- UID
- 1268173
- 在线时间
- 小时
- 注册时间
- 2017-3-13
- 最后登录
- 1970-1-1
- 主题
- 帖子
- 性别
- 保密
|
K is a set of numbers such that
i. if x is in K, then –x is in K, and
ii. if each of x and y is in K, then xy is in K.
Is 12 in K ?
1. 2 is in K.
2. 3 is in K.
Arithmetic Properties of numbers
1. Given that 2 is in K, it follows that K could be the set of all real numbers, which
contains 12. However, if K is the set {…, –16, –8, –4, –2, 2, 4, 8, 16, …}, then K
contains 2 and K satisfies both (i) and (ii), but K does not contain 12. To see that
K satisfies (ii), note that K can be written as {…, –24, –23, –22, –21, 21, 22, 23, 24,
…}, and thus a verification of (ii) can reduce to verifying that the sum of two
positive integer exponents is a positive integer exponent; NOT sufficient.
2. Given that 3 is in K, it follows that K could be the set of all real numbers, which
contains 12. However, if K is the set {…, –81, –27, –9, –3, 3, 9, 27, 81, …}, then K
contains 3 and K satisfies both (i) and (ii), but K does not contain 12. To see that
K satisfies (ii), note that K can be written as {…, –34, –33, –32, –31, 31, 32, 33, 34,
…}, and thus a verification of (ii) can reduce to verifying that the sum of two
positive integer exponents is a positive integer exponent; NOT sufficient.
Given (1) and (2), it follows that both 2 and 3 are in K. Thus, by (ii), (2)(3) = 6 is in K.
Therefore, by (ii), (2)(6) = 12 is in K.
The correct answer is C; both statements together are sufficient.
红色部分哪位高手能解释一下？谢谢
|
|
京公网安备11010202008513号 京ICP证101109号 京ICP备12012021号
发表于 2017-4-10 19:26:01
收藏
收藏
