【正确答案】 A

【答案解析】(1) If x has at least two prime factors, say p and q, then among the factors of x2 are p, q, pq, p2, q2,p2q, and pq2, each of which is less than x2 (because x2 ≥ p2q2). Thus, x cannot have at least two prime factors, otherwise, x2 would have more than four divisors less than x2. Therefore, x has the form x=pn for some prime number p and positive integer n. There are 2n divisors of x2 = (pn)2 =p2n that are less than x2, namely 1, p, p2, p3, ...,p2n-2, and p2n-1. Statement (1) implies that 2n = 4, and hence n = 2. It follows that x =p2 for some prime number p, and so x has exactly two divisors less than x, namely 1 and p). Alternatively, the last part of this argument can be accomplished in a more concrete way by separately considering the number of prime factors of p, p2, p3, etc.; SUFFICIENT.(2) Probably the simplest approach is to individually consider the divisors of 2x that are less than 2x for various values of x. If x = 1, then 2x = 2 has one such divisor, namely 1. If x = 2, then 2x = 4 has two such divisors, namely 1 and 2. If x = 3, then 2x = 6 has three such divisors, namely 1,2, and 3. If x = 4, then 2x = S has three such divisors, namely 1,2, and 4. At this point we have two integers satisfying statement (2),x = 3 and x = 4. Since x = 3 has one divisor less than x = 3 and x = 4 has two divisors less than x = 4; NOT sufficient.The correct answer is A; statement 1 alone is sufficient.