单选题 If a, b, and c are positive integers, can the product of then be multiple of 24?(1)a, b, c are consecutive integers.(2)a is an even number.

A、 Statement (1) ALONE is sufficient, but statement (16) alone is not sufficient to answer the question asked.
B、 Statement (2) ALONE is sufficient, but statement (15) alone is not sufficient to answer the question asked.
C、 BOTH statement (1) and (16) TOGETHER are sufficient to answer the question asked, but NEITHER statement ALONE is sufficient.
D、 EACH statement ALONE is sufficient to answer the question asked.
E、 Statement (1) and(16)TOGETHER are NOT sufficient to answer the question asked, and additional data specific to the problem are needed.

【正确答案】 C

【答案解析】在Statement (1)中，a，b，c是连续的正整数，3个连续的整数中必然有一个是3的倍数，同时也必然至少有一个数是偶数，即2的倍数，所以三个连续整数的乘积必然是6的倍数，但是我们还不能判断是否是24的倍数，比如4，5，6是24的倍数，但是5，6，7显然不是24的倍数，所以单独(1)不能回答问题。Statement (2)告诉我们a是偶数，不能判断abc是否是24的倍数。把(1)和(2)结合起来得到：a是偶数，b是奇数，c也是偶数，a，c为两个连续的偶数，它们的乘积是8的倍数，又因为其中有一个数必然是3的倍数，所以乘积abc是24的倍数，因此选择C。