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题库 / Prep2007E2-DS-197
The integers m and p are such that 2 < m < p and m is not a factor of p. If r is the remainder when p is divided by m, is r > 1 ?
(1) The greatest common factor of m and p is 2.
(2) The least common multiple of m and p is 30.
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.
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1）最大公约数是2，说明m ,p都可以被2 整除，m,p都是偶数，p/m 的余数不可能等于1，因为 被除数p=除数m乘以商再加上余数，m是偶数，m乘以商也是偶数，如果余数是1的话，加上1，得出的被除数p就是奇数了，矛盾。所以余数不是1. （1）充分
2)最小公倍数30=3*2*5，m,p的可能取值有：3，10；2，15；5，6，其中3，10的余数=1，不充分 回
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