做真题遇到的几道恶心题目

Ruisseau

mymengming

以下是引用esprit在2005-11-17 16:56:00的发言：

if n is positive integer,R is the remainder of (n^2-1)/24,then R=?

(1)2 is not a factor of n

(2)3 is not a factor of n

ANS:C

（n+1）(n-1)/24         (1)说明n是奇数，所以（n+1）(n-1)是8的倍数              （2）说明（n+1）、(n-1)中有一个是3的倍数。所以选C

One kilogram of a certain coffee blend consists of  x  kilogram of type I coffee and y kilogram of type II coffee ,THe cost of the blend is C dollars per kilogram where C=6.5x+8.5y,is x<0.8

(1)y>0.15

(2)C>=7.30

ANS:B

x+y=1,代入则c＝8.5－2x                     （1）得到x<8.5            (2)得到x<=0.6             所以选b

when 15n(positive integer) is divided by 6,remainder is X,then X=?

(1)WHen n is divided by 2 the remainder is 0

(2)When n is divided by 3 ,the remainder is 0

ANS:A

15n/6=3*5n/6                           （1）说明n中有2，所以remainder是0           （2）什么也不能说明。

这种题目都是问能整除的条件。

求解,谢谢

esprit

谢谢 ~~~~~~~~~~~~~~~~~~~~~~~~

t5oct2005

前两句推翻各自陈述,第三行提出不含2,3因子的n的通式

yangsh

if n is positive integer,R is the remainder of (n^2-1)/24,then R=?
(1)2 is not a factor of n
(2)3 is not a factor of n
ANS:C

(1) n,R = 1,0 or 3,8 ...
(2) n,R = 1,0 or 2,3 ...
(1)&(2): n = 6k+1 or 6k+5
for n=6k+1, n^2-1=6k(6k+2)=12k(3k+1), k无论奇偶, k(3k+1)总是偶, 故含有24这个因子, R=0
for n=6k+5, n^2-1=6(k+1)(6k+4)=12(k+1)(3k+2), k无论奇偶, (k+1)(3k+2)总是偶, 故含有24这个因子,R=0
therefore ... C

阴影部分是什么道理，请解释，谢谢

t5oct2005

if n is positive integer,R is the remainder of (n^2-1)/24,then R=?
(1)2 is not a factor of n
(2)3 is not a factor of n
ANS:C

(1) n,R = 1,0 or 3,8 ...
(2) n,R = 1,0 or 2,3 ...
(1)&(2): n = 6k+1 or 6k+5
for n=6k+1, n^2-1=6k(6k+2)=12k(3k+1), k无论奇偶, k(3k+1)总是偶, 故含有24这个因子, R=0
for n=6k+5, n^2-1=6(k+1)(6k+4)=12(k+1)(3k+2), k无论奇偶, (k+1)(3k+2)总是偶, 故含有24这个因子,R=0
therefore ... C

One kilogram of a certain coffee blend consists of  x  kilogram of type I coffee and y kilogram of type II coffee ,THe cost of the blend is C dollars per kilogram where C=6.5x+8.5y,is x<0.8
(1)y>0.15
(2)C>=7.30
ANS:B

已知1=x+y, C=6.5x+8.5y
(1) 0.15<y=1-x,则x<0.85, 无法知道x<0.8
(2) 7.3<=C=6.5x+8.5(1-x),则2x<1.2, x<0.6<0.8, 充分!

岁寒三宝

第一题,天山9的吧。欧用2，4，6，8和3，5，7，9分别试，n只可能为5

[此贴子已经被作者于2005-11-17 18:57:50编辑过]

yangsh

when 15n(positive integer) is divided by 6,remainder is X,then X=?

(1)WHen n is divided by 2 the remainder is 0

(2)When n is divided by 3 ,the remainder is 0

ANS:A

n能被2正处，15n is divisable by 6, so remainder is 0

the other two questions need NN help

esprit

if n is positive integer,R is the remainder of (n^2-1)/24,then R=?

(1)2 is not a factor of n

(2)3 is not a factor of n

ANS:C

One kilogram of a certain coffee blend consists of  x  kilogram of type I coffee and y kilogram of type II coffee ,THe cost of the blend is C dollars per kilogram where C=6.5x+8.5y,is x<0.8

(1)y>0.15

(2)C>=7.30

ANS:B

when 15n(positive integer) is divided by 6,remainder is X,then X=?

(1)WHen n is divided by 2 the remainder is 0

(2)When n is divided by 3 ,the remainder is 0

ANS:A

求解,谢谢