求助，PREP数学

麦兜woo

1.If ab≠0 and points (-a,b)and (-b,a) are in the same quadrant of the xy-plane, is point (-x,y)in this quadrant?
（1）xy＞0
 (2)  ax＞0  
我觉得单独（1）条件就可以了？答案是C

2. Acertain jar conains only b black marbles, w white marbles, and r red marbles. If one marble is to be chosen as random from the jar, is the probability that the marble chosen will be red greater than the probability that the marble chosen will be white?
(1) r／b+w ＞w／b+r
(2) b-w＞r

3. What is the greatest possible area of a triangular region with one vertex at the center of  circle of radius 1 and the other two vertices on the circle? 答案是1／2

4.In May Mrs Lee's earnings were 60 percent of the Lee's total income. In June, Mrs Lee earned 20 percent more than in May. If the rest of the family's income was the same both months, then in June, Mrs Lee's earnings were approximately what percent of the Lee family's total income?  答案是64%

5. Whenever Martain has a restaurant bill with an amount between $10and $99, he calculates the dollar amount of the tips as 2 times the tens digit of the amount of his billl. If the amount of Martain's most recent restaurant bill was between $10 and 99$, was the tip calculated by Martain on this bill greater than 15% of the amount of the bill?
(1) the amount of the bill was between $15 and $50
(2) the tip calculated by Martain was $8
答案选B，题目是什么意思呢？

6. A certain list consists of five different integers, Is the average of the two greatest integers in the list greater than 70?
 (1)the medain of the integers in the list is 70
（2）the average of the tegers in the list is 70
条件（1）知道可以推出结论，但条件（2）怎么推呢？

believezx

1、(-a,b)和(-b,a)在同一象限，可推出a、b为同号，同正或同负。
(-x,y)也在这个象限的话，说明   1.xy>0；    2.x要与a、b同号，因为-x要与-a、-b同号。
也可以用特殊值法核对一下答案。

2、要求r/b+r+w与w/b+r+w的大小
(r/b+r+w)-(w/b+r+w)=r-w/b+r+w    只需判断r-w的正负，条件一可以，条件二不行。

3、已知三角形两边长均为1，其面积S=1/2*（a*b*sinC）,C为a、b两边的夹角，求最大值，S=1/2*sinC，sinC最大值为1，故最大可能面积S=1/2

believezx

第4题很简单啊，设May家庭总收入为T，则女主人的收入为60%T，剩下其他来源的收入为40%T；女主人June的收入为(1+20%)60%T，其他收入不变。 女主人June的收入/女主人June的收入+其他收入即得到答案。我算的好像是约等于64%

believezx

5，题目意思是说   这个人将自己在餐厅账单介于10刀和99刀之间时，付小费时按账单金额的十位数*2来算，比如账单时45，小费就给4*2=8     我是这样理解的

believezx

6、条件2，说5个数的平均数位70，那5个数之和就是350，如果最大两个数的平均数<70，即最大两个数之和<140，表示剩下3个数之和>350-140=210, 表示剩下三个数的平均数>70，这显然不可能

个人之见

jake1

5，题目意思是说   这个人将自己在餐厅账单介于10刀和99刀之间时，付小费时按账单金额的十位数*2来算，比如账单时45，小费就给4*2=8     我是这样理解的

-- by 会员 believezx (2010/10/11 10:10:12)

我是设帐单费为10a+b, 题目要求2a与15%(10a+b)比较大小，化简以后就是求10a与3b的大小关系。b只能取0-9, 条件一不能确定，而条件二可以确定10a必然大于3b。

maximeason

我觉得第一题 之所以有B是因为 我们不知道x，y是否为零
因为 对于ab来说 只要ab同号且不为零 就成立
对于xy来说也是一样的 通过一我们知道xy同号
唯一欠缺的就是 x y 是否为零 由于a不是零
在条件二中 ax>0是为了证明x nonzero