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题库 / Prep2007E2-DS-80
If x and y are positive integers such that x = 8y + 12, what is the greatest common divisor of x and y ?
(1) x = 12u, where u is an integer.
(2) y = 12z, where z is an integer.
Statement (1) ALONE is sufficient, but statement (2) alone is not sufficient.
Statement (2) ALONE is sufficient, but statement (1) alone is not sufficient.
BOTH statements TOGETHER are sufficient, but NEITHER statement ALONE is sufficient.
EACH statement ALONE is sufficient.
Statements (1) and (2) TOGETHER are NOT sufficient.
题目要求x和y的最大公约数。条件一：x是12的倍数，所以y一定是3的倍数，但无法确定x和y的最大公约数（只能确定有公约数3，但并不知道是否最大）条件二：y是12的倍数，原式就可以变化成x=(8z+1)12 y=12z 所以最大公倍数是12，充分。选择B
条件二是原式可以变成12（z+1）=x，因为y=12z，z+1和z是互质的，所以 y和x的最大公约数可以确定为12.老师站在自己的角度想就跳过了很多说解的细节吧。gmatla讲真，挺烂的
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