有甲、乙、丙、丁四个人，各对某个两位整数的性质用两句话表述：_爱下问搜题

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问题解答题

有甲、乙、丙、丁四个人，各对某个两位整数的性质用两句话表述：

甲：“用2除余1”，“用3除余2”．

乙：“用4除余3”，“用5除余4”．

丙：“用6除余5”，“用7除余6”．

丁：“用8除余7”，“用9除余8”．

已知四人中每个人都只说对了一句话，而另一句话是错的．请问这个两位整数是几？

答案

将甲的第一句话用甲-①，第二句话用甲-②表示．

（1）先假设甲-①是错的．

如果甲-①是错的，乙-①所说的整数用4除余3，如果用2除会怎样呢？

用4除余3的整数，也可以说成是4的倍数加上余数3 的整数．4是2的倍数，那么能被4整除的数也一定能被2整除，余数是3，3被2除余1．

因此甲-①，乙-①所说的内容相同，既他们说的都是错的．用同样的思考方法可以说明丙-①和丁-①也都是错的．这时可以肯定甲-②、

乙-②、丙-②、丁-②、是正确的．

从各句话的除数与余数的关系来看，所有话中的余数都是除数减1，因此满足甲-②、乙-②、丙-②、丁-②条件的整数应该是3、5、7、9的公倍数减1的整数，而这样的整数最小的是314，不符合题目要求．

（2）假设甲-②是错误的，根据（1）的思路可知，丙-①、丁-②也是错误的，

因为丁-②是错的，则丁-①是正确的，

即甲-①，乙-①，丙-②，丁-①都是正确的，

则符合条件的是2、4、7、8的公倍数减1的整数，

经验证，这个数是56-1=55．

所以这个两位整数是55．

名词解释

商业银行的流动性需求

问答题

Exactly where we will stand in the long war against disease by the year 2050 is impossible to say. (46) But if developments in research maintain their current pace, it seems likely that a combination of improved attention to dietary and environmental factors, along with advances in gene therapy and protein targeted drugs, will have virtually eliminated most major classes of disease.

From an economic standpoint, the best news may be that these accomplishments .could be accompanied by a drop in health-care costs. (47) Costs may even fall as diseases ’are brought under control using pinpointed, short-term therapies now being developed. By 2050 there will be fewer hospitals, and surgical procedures will be largely restricted to the treatment of accidents and other forms of trauma. Spending on nonacute care, both in nursing facilities and in homes, will also fall sharply as more elderly people lead healthy lives until close to death.

One result of medicine’s success in controlling disease will be a dramatic increase in life expectancy. (48) The extent of that increase is a highly speculative matter, but it is worth noting that medical science has already helped to make the very old (currently defined as those over 85 years of age) the fastest growing segment of the population. Between 1960 and 1995, the U.S. population as a whole increased by about 45%, while the segment over 85 years of age grew by almost 300%. (49) There has been a similar explosion in the population of centenarians, with the result that survival to the age of 100 is no longer the newsworthy feat that it was only a few decades ago. U.S. Census Bureau projections already forecast dramatic increase in the number of centenarians in the next 50 years: 4 million in 2050, compared with 37, 000 in 1990.

(50) Although Census Bureau calculations project an increase in average life span of only eight years by the year 2050, some experts believe that the human life span should not begin to encounter any theoretical natural limits before 120. years. With continuing

(49) There has been a similar explosion in the population of centenarians, with the result that survival to the age of 100 is no longer the newsworthy feat that it was only a few decades ago.