What is the greatest common divisor of positive integers m and n?(1)m is a prim

游客2025-02-27 14

问题 What is the greatest common divisor of positive integers m and n?
(1)m is a prime number, n=2.
(2)m and n are consecutive integers.

选项 A、Statement (1) ALONE is sufficient, but statement (19) alone is not sufficient to answer the question asked.
B、Statement (2) ALONE is sufficient, but statement (18) alone is not sufficient to answer the question asked.
C、BOTH statement (1) and (19) TOGETHER are sufficient to answer the question asked, but NEITHER statement ALONE is sufficient.
D、EACH statement ALONE is sufficient to answer the question asked.
E、Statement (1) and(19)TOGETHER are NOT sufficient to answer the question asked, and additional data specific to the problem are needed.

答案 B

解析单独Statement (1)，m是质数，n=2，那么当m=2时，两者的最大公约数为2，当m为大于2的质数时，m，n的最大公约数为1，因为有两个可能值，因此单独(1)无法回答问题。单独Statement (2)，m，n是连续的整数，那么两者的最大公约数为1，因此单独(2)回答了问题，因此答案为B。

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