68. 3^19/10的余数？
答案：7
[討論]3之次方個位數為3,9,7,1之cycle, 19次個位為7, so余数7
69. 造一个矩形的篱笆,有一条边靠墙,给出另三条边的条件,问能不能求出面积最大值.（不全）
A.a+b=多少不记得了,反正这个是对的
B不记得了,反正不对的
答案：A
[討論]請補足
70. 告诉一点（4，5）问它关于X轴对称点的坐标，注意reflection.一开始我以为是映射呢结果没答案，结果是对称点
答案：（4，-5）
[討論]這是以x轴為中線對摺後得的結果.
hitlzc:因我个人疏忽，未注意此贴与另外一贴有一定重复，给大家带来不便，非常抱歉！
请各位考友参看下贴：
http://forum.chasedream.com/dispbbs.asp?boardid=22&id=176928&star=1#176928
作者: donald123 时间: 2006-6-12 02:44
71. 7 ^86 +4,问个位数。
答案：3
[討論]7的個位cycle為7,9,3,1, 所以以個位9+4=3
72. 说一人去存款,给复利，在存款总额低于1000时给2%的复利，在高于1000时给2.5%的复利。问哪个部分获利更多？
A。按2%时挣了65元（大概数字）
B。一共存了3年，
答案：C (not sure)
[討論]請參考由20樓開始的討論, 感謝yaoyao99和洛拉討論.
73. 画了一个文氏图，有三种人，either study B or O or both,these all together is 40 people. 25people study M and 10 study both.Then what is the percentage of people just study O not B of M. (不全)
答案：5/15
[討論]不太明白為何三种人B, O, B&O, 之後再有m, 請更正或提點.
74. 说一个人开车，一共要走多少mile问能否在3小时到达，后面给出1mile=1.6km，我算出总距离是200KM，这个就够了
A。这人一小时最快开65KM
B。这人5秒最慢开1KM，注意换算成KM/h，这个具体数记不清了，但最慢都能在三小时走完的。
答案：D
[討論]1)這可找3hours走多遠, ok 2)這亦可找3 hours走多遠, ,ok, d
75. 说有一个小孩玩chips,没回玩完总要丢一部分，丢的部分比原来的一半多一个，两次以后剩5个，问原来有多少个，给出五个范围。我好像是选 18~23
答案：26
[討論]第一次先將5x2+1=11, 第二次是11x2+1=23(但這個的一半不是整數)所以6亦試試看,6x2=12(12/2-1=5), 之後12x2+1=25, range在23-25間.
76. 说一家商店卖东西，俩个商品A、B上涨一样的amount,问原来谁的价格高？
A。B上涨后卖80元
B。上涨的幅度A为30%，B为30%，
答案：B
[討論]1)只知b’s price, 不可比, 2)由題目可知上涨一樣amount再加上涨一樣%, ok, b
77. (1/2)^3 / (1/7)
答案: 7/8
[討論](1/8)/7=7/8
78. 给了一个长方形的长和宽，然后一个三角形内接在长方形内，底边是长方形的一边，顶点在另一边上，让求面积。
答案：长方形的面积一半
[討論]同意筆者
作者: violetmoon925 时间: 2006-6-12 09:07
支持你！
作者: violetmoon925 时间: 2006-6-12 09:22
57. 一个圆，圆心X，B为圆上一点，XB与弦AC垂直相交与D，DB＝2，AC＝12，求圆周长。。。
答案：20pai
57. 一个圆，圆心X，B为圆上一点，XB与弦AC垂直相交与D，DB＝2，AC＝12，求圆周长。。。
答案：20pai
[討論]請指教
设圆半径为X，根据已知条件可得到：X^2=(X-2)^2+6^2, 可解得X=10. 那么周长就是2paiR=20pai
58. 1000本金投资，按年计算复利，12年本利和为4000，求8000是多少年本利和？
答案：18年
58. 1000本金投资，按年计算复利，12年本利和为4000，求8000是多少年本利和？
答案：18年
[討論]請指教
设年利率是r
根据已知条件可知：1000(1+r)^12=4000, 要求1000(1+r)^X=8000?
1000(1+r)^12=4000-->[(1+r)^6]^2=2^2, 因此, (1+r)^6=2
1000(1+r)^X=8000-->(1+r)^X=2^3, 则, X=18
作者: violetmoon925 时间: 2006-6-14 16:20
把它顶回第一页，不然好多CDer都看不到了！
作者: vicomte 时间: 2006-6-14 18:08
up
作者: seastone 时间: 2006-6-14 20:12
答案：90cm
[討論]這兩個是 similar triangle (三角全等), 設人和d点间的距离=x, 900/180=(549-x)/x, x=90
人和d点间的距离=x, 900/180=(540+X)/X ==> X=180
作者: zbaby 时间: 2006-6-14 21:44
請問第七樓
答案應為135而非180?
