数学题求教

guafafd

某人有bookcase, arrange 10 books per shelf and no books left. If he acquired 10 additional books, and arrange 12 books per shelf, no books left. Ask how many books he has before acquiring the addition 10 books 。

A 、before acquiring, his books less than 96

B 、before acquiring, his books more than 24

参考答案：a

问：不明白为什么选A?通过题目中的条件，我们不是可以推算出此人有50本书吗？

himba

A is correct. according to the conditions, we can get the equality: 10m+10=12n, m, n is integer. then, we can get n=5/6(m+1). it means that (m+1) must have factors of 6, such as 6, 12,24,48. the choice A tells us that 10m<96, then m<9.6. put them together, we can get m is five. thus the choice is A.

But I don't know how can you get the result without extra condition?