三道PREP数学题目，请求帮助！

yinshengsss

21.    1407-!-item-!-187;#058&000929
Is the integer n odd?

(1) n is divisible by 3.

(2) 2n is divisible by twice as many positive integers as n.
答案B

17.    2311-!-item-!-187;#058&002635
In a certain board game, a stack of 48 cards, 8 of which represent shares of stock, are shuffled and then placed face down.  If the first 2 cards selected do not represent shares of stock, what is the probability that the third card selected will represent a share of stock?

(A)  1/8
(B)  1/6
(C)  1/5
(D)  3/23
(E)  4/23
这题答案不确定是哪个？

62.    7564-!-item-!-187;#058&005577
Alice's take-home pay last year was the same each month, and she saved the same fraction of her take-home pay each month.  The total amount of money that she had saved at the end of the year was 3 times the amount of that portion of her monthly take-home pay that she did not save.  If all the money that she saved last year was from her take-home pay, what fraction of her take-home pay did she save each month?

(A) 1/2
(B) 1/3
(C) 1/4
(D) 1/5
(E) 1/6
答案D
请求大家帮忙解答下好吗？谢谢！！

yinshengsss

自己顶一下~~~请大家指点下下罗~~谢谢！

fullmoon558

第一题：条件一不能推出n是奇数，因为6能被3整除，但6不是奇数。条件二是说，2n的因子是n的两倍之多，当n是奇数时，比如5, 5的因子有两个，10 有4个。符合。当n是偶数时，比如6,6的因子有4个，12有5个，不符合。选B。
第二题：前两张牌已经抽完了，现在问第三张牌抽到是代表stock的概率，那前两个牌的概率就当1算了（因为已经抽完了），在抽第三张牌时，可选择的有46个（48-2），抽到的是stock，那么概率就是8/46=4/23
第三题：说每个月的pay是固定的，每月又抽出固定的数存上，问的是如果一年中存的总数是一个月（请注意，不是一年）存完后剩的数的三倍，问抽出的占pay的比例，设每月发a, 存b. 12b=3(a-b)=====》3a=15b====>a=5b所以是1/5

eflet222

第1题的2给出个推理:
如果n是奇数,有k个因子{f1,f2,f3,...,fk}(都不可被2整除)  那么{f1,f2,f3,...,fk, 2f1,2f2,2f3,...,2fk}必然是2n的因子,由由于前者都是不能被2整除的奇数,那么后者的集合里必然不存在重复的,所以2n有2k个因子.
如果n是偶数,那么必然前者里必然有1,2这2个因子,那么f2和2f1必然重复,所以偶数的因子必然少于2k个

yinshengsss

非常感谢楼上两位的解答！！！