请教费费数学题 (多谢)

刘民 · 发表于 2010-11-6 05:53:52

那位大侠可以帮一下吗？多谢！多谢！

19、问根号n是否大于100？
（1）根号(n+1)> 100
（2）最大的4个数都大于8

【答案】B
【思路】先考虑条件(1),-->n+1>10000--->n>9999--->n>=10000所以根号n可能大于100也可能等于100，所以条件(1)不sufficient.
条件(2)---->n-1<99^2-->n<9802<100000----->根号n<100
所以条件(2)可以推出，答案为B
I think the answer should be E, because from (2), we cannottell whether n>100^2. Because (2) tells the largest four numbers are greaterthan 8888, we can only tell this number can be 9999, 9999.8, 8999.9 or 99990 or999900. Because (2) does not tell us how many digits the number contains orwhether n is an integer.
(1)+(2) cannot tell us either, because still, the questiondoes not tell us whether n is an integer, then, we cannot exclude thepossibility that n is 9999.1 or 9999.2, and 9999.1+1 >10000. So, I think theanswer should be E.

If n is an integer, then, (1)+(2) can tell n>10000.Because from (1), we know n>=10000; from (2), we know that n>=9999, from(1)+(2), we know this number has greater than 9999, with the largest four unitsgreater than 8, then, it should be at least be 99990. Therefore, we know thatn>100.

Can anyone help me here or email me at shirley923[在] yahoo.com? Tons thanks.

xxgoodluck · 发表于 2010-11-6 06:01:16

are u sure the second condition is right?

xxgoodluck · 发表于 2010-11-6 06:02:18

It might be 根号(n-1) < 99.... if this is the case, the explaination makes sense.

刘民 · 发表于 2010-11-6 07:02:26

Thank you so much for your reply. However, I am still not sure the correct answer. I think it should be E.

But the answer was B:
思路】先考虑条件(1),-->n+1>10000--->n>9999--->n>=10000所以根号n可能大于100也可能等于100，所以条件(1)不sufficient.
条件(2)---->n-1<99^2-->n<9802<100000----->根号n<100
所以条件(2)可以推出，答案为B

I am confused by the second condition.
Thank you so so ... much for any reply.
Best

请教费费数学题 (多谢)

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