题目信息
If s is an integer, is 24 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.
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正确答案：
A:Statement (1) ALONE is sufficient, but statement (2) alone is not sufficient.
Arithmetic Properties of integers
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 = 24q, for some positive integer q. Thus, 24 is a divisor of s; SUFFICIENT. 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.
Tip If the integer n is divisible by each of the integers a and b and the greatest common factor of a and b is 1, then n is divisible by ab. However, if the greatest common divisor of a and b is greater than 1, then n may or may not be divisible by ab.
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 = 24q, for some positive integer q. Thus, 24 is a divisor of s; SUFFICIENT. 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.
Tip If the integer n is divisible by each of the integers a and b and the greatest common factor of a and b is 1, then n is divisible by ab. However, if the greatest common divisor of a and b is greater than 1, then n may or may not be divisible by ab.
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