单选题 If s is an integer, is 24 a divisor of s ?(1) Each of the numbers 3 and 8 is a divisor of s. (2) Each of the numbers 4 and 6 is a divisor of s.

A、 Statement (1) ALONE is sufficient, but statement (2) alone is not sufficient.
B、 Statement (2) ALONE is sufficient, but statement (1) alone is not sufficient.
C、 BOTH statements TOGETHER are sufficient, but NEITHER statement ALONE is sufficient.
D、 EACH statement ALONE is sufficient.
E、 Statements (1) and (2) TOGETHER are NOT sufficient.

【正确答案】 A

【答案解析】(1) If each of the numbers 3 and 8 is a divisor of s, then using the prime factorization of 8 gives s=23 × 3 × q= 24g, for some positive integer q. Thus, 24 is a divisor of s;SUFFICIENT.(2) If each of the numbers 4 and 6 is a divisor of s, then s could be 24 and it follows that 24 is a divisor of s. On the other hand, s could be 12 because 4 and 6 are both divisors of 12 and 24 is not a divisor of s;NOT sufficient.The correct answer is A;statement 1 alone is sufficient.