第一次做GMAT 四道错了的数学题 求解 谢谢

woshishizhan

1.     For every positive even integer n, the function h(n) is defined tobe the product of all the even integers from 2 to n, inclusive. If p is thesmallest prime factor of h(100)+1, then p is
(a) BTW 2 to 10
(b) BTW 10 to 20
(c)  BTW 20 to 30
(d) BTW 30 to 40
(e) Greater than 40
2.     If r and s are integers and rs+r is odd, which of the followingmust be even?
(a) r
(b) s
(c)  r+s
(d) rs-r
(e) r^2+s
3.     An investment of d dollars at k simple annual interest rate yields$600 interest over a 2-year period. In terms of d, what dollar amount investedat the same interest rate will yield $2400 interest over a 3-year period?
(a) 2d/3
(b) 3d/4
(c)  4d/3
(d) 3d/2
(e) 8d/3
4.     A basket contains 5 apples, of which 1 is spoiled and the rest aregood. If Henry is to select 2 apples from the basket simultaneously and atrandom, what is the probability that the 2 apples selected will include the spoiledapple?
(a) 1/5
(b) 3/10
(c)  2/5
(d) 1/2
(e) 3/5

socialelite

1. ? 2. b; 3.  e   4. c  请教了

woshishizhan

麻烦解释一下可以么

waliwali

2.     If r and s are integers and rs+r is odd, which of the followingmust be even?

rs+r=r(s+1)是单数，所以r和s+1都是单数，s肯定是双数。选B

3.     An investment of d dollars at k simple annual interest rate yields$600 interest over a 2-year period. In terms of d, what dollar amount investedat the same interest rate will yield $2400 interest over a 3-year period?

由题干，2kd=600 所以这个利率k=300/d。
由问题，3kd'=2400 将上式k带入得出d'=8d/3


4.     A basket contains 5 apples, of which 1 is spoiled and the rest aregood. If Henry is to select 2 apples from the basket simultaneously and atrandom, what is the probability that the 2 apples selected will include the spoiledapple?

五个苹果随机取2个有C（5,2）=10种取法。
取到一个苹果是坏的有4种取法。
4/10=五分之二

waliwali

1.     For every positive even integer n, the function h(n) is defined tobe the product of all the even integers from 2 to n, inclusive. If p is thesmallest prime factor of h(100)+1, then p is


做到h(100)+1=2*4*6……*98*100+1

做不下去了... 不过我会选E或者A... E可能性大一点

waliwali

1.     For every positive even integer n, the function h(n) is defined tobe the product of all the even integers from 2 to n, inclusive. If p is thesmallest prime factor of h(100)+1, then p is


做到h(100)+1=2*4*6……*98*100+1

做不下去了... 不过我会选E或者A... E可能性大一点

-- by 会员 waliwali (2011/12/13 15:22:51)

我选A，闲得慌用excel算了一下，p可以是3

xiaolulubai

第一题是E 因为H100=2*……98*100.  设想有一个小于40的数37，那么他一定是h100的一个质因数，因为37翻倍等于74一定在H100里面，刚好能约掉。  所以既然是H100的质因数就一定不是h100+1的质因数，因为相邻的两个数不可能有一样的质因数，还因为后者是奇数前者的因数里包含了所有小于50的数的倍数。   所以其实最小质因数应该是大于50的，所以E是对的。