【求助】菜鸟求助各位高手数学机经解答~~~

垂柳紫陌洛城东

Q13:
For any positive integer x, the 2-height of x is defined to be the greatest nonnegative integer n such that 2n is a factor of x.  If k and m are positive integers, is the 2-height of k greater than the 2-height of m ?
(1)      k > m
(2)        is an even integer.
    
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.
Answer: B


Q16:
If n is a positive integer and r is the remainder when (n-1)(n+1) is divided by 24, what is the value of r?
(1)      2 is not a factor of n.
(2)      3 is not a factor of n.
    
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.
Answer: C


Q37:
Working alone at their respective constant rates, machine A and machine B can fill a certain order in 3 hours and 6 hours, respectively.  If the two machines work simultaneously at their respective constant rates, how many hours does it take the two machines to fill 1/2 of that order?

A.    1/2
B.  3/4
C.  1
D.    1 1/4
E.    1 1/2
Answer: C



Q17:
Last year the price per share of Stock X increased by k percent and the earnings per share of Stock X increased by m percent, where k is greater than m.  By what percent did the ratio of price per share to earnings per share increase, in terms of k and m?

A.      %
B.    (k – m) %
C.    [100(k – m)] / (100 + k) %
D.    [100(k – m)] / (100 + m) %
E.    [100(k – m)] / (100 + k + m) %
Answer: D


Q32:
If x is a positive integer, is the remainder 0 when (3x + 1)/10?
(1)      x = 3n + 2, where n is a positive integer.
(2)      x > 4
    
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.
Answer: E


Q9:
If an integer n is to be chosen at random from the integers 1 to 96, inclusive, what is the probability that n(n + 1)(n + 2) will be divisible by 8?

A.    
B.    
C.    
D.    
E.    
Answer: D



Q4:
If S is the sum of the reciprocals of the consecutive integers from 91 to 100, inclusive, which of the following is less than S?

I.  
II.  
III.  


A.    None
B.    I only
C.    III only
D.    II and III only
E.    I, II, and III

 Answer: C

垂柳紫陌洛城东

Q9、题的四个选项是：A.1/4，     B.3/8，     C.1/2，     D.5/8，     E.3/4，答案为D.    
Q4、I. 1/8     II.   1/9     III.1/10



拜托各位高手能帮忙解答，以上这些题我想了很久也想不出解的方法，奈何我的机经只有答案没有解析，不得已请求各位高手帮帮我这个大菜鸟，每道题只需点明一下方法或是思路就行，谢谢，万分感激

垂柳紫陌洛城东

垂柳紫陌洛城东

Q17 所求值为价格除以收益的比率r：

r=(1+k/100)P/(1+m/10)E

增加比率为I=(r-P/E)/(P/E)=r/(P/E)-1=(1+k/100)(1+m/100)-1=(k-m)/(100+m)

=100(k-m)/(100+m)%

答案为D。

垂柳紫陌洛城东

Q9：解析：所有的偶数值 n 带入到 公式中 都能被8 整除。那么就看有多少个奇数能被8 整除。

当n 是奇数时， n+1 一定是偶数，那么 n+1=8*1, 8*2… , 8*11 和8*12, 一共有12组数可以被8 整除。所以加上偶数的n 能被8 整除， 是48个，一共是 60个数能被8 整除。60/96, 那么 n(n+1)(n+2) 被8 整除的概率就是 5/8.