作者: seastone 时间: 2006-6-15 03:49
同意ZBAY ,是我算错了!
是135
作者: yaoyao99 时间: 2006-6-16 03:41
62. 以d为顶点的两个角都是x度 => d is between the person and the wall. Otherwise, there'd only be 1 angle => It should be 540 minux x, not plus.
67. Here's how I solved it. R's rate verses S's rate = (10000/9)
5000/3) = 2/3
R/(R+S) = (2/3) / (2/3 + 1) = (2/3)/(5/3) = 2/5
作者: zhangla 时间: 2006-6-16 04:43
设最开始有X个
丢第一次后剩下: X - (X/2 + 1) = X/2 - 1
丢第二次后剩下: (X/2 - 1) - (( X/2 - 1)/2 + 1) = 5
So, X=26
答案：26
[討論]第一次先將5x2+1=11, 第二次是11x2+1=23(但這個的一半不是整數)所以6亦試試看,6x2=12(12/2-1=5), 之後12x2+1=25, range在23-25間.
作者: zhangla 时间: 2006-6-16 05:11
这道题这里有详细的解释:
http://forum.chasedream.com/dispbbs.asp?boardID=22&ID=177028&page=1
存款低于1000时，年利率2％，按天计复利（compound
daily），高于1000时，年利率2.5％，按天计复利，钱存进去就没有拿出过或者再存过，问到底是按2％记的利息高还是按2.5％记的利息高？两个
选项是1，按2.5％记的利息是25USD；2，总共存了三年。这个按天记复利实在是太搞，最后想了n久，也不肯定，选了个两个都不行，但是加起来可以
（c）
我还没有什么思路,估计就是背答案的份了. 大家多讨论啊.
72. 说一人去存款,给复利，在存款总额低于1000时给2%的复利，在高于1000时给2.5%的复利。问哪个部分获利更多？
A。按2%时挣了65元（大概数字）
B。一共存了3年，
答案：C (not sure)
[討論]請補充
作者: yaoyao99 时间: 2006-6-16 07:05
Discussions from the other posting (http://forum.chasedream.com/dispbbs.asp?boardid=22&replyid=1674731&id=176928&page=1&skin=0&Star=1)
74. 说一个人开车，一共要走多少mile问能否在3小时到达，后面给出1mile=1.6km，我算出总距离是200KM，这个就够了
A。这人一小时最快开65KM
B。这人5秒最慢开1KM，注意换算成KM/h，这个具体数记不清了，但最慢都能在三小时走完的。
答案：D
A??
A。这人一小时最快开65KM 200/65>3 能确定不能在3 个小时内到达.
B。这人5秒最慢开1KM，注意换算成KM/h，这个具体数记不清了，但最慢都能在三小时走完的。
最慢60/5*1=12KM/H 200/12 >3 不能确定能否在3 个小时之内到达!
最慢是3600秒/5秒/公里=720公里/小时吧?
以下是引用violetmoon925在2006-6-14 21:57:00的发言：同意楼上，应该是720公里/小时。如果这样的话，条件二肯定可以。因此选D
以下是引用二狼神在2006-6-14 21:05:00的发言：72. 说一人去存款,给复利，在存款总额低于1000时给2%的复利，在高于1000时给2.5%的复利。问哪个部分获利更多？
A。按2%时挣了65元（大概数字）
B。一共存了3年，
答案：C (not sure)
题干要有按什么期限进行复利的条件吧?
以下是引用洛拉在2006-6-15 10:59:00的发言：
这道题分情况讨论就可以了，现有条件下应该选E
以下是引用csi在2006-6-15 20:32:00的发言：这题目的意思是说
低于1000就用2%的复利,而高于1000就用2.5%的复利吗?
那这样为何还要问哪的获利多阿?看是低于或高于不就行了
还是这题意思是
一个总额(3000,假设),其中1000用2%,2000用2.5%
若这样的话
A:缺总额,期间
B:也还是无总额阿
不太懂什么叫问哪边获利多?若总额小于1000不就不要比了?
