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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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条件1，公因素是2，m=2a,p=2b, a,b互质，又因为2是最小的质数，后面的质数数列3，5，7，11...质数不可能是两个连续整数，所以余数r一定大于1
条件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
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