求助GMAT OG里一道数学问题

Question

如题所述

Answer 1

Does the integer K have at least three different positive prime factors?(1) K/15 is an integer (2) K/10 is an integer

答案是C. BOTH statements TOGETHER are sufficient, but NEITHER statement ALONE is sufficient.

书里给的解释是(1) prime factors of 15 are 3 and 5, so in this case k has least 2 different positive prime factors, but it is unknown if there are more positive prime factors;NOT sufficient. 同理(2) has at least 2 positive prime factors , 2 and 5. and (1)+(2) must be divisible by 2, 3, and 5. 所以答案是C。
但是楼主的困惑是 integer k 会不会是positive integer呢？在(1)+(2)情况下，可能 k= -30 , k/15和k/10都是负整数（负整数也是整数吧....楼主就是纠结在这个点上ORZ），那k的prime factors就可能是 -2, -5，-3这样的呀......楼主这么想的于是选了错误答案E Statement (1)and(2) TOGETHER are not sufficient.....ORZ解释太简单，楼主自己绕不出去了。。。求助热心肠小伙伴解救..... QAQ

你好，你想要搜的是这道题吗？
希望对你有帮助，望采纳。