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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) the greatest common factor of m and p is 2 --> both p and m are even (as both have 2 as a factor) --> even divided by even can give only even remainder (0, 2, 4, ...), since remainder is not zero (as pm≠integer), then remainder must be more than 1: 2, 4, ... Sufficient.
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