In each term in the sum a1+a2+...+an is either 7 or 77 and the sum equals 350, which of the following could be equal to n?
答案选40
Alice’s take-home pay last year was the same each month, and she saved the same fraction of her take-home pay each month. The total amount of money that she had saved at the end of year was 3 times the amount of that portion of her monthly take-home pay that she did not save. If all the money that she saved last year was from her take-home, what fraction of her take-home pay did she save each month?
答案为1/5 作者: Filter48 时间: 2015-7-2 01:57
First question: Since the unit digit of each term is 7 and hence only the sum of 10 terms will give you a result of which unit digit is zero (350 in this case), N must be a multiple of 10.作者: qq342573577 时间: 2015-7-2 17:32
1. 首先因为an 不是7就是77 ， 而总和为350 所以 n肯定是10的倍数（7和77的尾数都是7，而合是350）；如果所有的数都是7的话，n最大为50，但是an需要包括77，所以n只能是10 20 30 40 。接下来就看选项了。
2.假设Alice每月存钱的比例为a（其实带回来多少钱都没差，列出等式都能消掉），根据题目列出等式 ：12a=3（1-a），解出a=1/5.（12a的意思是去年存钱的总比例，1-a是每月没存的钱的比率） 其实等式两边需要乘以每月带回来的钱才是题目要表达的意思，但是可以消掉 所以也就无所谓了