题目信息
If x, y, and d are integers and d is odd, are both x and y divisible by d ?
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：
C:BOTH statements TOGETHER are sufficient, but NEITHER statement ALONE is sufficient.
Arithmetic Properties of integers
Determine whether both of the integers x and y are divisible by the odd integer d.
It is given that x + y is divisible by d. It is possible that both x and y are divisible by d, and it is possible that they are not both divisible by d. For example, if x = 4, y = 2, and d = 3, then 4 + 2 is divisible by 3, but neither 4 nor 2 is divisible by 3. On the other hand, if x = 3, y = 6, and d = 3, then 3 + 6 is divisible by 3, and both 3 and 6 are divisible by 3; NOT sufficient. It is given that x – y is divisible by d. It is possible that both x and y are divisible by d, and it is possible that they are not both divisible by d. For example, if x = 4, y = −2, and d = 3, then 4 − (−2) is divisible by 3, but neither 4 nor –2 is divisible by 3. On the other hand, if x = 3, y = −6, and d = 3, then 3 − (−6) is divisible by 3, and both 3 and −6 are divisible by 3; NOT sufficient.
Taking (1) and (2) together, x + y is divisible by d, so
is an integer and x – y is divisible by d, so 
is an integer. It follows that 
+ 
= 
is an integer and 
is an integer because d is odd. Similarly, 
− 
= 
is an integer and 
is an integer because d is odd.
The correct answer is C;both statements together are sufficient.
Determine whether both of the integers x and y are divisible by the odd integer d.
It is given that x + y is divisible by d. It is possible that both x and y are divisible by d, and it is possible that they are not both divisible by d. For example, if x = 4, y = 2, and d = 3, then 4 + 2 is divisible by 3, but neither 4 nor 2 is divisible by 3. On the other hand, if x = 3, y = 6, and d = 3, then 3 + 6 is divisible by 3, and both 3 and 6 are divisible by 3; NOT sufficient. It is given that x – y is divisible by d. It is possible that both x and y are divisible by d, and it is possible that they are not both divisible by d. For example, if x = 4, y = −2, and d = 3, then 4 − (−2) is divisible by 3, but neither 4 nor –2 is divisible by 3. On the other hand, if x = 3, y = −6, and d = 3, then 3 − (−6) is divisible by 3, and both 3 and −6 are divisible by 3; NOT sufficient.
Taking (1) and (2) together, x + y is divisible by d, so
is an integer and x – y is divisible by d, so is an integer. It follows that + = is an integer and is an integer because d is odd. Similarly, − = is an integer and is an integer because d is odd.The correct answer is C;both statements together are sufficient.
加入收藏
在线答疑
题目来源
