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.

单项选择题
阅读理解

It was midnight in Paris and we were rolling toward Avenue Bosguet. As we came to the Pont Alexandra Ⅲ, the taxi slowed down, for the traffic light was red against us, and then, without stopping, we sailed through the red in a sudden burst of speed. The same performance was repeated at the Alma Bridge. As I paid the driver, I asked him why he had driven through two red lights.

“You ought to be ashamed of yourself, breaking the law and endangering your life that way.” I protested.

He looked at me, astonished, “Ashamed of myself? I am a law abiding(守法的) citizen and have no desire to get killed either.” He cut me off before I could protest.

“No, just listen to me before you complain. What did I do? Went through a red light. Well, did you ever stop to consider what a red light is? What it means?”

“Certainly,”I replied. “It’s a stop signal and means the traffic is rolling in the opposite direction.”

“Half-right,”said the driver, “But incomplete. It’s only an automatic(自动的) stop signal. And it does not mean that there is cross traffic. Did you see any cross traffic during our trip? Of course not. I slowed down at the light, looked carefully to the right and to the left. Not another car on the street at this hour. Well, then! What would you have me do? Should I stop like a stupid animal because an automatic, brainless machine turns red every forty seconds? No, sir,”he shouted, “I am a man, not a machine. I have eyes and a brain and judgment, given me by God. Ashamed of myself, you say? I would only be ashamed of myself if I let those blinking lamps do my thinking for me. Good night,sir.”

小题1:At the Alma Bridge,__________.

A.the writer stopped the taxi and aid the driver

B.the taxi went through a red light again

C.there was a performance the writer had already watched

D.the writer began to criticize the driver小题2:To the taxi driver, a red light__________.

A.was not a stop signal

B.should not work at midnight

C.sometimes made mistakes in judgment

D.didn’t always mean that there was cross traffic小题3:The main reason the driver dared to drive through the red light was that________________.

A.he found there was no cross traffic there at that time

B.he thought it a shame to be controlled by a machine

C.he knew no other driver would see him at this hour

D.he didn’t trust any brainless machine小题4:According to the passage, the driver thought of what he had done was____________.

A.law abiding

B.law breaking

C.something to be proud of

D.something to be ashamed of