请指教
以下是引用seastone在2006-6-15 21:56:00的发言：
存款低于1000时，年利率2％，按天计复利（compound daily），高于1000时，年利率2.5％，按天计复利，钱存进去就没有拿出过或者再存过，问到底是按2％记的利息高还是按2.5％记的利息高？两个选项是1，按2.5％记的利息是25USD；2，总共存了三年
http://forum.chasedream.com/dispbbs.asp?boardID=22&ID=177028&page=1
以下是引用洛拉在2006-6-15 22:53:00的发言：
可能应该是25USD吧？既然72题的65USD是大概的数
以下是引用csi在2006-6-15 23:13:00的发言:
感谢
请问C确定是正确答案吗
若是,请教如何思考这题
作者: hitlzc 时间: 2006-6-16 09:11
hitlzc:因我个人疏忽，未注意此贴与另外一贴有一定重复，给大家带来不便，非常抱歉！
请各位考友参看下贴：
http://forum.chasedream.com/dispbbs.asp?boardid=22&id=176928&star=1#176928
作者: vicomte 时间: 2006-6-16 09:29
74. 说一个人开车，一共要走多少mile问能否在3小时到达，后面给出1mile=1.6km，我算出总距离是200KM，这个就够了
A。这人一小时最快开65KM
B。这人5秒最慢开1KM，注意换算成KM/h，这个具体数记不清了，但最慢都能在三小时走完的。
答案：D
[討論]1)這可找3hours走多遠, ok 2)這亦可找3 hours走多遠, ,ok, d 这道题我碰到的问题是时间是否大于3小时
这道题我碰到的问题是时间是否大于3小时
作者: k8897710 时间: 2006-6-16 09:51
设最开始有X个
丢第一次后剩下: X - (X/2 + 1) = X/2 - 1
丢第二次后剩下: (X/2 - 1) - (( X/2 - 1)/2 + 1) = 5
So, X=26
答案：26
[討論]第一次先將5x2+1=11, 第二次是11x2+1=23(但這個的一半不是整數)所以6亦試試看,6x2=12(12/2-1=5), 之後12x2+1=25, range在23-25間.
up zhangla
i m 26 2
作者: yaoyao99 时间: 2006-6-16 09:53
I agree. 丢的部分比原来的一半多一个 => the previous time = (leftover + 1) * 2
3rd time: 5 => 2nd time: (5 + 1)*2 = 12 => 1st time: (12+1)*2 = 26
作者: violetmoon925 时间: 2006-6-16 10:19
不是jj的疏忽，是我太着急讨论了，所以就先开了个讨论贴。现在donald123已经把题目补充进来了，jj可以把我的那个贴子删掉，免得大家分散讨论。谢谢了！
作者: 洛拉 时间: 2006-6-16 10:44
Note: The interpretation here isn't quite correct. You can skip this and go straight to the 22nd floor for the final solution if you'd like.
72. Hmm.. if both are compound daily interest and one interest is higher than the other, there's nothing to calculate.
I'm guessing the question is: (Let saving = x)
when x < 1000 => 2% compound daily interest => annual interest = x * (1+0.02/365)^365 - x
when x > 1000 => 2.5% compound annual interest => annual interest = x * (1 + 0.025) - x
1) 0.025x = 25 => x = 1000
with 2% interest, interest = 1000 * (1+0.02/365)^365 - 1000 = about 20 (see note below)
2.5% gets better annual interest
2)
2.0%: x * (1 + 0.02/365)^(365*3) - x = about 0.06x
2.5%: x * (1 + 0.025)^3 - x = about 0.075x
2.5% has better rate for 3 years
Just for fun, for n years
2.0%: x * (1 + 0.02/365)^(365*n) - x = about 0.02*n*x
2.5%: x * (1 + 0.025)^n - x = about 0.025*n*x
2.5% annual interest rate is ALWAYS better. You don't need any condition? 
Note: for (1 + alpha)^x, when alpha is reasonably small, the value is approximately 1 + alpha*x
Simple Interest: interest = principal * interest rate * time
Interst compounded annually: interest = principal * (1 + annual interest rate) ^ number of years - principal
Interst compounded during the year: interest = principal * (1 + annual interest rate / num of times interest is compounded) ^ (num of times interest is compounded * num of years) - principal
版主，这一步有点儿问题吧？“0.025x = 25 => x = 1000”
这道题的意思是说，存钱的时候本金是不足1000元的，此时给是复利息2%，存了一段时间，连本带利总共超过了1000元，在此之后给的是复利息2.5%， 问，连本带利超过1000元之后形成的这个“新的本金”适用2.5%的利息率一共有多少利息，这一部分利息和25元相比谁大谁小？所以0.025和原本金是不能乘到一块儿去的
讨论
作者: yaoyao99 时间: 2006-6-16 11:06
Note: The interpretation here isn't quite correct. You can skip this and go straight to the 22nd floor for the final solution if you'd like.
Ahhh.. thank you 洛拉! That makes much more sense.
