Prep07数学错题疑问集ps（1）【至5.15未解答状态1/19】

灵狩Icy

未解答：

15.  图出不来，手动描述，一个等边三角形的三个顶点都在圆上，三角形周长为24，求圆直径。
(A) 5(B) 8(C) 11(D) 15(E) 19
答案：C
我算出的半径是8/√3，√3=1.7，直径算出来是9.41啊，为什么答案是C？？

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1. A certain taxi company charges $3.10 for the first 1/5 of a mile plus $0.4 for each addtional 1/5 of a mile. What would this company charge for a taxi ride that was 8 miles long?【已解答D，谢谢pri344926443】

(A)  $15.60

(B) $16.00

(C)  $17.50

(D)  $18.70

(E)   $19.10

3.1+2*(8-0.2)

2. For every positive even integer n, the function h(n) is defined to be the product of all the even integers from 2 to n, inclusive.  If p is the smallest prime factor of h(100) + 1, then p is【已解答E，谢谢pri344926443】

(A) between 2 and 10

(B) between 10 and 20
(C) between 20 and 30
(D) between 30 and 40
(E) greater than 40
*两个连续整数没有公因数，h（100）可算出因数是1-50的所有整数，因此h（100）+1的因数不包含1-50

3. When 2/3 of the garments in a shipment were inspected, 18 of the garments passed inspection and the remaining 2 garments failed.  How many of the uninspected garments must pass inspection in order that 90 percent of the garments in the shipment pass? 【已解答B，谢谢pri344926443】
(A)  10
(B)  9
(C)  8
(D)  7
(E)  5
90%*[（18+2）*3/2]-18

4.(1+0.0001)/(0.04+10)
The value of the expression above is closest to which of the following? 【已解答C，谢谢Joyce_lzy】

(A)  0.0001

(B)  0.001
(C)  0.1
(D)  1
(E) 10
不用管小数

5. The value of(10^9-10^4)/(10^8-10^5) is closest to which of the following?【已解答B，谢谢Joyce_lzy】

(A) 1

(B) 10
(C) 102
(D) 103
(E) 104
（10^5-1）/(10^4-10)

6. There are 10 children in a company's day-care center, and a pair of children is to be selected to play a game.  At most, how many different pairs are possible?
【已解答D，谢谢pri344926443】

(A) 100

(B) 90
(C) 50
(D) 45
(E) 25
答案是45，C10里挑2个
为什么不能是从10个里先挑1个*9个里挑1个=90？先挑A后挑B和先挑B后挑A重复了，需要除2.

7.图片老是显示不出来：就是数轴上，以O点为圆心，在一二象限有个半圆，半圆上有P点（-√3，1），Q点（s，t），线段PO和QO形成一个直角，问Q的横坐标。
In the figure above, points P and Q lie on the circle with center O.  What is the value of s ?【已解答B，谢谢pri344926443】
(A)  1/2
(B)  1
(C)  √2
(D)  √3
(E)  √2/2
这道题完全没思路啊，求助，答案是B

8.Rates for having a manuscript typed at a certain typing service are $5 per page for the first time a page is typed and $3 per page each time a page is revised.  If a certain manuscript has 100 pages, of which 40 were revised only once, 10 were revised twice, and the rest required no revisions, what was the total cost of having the manuscript typed? 【已解答 D】
(A) $430
(B) $620
(C) $650
(D) $680
(E) $770
这道题一不小心就掉进去了，答案是D，100*5+（40+10）*3+10*3
所有的page都type一遍，500刀；40pagerevise 第二次、10page也revise第二次，50*3刀；10page revise第三次，30刀

9.From a bag containing 12 identical blue balls, y identical yellow balls, and no other balls,one ball will be removed at random. If the probability is less than 2/5 that the removed ballwill be blue, what is the least number of yellow balls that must be in the bag? 【已解答C，谢谢xiangzhjs】
A. 17
B. 18
C. 19
D. 20
E. 21
概率问题，分母为总事件12+y，分子是从12个篮球中任选1个，因此是12/(12+y)<2/5，解出来y>18 ,最小是19

10.  50-59分的有2人，60-69分的有10人，70-79分的有16人，80-89分的有27人，90-99分的有18人。问which score interval contains the median of the 73 scores?
【已解答C，谢谢 荣耀和勇敢】
A. 60-69
B. 70-79
C. 80-89
D.90-99
E. can not be determined.
。。唉，题目问的是，这73个分数中，中位数在哪个区间。。。“73 scores”

