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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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#repost Ron's comment
in statement 1, both m and p are even. therefore, the remainder is even, so it's greater than 1.
done.
sufficient.
--
statement (2)
just pick various numbers whose lcm is 30.
notice the numbers selected above:
5 and 6 --> remainder = 1
10 and 15 --> remainder = 5 > 1
insufficient.
这个思路很赞
赞
少考虑了10 和 15的组合，所以就做错了
赞
the second, m and p could be 6 and 10,or 5 and 6 and in this case, the r is 4 or 1 respectively. so in the second assumption, there are several possibilities of r. the answer could be no = or Yes > .
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