So when x < 1000, interest is about 0.02x and when x > 1000, interest is about 0.02 * 1000 - 0.025 * (x-1000) = 0.025x - 5
1) x = 2000 because 0.025 * (x-1000) = 25 => interest from 2% = 20 less than interest from 2.5%
2) when x < 1000, there's only interest from 2%
when x > 1000, interst is about 0.02*3*1000 from 2% and 0.025*3*(x-1000) from 2.5%
interest from 2% = 60 whereas interest from 2.5% = 0.075x - 75 (inconclusive without the value of x)
Answer is A?
作者: 洛拉 时间: 2006-6-16 11:51
Note: The interpretation here isn't quite correct. You can skip this and go straight to the 22nd floor for the final solution if you'd like.
Ahhh.. thank you 洛拉! That makes much more sense.
So when x < 1000, interest is about 0.02x and when x > 1000, interest is about 0.02 * 1000 - 0.025 * (x-1000) = 0.025x - 5
1) x = 2000 because 0.025 * (x-1000) = 25 => interest from 2% = 20 less than interest from 2.5%
2) when x < 1000, there's only interest from 2%
when x > 1000, interst is about 0.02*3*1000 from 2% and 0.025*3*(x-1000) from 2.5%
interest from 2% = 60 whereas interest from 2.5% = 0.075x - 75 (inconclusive without the value of x)
Answer is A?
这道题我算完觉得如果2%时利息是25元，那么选C，如果是65元，就得选E
因为过程实在太长，我只写个大概意思，分情况讨论，不是复利息嘛，就分成第一种情况：x *（1+2%）只出现了1年（由25元得出一个本金1，代入蓝色的式子里），后面2年因为都超过了1000元所以用2.5%的利率，即{[x* （1+2%）] * （1+2.5%) ^2} - [x *(1+2)]），第二种情况：x *（1+2%）出现了2年（由25元得出本金2代入红色的式子里），只有最后1年是2.5%的利率, 即{[x *（1+2%）] ^2} * (1+2.5%) - [x *（1+2%）] ^2), 得出两种情况的利息看看是否都一致地大于或者小于25元，如果一致则选C，如果不一致，就选E无法判定。如果是按天计算复利息也同理分成类似上述两种情况就行了。
版主看看对不对？
作者: yaoyao99 时间: 2006-6-16 12:30
, I see what you mean now. What about this:
2) Interest from year 1 = x * 0.02 (assume x < 1000), let the total $ in the bank at the end of year 2 = x2 and the total at the end of year 3 = x3
year 2 | total interest at 2nd year end | year 3 | total interest at 3rd year end | total interest from 2% | total interest from 2.5% | |
1 | x2 < 1000 | x * 1.02 * 1.02 – x | x3 > 1000 | x * 1.02 * 1.02 * 1.025 - x | 0.04x | 0.066x – 0.04x = 0.026x< 0.04x |
2 | x2 > 1000 | x * 1.02 * 1.025 - x | x3 > 1000 | x * 1.02 * 1.025 * 1.025 - x | 0.02x | 0.071x – 0.02x= 0.051x> 0.04x |
Now let's look at condition 1)
If interest from 2% is $65, then both case 1 and 2 are invalid (x > 1000). => invalid condition?
If
interest from 2.5% is $25, then it's also an invalid condition:
case 1: 0.026x = 25 => x = $960 (invalid) => x3 < 1000 and case 2: 0.051x = 25 => x = $490 (invalid) => x3 < 1000
If interest from 2% is $25, then:
case 1: 0.04x = 25 => x = $625 (valid) => we know that interest from 2.5% < interest from 2%
case 2: 0.02x = 25 => x = $1250 (invalid, we assumed x, the principal, to be less than 1000 at the beginning of the first year)
answer C (only interest from 2% is $25 is a valid condition)
Note, (1+n%)^m 约等于 (1+n%*m), based on Taylor's Expansion (for (1 + alpha)^x, when alpha is reasonably small, the value is approximately 1 + alpha*x). This should save you some time on the test even if it says interest compounded daily/month/whatever. In case the numbers are different, you can calculate the interest as compounded annually even if it says compounded several times during the year.
Simple interest: interest = principal * annual interest rate * num of years
Interst compounded annually: interest = principal * (1 + annual interest rate) ^ number of years - principal
Interst compounded several times during the year:
interest = principal * (1 + annual interest rate / num of times interest is compounded) ^ (num of times interest is compounded * num of years) - principal
作者: 洛拉 时间: 2006-6-16 13:29
Note: The final solution is summarized in the 22nd floor.
