[讨论]2004年3月数学JJ 61-80讨论稿

橙子

三月数学JJ滚动总结在这里dispbbs.asp?boardid=22&id=39950&star=1#39950

61.ps.-30, -20,-10, 0, 10, 20,30,     上面有五点，求各点之间的 和的绝对值大小
橙子评价：题目不完整，待补充



62.ps 一个圆环的面积和里面小环的面积之比为4，求大圆和小圆的周长比。（有图）
橙子评价:设大环的半径为R,小环的半径为r,所以(R^2-r^2)/r^2=4:1-->R:r=5^(1/2):1,所以S大圆:S小圆=5^(1/2):1

63.ds: x.y.z are integers, whether xy is even?
(1) xz is even
(2) yz is even
橙子评价:E,不确定z的奇偶性,z为偶数时,x,y可奇可偶

64.ps.a function f(x) (x is positive integer) is defined as the number of intergers which are less than x and do not have common factor with x other than 1, if p is any prime number, f(p)=?
(1) p-2
(2) p-1
(3) (p+1)/2
(4) (p-1)/2
(5) 2
橙子评价:选(2),因为p是质数,所以只有1和p两个因数,所以除去p本身,p-1个数是比p小且与p没有除1以外的公因子.如果求稳,大家可以举几个例子检验

65.ds: 一个三角形PQR(有图），角PQR为x,问PR>QR吗？
（1）PQ=PR
(2) x不等于60度
橙子评价:选E,因为条件1+条件2有两种可能,x>60度,PR>QR,X<60度,PR<QR

66.ps: 8！=2的J次方乘以3的K次方乘以5的L次方乘以7的M次方，问J+K+M+L=?(类似出现过的jj 题）
橙子评价:8!=1*2*3*4*5*6*7*8=2^7*3^2*5*7,所以J+K+M+L=7+2+1+1=11

67. ps.In a company 50% of male employees and 40% of female employees are more than 35 years old, 42% of total employees are more than 35 years,ask female employees is what percent of total employees.
橙子评价:80%,设男职员人数为x,女职员为y,所以50%x+40%y=42%(x+y)-->y=4x-->y/(x+y)=4/5=80%

68.ds: in a x-y plane, line l and line k intersect at a point (-4/5, 8/5) ( 数字不准，但不影响），ask the slope of line l.(重复两次)
(1) line l is perpendicular to line k
(2) link k 过原点
橙子评价:选C,由条件2确定line K的斜率=8/5/(-4/5)=-2,条件1,互相垂直的两条直线的斜率为负倒数,所以line l的斜率为-1/2

69.DS: line k 过原点,whether point (-2/3,3/4) is on the line k?
(1) (-2,3)在line k 上
(2) (2,-3)在line k 上( 数字不准，但不影响）
橙子评价:选D,题干+条件1确定y=(-3/2)x,所以确定(-2/3,3/4)不在K上;题干+条件2->y=(-3/2)x,确定(-2/3,3/4)不在K上

70.PS: a manager 召集m个directors 开会,每个director 又召集了n个 salespersons 开会(一起),问总共有多少人包括directors and salespersons 开会?
橙子评价:m+mn

71.PS: an item is sold at a listed prix $210.00, including 5% tax, what is the price of the item before tax?
(1)$199.50
(2)$200.00
(3).(4).(5) 都大于$200.00
橙子评价:选(2),设税前价格是X,所以X+0.05X=210->X=200

72.DS: what is the value of x的平方?
(1)x^2<5 (2)x is an integer
橙子评价: 选E,条件1+条件2,推出两种可能,1和4

73.PS: what percent of 10 equal to 10 percent of 1?(2月JJ类似题)
(1)0.01%
(2)0.1%
(3)1%
(4)10%
(5)100%
橙子评价:选(3),10% of 1=0.1, 0.1/10=1%

74. PS: a machine makes 100 units in 5 hours, if add a distinct machine, two machines together make 100 units in 2 hours, how many units does this added machine make in an hour?
(1) 10
(2) 20
(3) 30
(4) 40
(5) 50
橙子评价:选3,已知机器的速度为20units/hour(100/5)->两小时生产40units->后加的机器两小时生产了60units(100-40),所以后加机器的速度为30units/hour

