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(1)In the integer 3589 the digits are all different and increase from left to right、 How many integers between 4000 and 5000 have digits that are all different and that increased from left to right?
比较题目：(2)In the integer 3589 the digits are all different and increase from left to right、 How many integers between 30000 and 50000 have digits that are all different and that increased from left to right?
(3)If p, r, m are three different prime numbers greater than 2, and n=p*r* m, how many positive factors, including 1 and n, does n have?
比较题目：(4)If p, r, m, n, t and s are six different prime numbers greater than 2, and n=p*r*s*m*n*t, how many positive factors, including 1 and n, does n have?
(5)If someone throws a dice twice, on the first time he gets a points, and on the second he gets b points, what is the probability a/b>1?
比较题目：(6)If someone throws a dice twice, what is the probability that the point he gets on one throw is bigger than the other?
以上是SAT数学难题之数学概率题的详细内容，SAT数学虽然是中国考生的强项，但大家还是要在备考中多多注意，不要轻敌。
我们再来看看
1、 SAT数学解题法，代入法是最普遍的一个，也是最简单，最有效的一个。
例题：If x and y are two different integers and the product 35xy is the square of an integer, which of the following could be equal to xy?
A、 5 B、70 C、 105 D、 140 E、 350
解答：将答案依次带入，发现只有D选项35xy=35×140=35×35×4=(35×2)2。
2、 特殊值法适用于那些没有固定数字的答案的题目。
例题：xy=x+y、 If y>2, what are all possible values of x thatSATisfy the equation above?
A、 x<0, B、 02
解答：y>2,不妨假设它为3，3x=x+3,x=3/2, 一目了然D即为正确选项。
3、 巧解法在SAT数学解题方法中就是有一点复杂
例题：At a certain diner, Joe orders 3 doughnuts and a cup of coffee and is charged $2.25、 Stella orders 2 doughnuts and a cup of coffee and is charged $1.70、 What is the price of 2 doughnuts?
A、 $ 0.55 B、 $ 0.60 C、 $ 1.10 D、 $ 1.30 E、 $ 1.80
解答：按照常规的解题思路，我们可以用字母x和y分别指代“炸面包圈”和“咖啡”的价格，然后建立2个方程式3 x+y= $ 2.25 , 2 x+y= $ 1.70，最后求出方程组的解x=$ 0.55,
y =$ 0.6。
但是只要稍作思考，我们不难发现解题的捷径—— 3个炸面包圈加1杯咖啡的价格与2个炸面包圈加 1 杯咖啡的价格相减，余额就是1个炸面包圈的价格：$ 2.25 -$ 1.70 =$ 0.55 。此时，我们还要注意的是, 千万不能掉入命题者的陷阱而选择A，因为A选项只是1个炸面包圈的价格。所以，正确答案应该是C选项。
除了SAT数学解题可以用代入法，还有很多方法大家可以在备考SAT数学当中使用，关键是打好基础，找到解题的关键，才能获取成功。
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