, I see what you mean now. What about this:
2) Interest from year 1 = x * 0.02 (assume x < 1000)
case year 2 total interest at year end year 3 total interest at year end 1 x2 < 1000 x* 1.02*1.02 – x x3 > 1000 x* 1.02*1.02 * 1.025 – x 2 x2 > 1000 x *1.02 * 1.025 - x x3 > 1000 x * 1.02 * 1.025 * 1.025 – x
At the end of year 3
Case 1: interest from 2% is about 0.04x and interest from 2.5% is about:
0.066x – 0.04x = 0.026x < 0.04x
Case 2: interest from 2% is about 0.02x and interest from 2.5% is about:
0.071x – 0.02x = 0.051x > 0.02x
Now back to 1)
If interest from 2% is $25, then
case 1: 0.04x = 25 => x = $625 (valid) => interest from 2.5% < interest from 2%
case 2: 0.02x = 25 => x = $1250 (invalid, we assumed the principal to be less than 1000)
C
版主到底是版主啊！能把乱七八糟的一片列成这么清晰的表！
我再写清楚点儿：设一开始的本金是x
第一种情况：2%的利率只用了1年，x*( 1+2%)的积就已经大于1000元了，此时， x*2%=25， x=1250，于是，1250 * （1 + 2%）* （1 + 2.5%) ^2 - 1250 * ( 1+ 2%) 就等于用2.5% 时产生的利息啦！等于64.546875. 注意这个地方要不是减去最初的本金x，而是减去1250 * （1 + 2%），因为这是适用2.5%利率时的“新的本金”了嘛！我的意思也不知道说清楚没有？这道题出现2个复利息的利率，就相对应2个本金啊，一个是初始本金，一个是初始本金按2%利率计算以后因为超出1000元了就构成了“适用2.5%利率的基础，也就是新本金”，等于让你算，新本金在2.5%的利率情况下产生的利息多呢？还是原始本金在2%的利率情况下产生的利息25元多？
第二种情况：2%的利率用了2年，连本带利才超过1000元能用2.5%，此时 x * （1+2%）^2 - x = 25，x约等于618.8，于是，618.8 * (1 + 2%)^2 * ( 1+ 2.5%) - 618.8 * (1 + 2%）^2 ，约等于16.094988
多谢多谢版主啊！我这次为了准确用计算器算，才发现自己之前手算有错误，真不好意思误导了你吧？一种情况大于25，一种情况小于25，所以如果题目是25，那也是E了（应是C了，1250那种情况无效）
唉，这种题，算错一点都白费
辛苦版主了！再看看对吗？
作者: yaoyao99 时间: 2006-6-16 13:42
Hee hee, I just fixed my answer in 第 22 楼 and added the various versions of condition 1. What do you think?
Here's the table again, summarizing what you wrote:
year 2 | total interest at year end | year 3 | total interest at year end | Interest from 2% | Interest from 2.5% | |
情况2 | x2 < 1000 | x* 1.02*1.02 – x | x3 > 1000 | x* 1.02*1.02 * 1.025 - x | 0.04x | 0.066x – 0.04x = 0.026x |
情况1 | x2 > 1000 | x *1.02 * 1.025 - x | x3 > 1000 | x * 1.02 * 1.025 * 1.025 - x | 0.02x | 0.071x – 0.02x= 0.051x |
Note: x=1250 isn't a valid answer because we assumed x < 1000
BTW, (1+n%)^m 约等于 (1+n%*m), based on Taylor's Expansion. That should save you some time on the test, in case the numbers are different.
作者: 洛拉 时间: 2006-6-16 14:21
Note: The final solution is summarized in the 22nd floor.
Hee hee, I just fixed my answer in 第 22 楼 and added the various versions of condition 1. What do you think?
Here's the table again, summarizing what you wrote:
year 2 | total interest at year end | year 3 | total interest at year end | Interest from 2% | Interest from 2.5% | |
情况2 | x2 < 1000 | x* 1.02*1.02 – x | x3 > 1000 | x* 1.02*1.02 * 1.025 - x | 0.04x | 0.066x-0.04x = 0.026x |
情况1 | x2 > 1000 | x *1.02 * 1.025 - x | x3 > 1000 | x * 1.02 * 1.025 * 1.025 - x | 0.02x | 0.071x – 0.02x= 0.051x |
Note: x=1250 isn't a valid answer because we assumed x < 1000
BTW, (1+n%)^m 约等于 (1+n%*m), based on Taylor's Expansion. That should save you some time on the test, in case the numbers are different.
版主，应该保留你的原表，我改动你的表时顾此失彼了。你列表的方法很值得学习！感谢帮助！！
作者: 洛拉 时间: 2006-6-16 14:24
真希望考试时候不要遇到这种题！否则像我这种学文科的，计算能力又差，算不了几步就晕菜了！
作者: yaoyao99 时间: 2006-6-16 14:35
Note: The final solution is summarized in the 22nd floor.
