TT GWD9 Q32

yalemba

Q32:

What is the remainder when the positive integer x is divided by 8?

(1)     When x is divided by 12, the remainder is 5.

(2)     When x is divided by 18, the remainder is 11.

                  

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.

Answer: D E

余数问题总搞不清，大家帮帮偶，谢谢谢谢

BruceNornia

题目的意思是：

 

请问正整数X被8除的余数是多少？

1）当X被12除时，余数为5

2）党X被18除时，余数为11

 

1）X可以写为: X = 12n+5，其中n为整数，

当n为偶数时，X除8余数为5，

当n为奇数时，X除8余数为1；

NOT SUFFICIENT

 

2）X可以写为: X = 18m+11，其中m为整数，

当n为4的倍数时，X除8余3，

当n被4除余1时，X除8余5，

当n被4除余2时，X除8余7，

当n被4除余3时，Xn除8余1，

NOT SUFFICIENT

 

1)+2) 可以得到 12n + 5 = 18m + 11 从而 12 (n-m) = 6(m+1) 即 2(n-m) = m +1 这里仅仅可以看出m是一个奇数，但当m为奇数时，X除8的余数可以是5也可以是1

事实上 当 X= 29 时，满足1)+2)，被8除的余数是5

         当 X= 65时，满足1)+2)，被8出的余数是1

NOT SUFFICIENT

 

The correct answer is E; Both statements together are still NOT sufficient.

qianrener

x=12m+5=18n+11

12m+5+7=18n+11+7

12(m+1)=18(n+1)

2(m+1)=3(n+1)

m=3p-1

x=12(3p-1)+5=36p-7

...so E