≤ n < 1100

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题目： If F is the prime factorization of N!, how many factors in F have an exponent of 1?Statement #1: 32 ≤ N ≤ 40 Statement #2: 27 ≤ N ≤ 35

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题目： In an election for class president, each of 32 students voted for exactly one candidate, Ann, Bob or Carl. Did Bob receive the most votes?(1) Bob received 9 votes.(2) Carl received 13 votes.

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题目： A drawer contains 36 socks, and 2 socks are selected at random without replacement. What is the probability that both socks are black?(1) The probability is 4/9 that the first sock is black.(2) The number of white socks in the drawer is 4 more than the number of black socks.

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题目： In the diagram above, coordinates are given for three of the vertices of quadrilateral ABCD. Does quadrilateral ABCD have an area greater than 30?Statement #1: point B has an x-coordinate of 4Statement #2: quadrilateral ABCD is a parallelogram

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题目： Is quadrilateral ABCD a square?Statement #1: angle A = angle C = 90ºStatement #2: AB = AD

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题目： If $$wxy \neq 0$$, does x = y ?(1) $$w^x = w^y$$(2) $$wxy \neq xy$$

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题目： The numbers D, N, and P are positive integers, such that D < N, and N is not a power of any other positive integer. Is D a prime number?Statement #1: N has exactly four factors, and D is a factor of NStatement #2: $$D = (3^P) + 2$$