But x * 1.02 * 1.025 - x * 1.02 gives you the interest from the 2nd year ONLY. I'm doing accummulated interest where the "total interest at 2nd year end" = interest from year 1 + interest from year 2 and "total interest at 3rd year end" = TOTAL interest from year 1 to 3
I don't understand how you got to the equations in the final column (interest from 2.5%).
Your equation x* 1.02*1.02 * 1.025 - x*(1.02)*(1.02) already gave you interest from 2.5% (interest from the 3rd year ONLY) which is the same as what I have 1.066x - 1.04x = 0.026x.
Similarly, your equation x * 1.02 * 1.025 * 1.025 - x*(1.02) gave you interest from 2.5% in 情况1, which is the same as what I have as well, 1.071x - 1.02x = 0.051x.
Anyway, I think the answer is C because only 第二种情况 is valid so we know interest from 2% is greater than interest from 2.5%. Assuming interest from 2% is $25 and we're calculating interests from a 3 year period.
作者: 洛拉 时间: 2006-6-16 15:13
Note: The final solution is summarized in the 22nd floor.
But x * 1.02 * 1.025 - x * 1.02 gives you the interest from the 2nd year ONLY. I'm doing accummulated interest where the "total interest at 2nd year end" = interest from year 1 + interest from year 2 and "total interest at 3rd year end" = TOTAL interest from year 1 to 3
I don't understand how you got to the equations in the final column (interest from 2.5%).
Your equation x* 1.02*1.02 * 1.025 - x*(1.02)*(1.02) already gave you interest from 2.5% (interest from the 3rd year ONLY) which is the same as what I have 1.066x - 1.04x = 0.026x.
Similarly, your equation x * 1.02 * 1.025 * 1.025 - x*(1.02) gave you interest from 2.5% in 情况1, which is the same as what I have as well, 1.071x - 1.02x = 0.051x.
Anyway, I think the answer is C because only 第二种情况 is valid so we know interest from 2% is greater than interest from 2.5%. Assuming interest from 2% is $25 and we're calculating interests from a 3 year period.
感谢版主指出我的纰漏！讨论还是给我很大帮助的！
作者: 洛拉 时间: 2006-6-16 17:05
我忽略了1250无效的情况，同意选C。
作者: LilyJune 时间: 2006-6-16 20:21
70. 告诉一点（4，5）问它关于X轴对称点的坐标，注意reflection.一开始我以为是映射呢结果没答案，结果是对称点
答案：（4，-5）
[討論]這是以x轴為中線對摺後得的結果.
映射是虾米东东？应该以前高中学过，但是过了太久了，偶只是听过完全没有概念了。。。
谢谢~
作者: 二狼神 时间: 2006-6-16 20:56
我忽略了1250无效的情况，同意选C。
就是说不管A说65元还是25元都选C吧?
这种DS能不能不算具体的值呢?好费时间
作者: LilyJune 时间: 2006-6-16 21:29
设最开始有X个
丢第一次后剩下: X - (X/2 + 1) = X/2 - 1
丢第二次后剩下: (X/2 - 1) - (( X/2 - 1)/2 + 1) = 5
So, X=26
答案：26
[討論]第一次先將5x2+1=11, 第二次是11x2+1=23(但這個的一半不是整數)所以6亦試試看,6x2=12(12/2-1=5), 之後12x2+1=25, range在23-25間.
同意，我也觉得应该是这样列方程，算出具体数值，题目中怎么会出现范围呢？
作者: yaoyao99 时间: 2006-6-16 22:07
就是说不管A说65元还是25元都选C吧?
这种DS能不能不算具体的值呢?好费时间
$65 from 2% and $25 from 2.5% are both invalid conditions (see 第 22 楼 for details). It must be $25 from 2% or something else.
作者: zhangla 时间: 2006-6-17 01:44
hehe, 我肯定比你差,今天GMATPrep数学错了12个,我下周一考
作者: 洛拉 时间: 2006-6-17 15:00
hehe, 我肯定比你差,今天GMATPrep数学错了12个,我下周一考
作者: violetmoon925 时间: 2006-6-17 21:36
pf洛拉mm和yaoyao斑竹！我看了好几遍才好像大概明白了你们的讨论。真的是挺复杂的！我有一个问题啊，要是考试的时候遇到这种难度的题，怎么办？Give up? 而且，这道题如果不算出确切值好像不太好判断答案吧？ETS什么时候开始出这么复杂的题了？换了我上学的时候，光讨论就能写好几张纸呢。
作者: yaoyao99 时间: 2006-6-17 22:33
Oh never give up! Stay calm and treat it as any other questions and at least make an educated guess if you have to. Eliminate as many "bad" choices as you can.
