分享gmatclub的数学知识点汇总贴

LightCyan29 · 发表于 2016-11-1 01:22:54

这个帖子对我很有帮助，适合想要过一遍的同学，也非常适合查缺补漏，很全面有很多小技巧，附上网址分享给大家～
http://gmatclub.com/forum/gmat-math-book-in-downloadable-pdf-format-130609.html

摘抄一点我认为有用的：

LAST DIGIT OF A POWER

Determining the last digit of (xyz)n(xyz)n:

1. Last digit of (xyz)n(xyz)n is the same as that of znzn;
2. Determine the cyclicity number cc of zz;
3. Find the remainder rr when nn divided by the cyclisity;
4. When r>0r>0, then last digit of (xyz)n(xyz)n is the same as that of zrzr and when r=0r=0, then last digit of (xyz)n(xyz)n is the same as that of zczc, where cc is the cyclisity number.

• Integer ending with 0, 1, 5 or 6, in the integer power k>0, has the same last digit as the base.
• Integers ending with 2, 3, 7 and 8 have a cyclicity of 4.
• Integers ending with 4 (eg. (xy4)n(xy4)n) have a cyclisity of 2. When n is odd (xy4)n(xy4)n will end with 4 and when n is even (xy4)n(xy4)n will end with 6.
• Integers ending with 9 (eg. (xy9)n(xy9)n) have a cyclisity of 2. When n is odd (xy9)n(xy9)n will end with 9 and when n is even (xy9)n(xy9)n will end with 1.

Example: What is the last digit of 1273912739?
Solution: Last digit of 1273912739 is the same as that of 739739. Now we should determine the cyclisity of 77:

1. 7^1=7 (last digit is 7)
2. 7^2=9 (last digit is 9)
3. 7^3=3 (last digit is 3)
4. 7^4=1 (last digit is 1)
5. 7^5=7 (last digit is 7 again!)
...

So, the cyclisity of 7 is 4.

Now divide 39 (power) by 4 (cyclisity), remainder is 3.So, the last digit of 1273912739 is the same as that of the last digit of 739739, is the same as that of the last digit of 7373, which is 33.

ysycoco · 发表于 2016-11-1 07:25:15

感谢分享！

Rrrrey · 发表于 2019-7-30 01:34:54

感谢分享！

JannyYan · 发表于 2019-7-30 22:36:38

谢谢

瓶子叮咚响 · 发表于 2021-8-25 16:23:16

感谢分享！

想放飞的blue · 发表于 2021-10-14 17:59:57

看一下！

[原始] 分享gmatclub的数学知识点汇总贴

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