11. If a certain sample of data has a mean of 20.0 and a standard deviation of 3.0, whichof the following values is more than 2.5 standard deviations from the mean? 【已解答A】
(A) 12.0
(B) 13.5
(C) 17.0
(D) 23.5
(E) 26.5
more than 2.5 standard deviation 的意思是原标准方差的2.5倍，所以是在上下7.5sd的区间内（12.5，27.5）。只有A不在这个区间内，是more than。

12.If m = 9/25, w = 15/32, and m + w + c = 1, which of the following gives the values ofm, w, and c in increasing order?【已解答A 谢谢 iriswine】
(A) c, m, w
(B) c, w, m
(C) m, w, c
(D) w, c, m
(E) w, m, c
把m，w大小算出来后，可以根据等式来排除选项。

13. The residents of Town X participated in a survey to determine the number of hours per week each resident spent watching television.  The distribution of the results of the survey had a mean of 21 hours and a standard deviation of 6 hours.  The number of hours that Pat, a resident of Town X, watched television last week was between 1 and 2 standard deviations below the mean.  Which of the following could be the number of hours that Pat watched television last week?
【已解答D，谢谢lululuna】
(A) 30
(B) 20
(C) 18
(D) 12
(E) 6
在（21-6，（21-6）*2）的区间内，只有D符合。

14. For all positive integers m,  【m】 = 3m， when m is odd and m = 【1/2】 m ，when m is even.  Which of the following is equivalent to 【9】 x 【6】  ?
【已解答D，谢谢lululuna】
(A)  【81】
(B)  【54】
(C)  【36】
(D)  【27】
(E)  【18】
题目出错：For all positive integers m,  【m】 = 3m， when m is odd and 【m】 = 1/2 m ，when m is even.  Which of the following is equivalent to 【9】 x 【6】  ?

16. Last month 15 homes were sold in Town X.The average (arithmetic mean) sale price of the homes was $150,000 and the median sale price was $130,000.Which of the following statements must be true?【已解答A 谢谢 iriswine】
I.At least one of the homes was sold for more than $165,000.
II.At least one of the homes was sold for more than $130,000 and less than $150,000.
III.At least one of the homes was sold for less than $130,000.
A.I only
B.II only
C.III only
D.I and II
E.I and III
算总价，举反例核对

17. 187. If 0 < r < 1 < s < 2, which of the following must be less than 1 ? 【已解答A 谢谢 iriswine】
I. r/s
II. rs
III. s-r
(A) I only(B) II only(C) III only(D) I and II(E) I and II
这种题要拿两端来带入。
r=0.99, s=1.99 =>rs >1

18. If x>y^2>z^4, which of the following statements could be true? 【已解答E 谢谢 iriswine】
I. x>y>z
II. z>y>x
III. x>z>y

(A) I only
(B) I and II only
(C) I and III only
(D) II and III only
(E) I, II, and III
取test point的3个范围设定好，不会有重复。且x>0

19. If x is positive, which of the following could be the correct ordering of 1/x,2x,x^2？【已解答E 谢谢 iriswine】
I.x^2<2x<1/x
II. x^2<1/x<2x
III. 2x<x^2<1/x
(A) None
(B) I only
(C) III only
(D) I and II only
先把不等式换成等式，求出界限值。再取test point

pri344926443

第一题我觉得选D
1/5 of a mile 就是0.2 mile
收费规则是 前0.2mile收取3.1元 之后每0.2mile收费0.4元 也就是之后每mile收费2元
那么8mile就要收费 3.1+2*（8-0.2）=18.7元

pri344926443

第二题是选E吗？
对于所有的正整数且为偶数的n来说，h(n)定义为从2到n所有偶数的乘积，且包括2和n。问的是h(100)+1的最小质因数p的取值范围。
h(100)=2*4*6*8*…*100=(2*1)*(2*2)*(2*3)*…*(2*50)=2的50次方*(1*2*3*…*50)=2^50*(50!)
h(100)+1=2^50*(50!)+1
楼主是否知道 任意两个连续整数 比如20和21 除了1以外是没有任何的公因数的
那么h(100)和h(100)+1这两个连续整数之间除了1以外也是没有公因数的，那么h(100)+1的因数中不会有h(100)的因数。而从h(100)=2^50*(50!)可以知道，h(100)的因数是从1到50的所有整数，那么h(100)+1的因数肯定都是大于50的啦。选E