For interest rates, see if you can list the rates year by year (assuming the number of years is reasonably small) and draw a table so you can compare the difference from year to year. The questions are generally about 1. difference in interests or 2. final interest.
Plus, it's not as bad as it looks. We spent a lot of time trying to figure out which version of the jj is valid. You won't have to worry about that on the real test. So all you have to deal with is really the table and the two equations at the end.
作者: numberunique 时间: 2006-6-18 20:29
楼主! 58题之前 还有一个不完整JJ 如下
10。5是N的因子，求N除以6的余数
i）N^4 个位不等于1
ii) N^12 个位。。。。忘了，没来得及做的最后一题
大家做何解
作者: 梦不落 时间: 2006-6-18 22:40
楼主! 58题之前 还有一个不完整JJ 如下
10。5是N的因子，求N除以6的余数
i）N^4 个位不等于1
ii) N^12 个位。。。。忘了，没来得及做的最后一题
大家做何解
第二个条件不知道。不太好说。从题干得到N应该个位数不是5就是0.而这样的话除以6余数有很多。可以举例验证下。
第一个条件 N^4个位不是一，不能得出余数是否唯一的结论。因为个位是5或者0的话，本身四次方的个位不是一了。
第二个条件未提供。
但我个人觉得这道题恐怕和真题有出入。因为就算能定下来N个位数是多少，也不能保证余数唯一。除非这个数能够计算出来，或者此类数能得出一种通项公式。
不知道这样理解是否正确。现在就是盼着yaoyao考完回来给我们打气呵呵：）
作者: yaoyao99 时间: 2006-6-18 23:23
Haha, go sleep! I haven't left yet. My test is in the afternoon.
作者: violetmoon925 时间: 2006-6-19 00:08
楼主! 58题之前 还有一个不完整JJ 如下
10。5是N的因子，求N除以6的余数
i）N^4 个位不等于1
ii) N^12 个位。。。。忘了，没来得及做的最后一题
大家做何解
从条件1能得到：N这个数的个位不能是：1，7，9。但是，即使不用条件1，也能知道这个啊，因为，题目说了5是N的因子，所以，N的个位只能是0或者5啊。所以，不明白这个条件有什么用。
作者: numberunique 时间: 2006-6-19 10:59
有理
my test is in the afternoon too
作者: maxin18 时间: 2006-6-19 21:00
59. 答案是C吧，要有<8的条件才可以啊
作者: numberunique 时间: 2006-6-19 21:12
59. 答案是C吧，要有<8的条件才可以啊
i）每天投的小于8封
ii）每天都的数目两两都不一样
答案：B
[討論]1)明顯不足; 2) b 每天都的数目两两都不一样
What if 有一天投O？
Then 0+1+2+3+4+5+6=21 < 27 so B insufficient
even if 有<8的条件 insufficient
Hence E??
作者: 村愚 时间: 2006-6-22 07:32
标题: 此题选a;请高人指正。
, I see what you mean now. What about this:
2) Interest from year 1 = x * 0.02 (assume x < 1000), let the total $ in the bank at the end of year 2 = x2 and the total at the end of year 3 = x3
year 2 | total interest at 2nd year end | year 3 | total interest at 3rd year end | total interest from 2% | total interest from 2.5% | |
1 | x2 < 1000 | x * 1.02 * 1.02 – x | x3 > 1000 | x * 1.02 * 1.02 * 1.025 - x | 0.04x | 0.066x – 0.04x = 0.026x< 0.04x |
2 | x2 > 1000 | x * 1.02 * 1.025 - x | x3 > 1000 | x * 1.02 * 1.025 * 1.025 - x | 0.02x | 0.071x – 0.02x= 0.051x> 0.04x |
Now let's look at condition 1)
If interest from 2% is $65, then both case 1 and 2 are invalid (x > 1000). => invalid condition?
If
interest from 2.5% is $25, then it's also an invalid condition:
case 1: 0.026x = 25 => x = $960 (invalid) => x3 < 1000 and case 2: 0.051x = 25 => x = $490 (invalid) => x3 < 1000
If interest from 2% is $25, then:
case 1: 0.04x = 25 => x = $625 (valid) => we know that interest from 2.5% < interest from 2%
case 2: 0.02x = 25 => x = $1250 (invalid, we assumed x, the principal, to be less than 1000 at the beginning of the first year)
answer C (only interest from 2% is $25 is a valid condition)
Note, (1+n%)^m 约等于 (1+n%*m), based on Taylor's Expansion (for (1 + alpha)^x, when alpha is reasonably small, the value is approximately 1 + alpha*x). This should save you some time on the test even if it says interest compounded daily/month/whatever. In case the numbers are different, you can calculate the interest as compounded annually even if it says compounded several times during the year.
