唔該~數學f.2升f.3問題[要列式]

2007-09-02 11:38 pm
Given a four-digit odd no. which is greater than 9000and is divisible by 13. When rounded off to 3 significant figures, it's divisible by 4. When rounded off to 2 significant figures, it's divisible by 11. Find the no..

回答 (2)

2007-09-03 1:12 am
✔ 最佳答案
Let x be the no.
1. When rounded off to 2 significant figures, it's divisible by 11.
If it is divisible by 11, the first two digits of the rounded off no. must be equal, i.e.
11, 22, 33, 44, 55, 66, 77, 88, 99.
Since it is greater than 9000, the first two digits of the rounded off no. = 99.
Hence, 9850 <= x <= 9949 --------------------------------------------------(1)
2. When rounded off to 3 significant figures, it's divisible by 4. --------------(2)
To satisfy (1) and (2), the first three digits of the rounded off no. should be
986, 988, 990, 992, 994 --------------------------------------------------(3)
Hence, 9855 <= x <= 9944 ---------------------------------------------------(4)
3. It's divisible by 13. --------------------------------------------------(5)
To satisfy (4) & (5), the possible values of x are
9867, 9880, 9893, 9906, 9919, 9932 -----------------------------------------------(6)
Further to (6), since x is odd, the possible values of x are
9867, 9893, 9919 ------------------------------------------------(7)
Further to (7), to satisfy (3), the only possible value of x = 9919
2007-09-02 11:44 pm
9919呀
參考: 自己


收錄日期: 2021-04-13 13:15:05
原文連結 [永久失效]:
https://hk.answers.yahoo.com/question/index?qid=20070902000051KK02598

檢視 Wayback Machine 備份