请教2道菜鸟级问题

fordyang

昨天做了princeton的模考，但2道数学题的答案把我搞晕了，请高手帮助答疑
1.What is the largest integer X such that 8 less than 5 times X is less than 43?
the answer is 10
请高手列出解体思路
2. For all integers P, f is the number of distinct factors of P that divisible by 3 or 2, if P=36,f=?
answer is 8
factor是否包含1和本身？
多谢

smart

对不起，我也没能很好的理解题意，不能给出解题思路。


请高手指教。

dancingforum

1st question:

5 * X - 8 < 43 ===> X < 10.2
the largest integer satisfying the above is of course 10

dancingforum

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2. For all integers P, f is the number of distinct factors of P that divisible by 3 or 2, if P=36,f=?
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my thought:

step 1: Understand what the question says about F

F is the number of P's factors such that:
a) each factor has to be DISTINCT ( unique)
b) each factor has to be divisible by EITHER 3 OR 2 OR 2*3

step 2: solve the problem which is actually a combination question

P = 36 = 2 * 2 * 3 * 3

F = C(1,4)/2 + C(2, 4)/2 + C(3,4)/2 + C(4,4) = 8

Done

Regarding to fordyang's question:

Factors of course include 1 and P itself, but in this quesiton, 1 can not be
counted because it can not be divisible by either 2 or 3.

[此贴子已经被作者于2004-3-17 1:16:41编辑过]

dancingforum

sorry my new system has no chinese installed yet, but i will do that later

smart

谢谢dancingforum