题目信息
If n is an integer, is 
an integer?
an integer?
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.
参考答案及共享解析
共享解析来源为网络权威资源、GMAT高分考生等； 如有疑问，欢迎在评论区提问与讨论
本题耗时：
已选答案：
正确答案：
B:Statement (2) ALONE is sufficient, but statement (1) alone is not sufficient.
Arithmetic Properties of integers
We are given that
is an integer. If n = 15, then 
is an integer and 
is an integer. However, if n = 5, then 
is an integer and 
is not an integer; NOT sufficient.
We are given that 
= k, where k is an integer. Since 8n = 15k, it follows that both 3 and 5 are factors of 8n. Therefore, the prime factorization of 8n = 23 × n includes at least one factor of 3 and at least one factor of 5, and it is clear that each of these factors must be among the prime factors of n. Thus, both 3 and 5 are factors of n, and hence n is divisible by 15.
Alternatively, since 15 divides 8n, and 8 and 15 are relatively prime, then it follows that 15 divides n; SUFFICIENT.
The correct answer is B;statement 2 alone is sufficient.
We are given that
is an integer. If n = 15, then is an integer and is an integer. However, if n = 5, then is an integer and is not an integer; NOT sufficient.
We are given that = k, where k is an integer. Since 8n = 15k, it follows that both 3 and 5 are factors of 8n. Therefore, the prime factorization of 8n = 23 × n includes at least one factor of 3 and at least one factor of 5, and it is clear that each of these factors must be among the prime factors of n. Thus, both 3 and 5 are factors of n, and hence n is divisible by 15.Alternatively, since 15 divides 8n, and 8 and 15 are relatively prime, then it follows that 15 divides n; SUFFICIENT.
The correct answer is B;statement 2 alone is sufficient.
加入收藏
在线答疑
题目来源