75.ds: S and M respectively drived t hours, S covered 350 miles and M covered 325 miles, what is M's speed?
(1)t=5
(2)S's speed is 5 mile/hour greater than M's
橙子评价:选D,条件1->M'speed=325/t=325/5=65miles/hour, 条件2->350/t-325/t=5->t=5,所以M'speed=325/t=325/5=65miles/hour

76.ds. Tom paid income tax at a rate of 6% of annual income in 1999,Tome paid what percent of income in 2000 ?
(1)the taxable income of Tom is $34,200(数字不准) in 1999
(2)in 2000 Tome paid $600.00 more than what he paid in 1999
橙子评价:选E,条件1+条件2只能推出2000年缴税额,缺少条件,未知2000年总收入

77.ps.一個正方體 每邊長4, X and Y 是 其中兩邊的中點 (有圖) what is the length of the line segment of the endpoint of X and Y(it does not show in the graph)?
橙子评价:缺图,如果x,y,在上底和下底相对两边上,则XY=4*2^(1/2)

78.ps.Anny travels from City A to B in 4 hours with the average hour speed between 25 and 45; while Ross travels from City A to B on the same route in 2 hours with the average speed between 45 and 65. The distance could be which of the following. a. 95, b. 115 c.160 e.180
橙子评价:选b,由Anny确定路程距离的范围为100(25*4)-180(45*4),由Ross确定距离的范围为90(45*2)-130(65*2),联合得到距离的范围为100-130,只有b满足.

79.ps.一列数,mean是m,一倍标准差(还是方差)是n,已知68%的数字分布within m and n,问多少percent的数字位于〉M+N。
作者答案16%
橙子评价:同意,思路同3月JJ第7题类似题

80.ps.whichis the least: &#189;^5; 1/ 2^6; 1/ 2^7; 3/ 2^7; 7/ 2^9
橙子评价:1/2^7

请大家在讨论稿中讨论JJ,暂时没有列入讨论稿的题目请另开贴讨论,谢谢合作!

[此贴子已经被作者于2004-3-27 10:57:38编辑过]

donna

谢谢，橙子ＭＭ


辛苦了，只是字体太小，能不能编辑一下，谢谢！！！

耳朵

70.PS: a manager 召集m个directors 开会,每个director 又召集了n个 salespersons 开会(一起),问总共有多少人包括directors and salespersons 开会?
橙子评价:am+amn
这个题目是否应该理解成“一个经理召集m个负责人开会，每个负责人又找了n个销售人员开会”，那么答案应该是mn+1。

ohayo

64.             (P-1)/2        


                                 举几个例子就知了.


70.     M+MN

sdfjy

63.ds: x.y.z are integers, whether xy is even?
(1) xz is even
(2) yz is even
橙子评价:E,不确定z的奇偶性,z为偶数时,x,y可奇可偶


我认为是C,因为如果z为奇数,根据1,2, X 和Y必须都是奇数,所以XY是偶数


如果Z为偶数,根据1,2, X,Y 必须都是偶数,所以XY也是偶数.

sdfjy

70 不知道题目是怎么问的,如果是问总共有多少人开会,应该是MN+M+1 要把总的MANAGEMENT算进去吧

橙子

以下是引用sdfjy在2004-3-27 4:08:00的发言：
63.ds: x.y.z are integers, whether xy is even?
(1) xz is even
(2) yz is even
橙子评价:E,不确定z的奇偶性,z为偶数时,x,y可奇可偶



我认为是C,因为如果z为奇数,根据1,2, X 和Y必须都是奇数,所以XY是偶数


如果Z为偶数,根据1,2, X,Y 必须都是偶数,所以XY也是偶数.

Z是奇数的时候,X和Y一定是偶数,奇数*奇数=奇数,偶数*奇数=偶数,偶数*偶数=偶数,Z是偶数时,X,Y可奇可偶

ohayo

64 还是橙子MM的对.

rt316

73 我认为或许有个trick，问的是what percent of 10而不是what of 10，所以我认为答案应该是E，100％＝1；则1 percent of 10 = 0.1