Joyce_lzy

第四题和第五题是类似的：
4. (1+0.0001)/(0.04+10)=1/10  （请忽略小数，它们不重要）
5. 上下分别提取10^4和10^5之后变成了 （10^5-1）/10（10^3-1)=（请忽略1）=10^5/10^4=10

第二题我觉得我的方法有问题：我就是从n=2还是往后面代进去，最小质数是3然后是5，7.......100肯定大于40了

pri344926443

第三题选B
When 2/3 of the garments in a shipment were inspected, 18 of the garments passed inspection and the remaining 2 garments failed.  How many of the uninspected garments must pass inspection in order that 90 percent of the garments in the shipment pass?
当2/3的衣服被检测时，有18件检测合格，2件检测不合格。这里我们就可以知道一共有20件被检测，这20件占了总数的2/3，那么shipment上garment的总件数就是30件。问题是，如果90%的衣服检测合格的话，剩余的未检测的衣服里一定合格的件数是多少？ 没检测的有10件，10*90%=9 件 就是B啦。

pri344926443

关于第6题，题中问how many different pairs are possible，举个例子 选小红小明 和 选小明小红 这两种情况就不是different。按你的想法，10*9有一半是重复的，比如说从十个人里先选了小红，再从剩下九个人里选了小明；或者先从十个人里选了小明，再从剩下九个人里选了小红。既然问的是different pairs，就要排除重复情况，直接用C10 2做：(10*9)/2=45。

pri344926443

第七题 按你的描述画了图

有没有觉得P点坐标(-根3, 1)这两个数字很有感觉呢？从P点如图做辅助线，已知两直角边长分别为根号3，1，勾股定理能求出PO也就是半径为2，而且那个特殊角是30°。
PO和QO垂直，那么推导一下就知道QO和y轴夹角是30°。已知QO=半径=2，就知道Q的横坐标是1啦。

灵狩Icy

第九题： 12/(12+y)<2/5，解出来y>18 ,最小是19
------xiangzhjs 5.11 回复

灵狩Icy

“第十题楼主理解有问题，题干问的是这73个数的中位数落在哪个区间，再仔细读几遍题就好”
————————荣耀和勇敢   回复时间：5.12 16:00

灵狩Icy

第十二题：
http://forum.chasedream.com/foru ... amp;fromuid=1055392

灵狩Icy

第13题：
http://forum.chasedream.com/foru ... ;extra=#pid21736766

lululuna

14. For all positive integers m,  【m】 = 3m， when m is odd and m = 1/2 m ，when m is even.  Which of the following is equivalent to 【9】 x 【6】  ?

注意黄色部分，题主你是不是抄错题目了，M是正整数，你的【1/2】显然不符合题意啊

解答：
【9】,9是奇数，所以【9】=9*3=27

【6】,6是偶数，所以【6】=1/2*6=3；

综上【9】*【6】=27*3=【27】

灵狩Icy

17、18题：iriswine
http://forum.chasedream.com/foru ... ;page=1#pid21739388

灵狩Icy

18，19题
http://forum.chasedream.com/thread-1002744-1-1.html

灵狩Icy

pri344926443 发表于 2015-5-2 20:32
第一题我觉得选D
1/5 of a mile 就是0.2 mile
收费规则是 前0.2mile收取3.1元 之后每0.2mile收费0.4元 也就 ...

啊，原来是这样，我以为是前1/5的路程，我懂啦！谢谢！后面的题也求助~~

pri344926443

4题5题就像5楼说的那样啦~
题中说closest，近似算出答案就好啦~考试是不会考计算量大到要用计算器的题的

灵狩Icy

pri344926443 发表于 2015-5-2 20:50
第二题是选E吗？
对于所有的正整数且为偶数的n来说，h(n)定义为从2到n所有偶数的乘积，且包括2和n。问的是h ...

啊好详细！！这么说我懂了。但是E是大于40，其实也不完全对是吧？

灵狩Icy

Joyce_lzy 发表于 2015-5-2 20:52
第四题和第五题是类似的：
4. (1+0.0001)/(0.04+10)=1/10  （请忽略小数，它们不重要）
5. 上下分别提取10^ ...

OTZ，第四题就直接忽略了，原来如此。。这么看来我好蠢〒▽〒

第五题也是！OTZ 醉了，这种题原来是这样算。。我折腾了半天。。谢谢解答！！

灵狩Icy

pri344926443 发表于 2015-5-2 21:01
第三题选B
When 2/3 of the garments in a shipment were inspected, 18 of the garments passed inspectio ...

听你这么说就明白啦，这题看的我头晕，感觉根本没理解在说什么OTZ