Simple interest: interest = principal * annual interest rate * num of years
Interst compounded annually: interest = principal * (1 + annual interest rate) ^ number of years - principal
Interst compounded several times during the year:
interest = principal * (1 + annual interest rate / num of times interest is compounded) ^ (num of times interest is compounded * num of years) - principal
设共存了X年，2%利率持续了n年，2.5%利率持续了x-n年。本金为a
哪个部分获利更多:
a(1+2%）ｎ（１＋２．５％）ｘ－ｎ－ａ（１＋２％）ｎ［２．５％部分］－[a(1+2%)n-a] (２％部分)
条件１：2%时挣了65元，即a(1+2%）ｎ＝６５
则原式＝６５Ｘ１．０２５ｘ－ｎ－６５－６５＋ａ＝６５（１．０２５ｘ－ｎ－２）＋ａ；
须判定原式＞，＜，＝０的性质是否唯一。则６５（１．０２５ｘ－ｎ－２）＋ａ＞０＜＝＝＞１．０２５ｘ－ｎ－２＞－ａ／６５
由条件a(1+2%）ｎ＝６５，得：１．０２５ｘ－ｎ－２＞ａ／ａ１．０２ｎ＜＝＝＞１．０２５ｘ－ｎ １．０２ｎ＞２－１．０２ｎ
ｎ＞＝０，１．０２ｎ＞＝１；ｘ＞＝ｎ，１．０２５ｘ－ｎ＞＝１；
所以，右边，２－１．０２ｎ最大为１；左边ｎ与ｘ－ｎ不可能同时为０，所以１．０２５ｘ－ｎ １．０２ｎ恒大于２－１．０２ｎ
即，2．５%利恒大于2%利；
2%时挣了65元， 为充分。
条件2:共存3年；既x=3,0<=n<=3,
a(1+2%）ｎ（１＋２．５％）ｘ－ｎ－ａ（１＋２％）ｎ－[a(1+2%)n-a]
=a(1+2%）ｎ(1.025x-n-2)+a ; ＞，＜，＝０的性质是否唯一。
设，a(1+2%）ｎ(1.025x-n-2)+a>0<==>1.02n(1.025x-n-2)>-1;
但，n=1时，1.02n(1.025x-n-2）=-0.9877>-1;
而 n=3时，1.02n(1.025x-n-2=-1.02<-1
所以，共存3年的条件，不充分。
所以，此题选a;请高人指正。
作者: donald123 时间: 2006-6-22 08:56
59. 一周7天每天投信，总共一周投信数是否大于27封
i）每天投的小于8封
ii）每天都的数目两两都不一样
答案：B
[討論]1)明顯不足; 2) b 每天都的数目两两都不一样
What if 有一天投O？
Then 0+1+2+3+4+5+6=21 < 27 so B insufficient
even if 有<8的条件 insufficient
Hence E?? everyday letter(s) is posted
作者: donald123 时间: 2006-6-22 09:01
从条件1能得到：N这个数的个位不能是：1，7，9。但是，即使不用条件1，也能知道这个啊，因为，题目说了5是N的因子，所以，N的个位只能是0或者5啊。所以，不明白这个条件有什么用。
作者: violetmoon925 时间: 2006-6-22 10:26
回45楼，我不太看得懂你列的式子。
a(1+2%）ｎ（１＋２．５％）ｘ－ｎ－ａ（１＋２％）ｎ［２．５％部分］－[a(1+2%)n-a] (２％部分)
作者: 洛拉 时间: 2006-6-22 13:06
回45楼，我不太看得懂你列的式子。
a(1+2%）ｎ（１＋２．５％）ｘ－ｎ－ａ（１＋２％）ｎ［２．５％部分］－[a(1+2%)n-a] (２％部分)
作者: 洛拉 时间: 2006-6-22 13:15
回45楼村愚：2%时挣了65元，即a(1+2%）ｎ＝６５，
挣了65元应该指除了本金之外的利息是65元吧？你这个式子成了本金合计65元
另，这题还有个2%时挣了25元的版本
作者: 村愚 时间: 2006-6-22 23:51
回45楼村愚：2%时挣了65元，即a(1+2%）ｎ＝６５，
挣了65元应该指除了本金之外的利息是65元吧？你这个式子成了本金合计65元
另，这题还有个2%时挣了25元的版本
作者: heqingyu 时间: 2007-6-28 09:53
第62题的答案应该是90吧。计算公式如下：
900/180=(540-X)/X ==> X=90
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