TTGWD2---32 ，为什么选D不选C

julyyuren

找了相关贴子，可是查不到这道题目。是不是我太笨啊：（

 

Q32:

What is the remainder when the two digit, positive integer x is divided by 3?

 

 

(1)    The sum of the digits of x is 5.

(2)    The remainder when x is divided by 9 is 5.

                  

A. Statement (1) ALONE is sufficient, but statement (2) alone is not sufficient.

B. Statement (2) ALONE is sufficient, but statement (1) alone is not sufficient.

C. BOTH statements TOGETHER are sufficient, but NEITHER statement ALONE is sufficient.

D. EACH statement ALONE is sufficient.

E. Statements (1) and (2) TOGETHER are NOT sufficient.                                                                                     

 

正确答案是D ,我现在只能作出C，麻烦各位解答一下！谢谢！

[此贴子已经被作者于2006-8-7 6:48:21编辑过]

yaoyao99

condition 1 => x = 14, or 23, or 32, or 41, or 50 where the remainder is always 2 when divided by 3 => condition 1 by itself is sufficient

condition 2 => x = y * 9 + 5 = (y * 3 + 1) * 3 + 2 => remainder is 2 => condition 2 by itself is also sufficient

D

[此贴子已经被作者于2006-8-7 7:29:07编辑过]

mymengming

N

nebelstreif

请问题干问的是一个两位的正整数x被3除的余数是多少吗？

我怎么看不出里面说余数是2呢？

lovetiky

以下是引用nebelstreif在2006-8-7 9:14:00的发言：

请问题干问的是一个两位的正整数x被3除的余数是多少吗？

我怎么看不出里面说余数是2呢？

所有位之和是3的倍数，则可以被3整除。条件(1)中之和为5，说明若个位加1就可被3整除，即原来被3除余2

条件(2)yaoyao已经说得很明白啦

nebelstreif

谢谢！yaoyao的推理没问题，我想我是没明白此题的意图。

照此来说，此题的意图是问，所给的两个条件是否sufficient求出题干中的余数，而不是问余数是多少，是吧？

yaoyao99

Yes.

In case the questions asks "is the remainder always 1", D is also the correct answer because based on either condition, you can figure out "no, the remainder is never 1."

SBGMAC

(1) Assume X = 10a+b, then a+b=5, b=5-a. Plug b=5-a into first equation. X = 10a+5-a=9a-5

since 9a is divisible by 3, the remainder of X divided by 3 is equale to the the remainder of 5 divided by 3, which is 2.

So (1) alone is enough.

(2) Given that The remainder when x is divided by 9 is 5. Assume X = 9c +5. Same reason as (1), since 9c is divisible by 3, the remainder of X divided by 3 is equale to the the remainder  of 5 divided by 3, which is also 2.

So (2) alone is enough.

Therefore, answer should be D.