PREP1 ＭＡＴＨ模拟错题６道请教！

ktj

162.If n and y are positive integers and 450y = n^3, which of the following must be an integer?  (2)

　  1) y/ 3^2*2*5^2     2)y/3*2^2*5    3)  y/ 3*2*5^2

我疑惑：代入后，（n／３＊２＊５）＾３就一定是integer吗？　如果n＝７呢？

４３．A committee of three people is to be chosen from four married couples.  What is the number of different committees that can be chosen if two people who are married to each other cannot both serve on the committee?　　（Ｅ）

 

(A)  16　(B)  24　(C)  26(D)  30　(E)  32

119.       12086-!-item-!-187;#058&008079

A contractor combined x tons of a gravel mixture that contained 10 percent gravel G, by weight, with y tons of a mixture that contained 2 percent gravel G, by weight, to produce z tons of a mixture that was 5 percent gravel G, by weight.  What is the value of x ?　　（Ｄ）

 

(1) y = 10　　　　　(2) z = 16

23.       1653-!-item-!-187;#058&000843

At least 100 students at a certain high school study Japanese. If 4 percent of the students at the school who study French also study Japanese, do more students at the school study French than Japanese?　　（Ｂ）

 

(1)  16 students at the school study both French and Japanese.

 

(2)  10 percent of the students at the school who study Japanese also study French.

79.       6946-!-item-!-187;#058&005390

If the terms of a sequence are t1, t2, t3, . . . , tn, what is the value of n ?　　　（Ｃ）

 

(1)  The sum of the n terms is 3,124.

 

(2)  The average (arithmetic mean) of the n terms is 4.

．．If x is positive, which of the following could be the correct ordering of 1/x, 2x, and x^2?

   I,x^2<2x<1/x      II, x^2<1/x<2x   III......

        answer is       D I and II only

ＢＴＷ，请问考到５０，５１分允许错几个？

[此贴子已经被作者于2007-10-28 0:42:18编辑过]

CindyFarer

这题我记得选E吧

actionone

．．If x is positive, which of the following could be the correct ordering of 1/x, 2x, and x^2?

   I,x^2<2x<1/x      II, x^2<1/x<2x   III......

        answer is       D I and II only

这题把三条曲线画出来,昨天别人给我讲的,一下就可以看出来, 这样想的话, 容易漏条件.

actionone

162.If n and y are positive integers and 450y = n^3, which of the following must be an integer?  (2)

　  1) y/ 3^2*2*5^2     2)y/3*2^2*5    3)  y/ 3*2*5^2

我疑惑：代入后，（n／３＊２＊５）＾３就一定是integer吗？　如果n＝７呢？

原题即为 2*3^2*5^2y=n^3, 因此可以推出 y一定等于2^2*3*5 才能满足(2*3*5)^3=n^3, 所以 2) y/3*2^2*5  一定是整数

actionone

４３．A committee of three people is to be chosen from four married couples.  What
is the number of different committees that can be chosen if two people
who are married to each other cannot both serve on the committee?　　（Ｅ）

 

(A)  16　(B)  24　(C)  26(D)  30　(E)  32

C(3,4)*2^3=32

ktj

以下是引用actionone在2007-10-28 9:49:00的发言：

．．If x is positive, which of the following could be the correct ordering of 1/x, 2x, and x^2?

   I,x^2<2x<1/x      II, x^2<1/x<2x   III......

        answer is       D I and II only

这题把三条曲线画出来,昨天别人给我讲的,一下就可以看出来, 这样想的话, 容易漏条件.

X=2时, X^2>1/X; 就这一条答案就都不符合,why????.

--------------   162.If n and y are positive integers and 450y = n^3, which of the following must be an integer?  (2) 　  1) y/ 3^2*2*5^2     2)y/3*2^2*5    3)  y/ 3*2*5^2 我疑惑：代入后，（n／３＊２＊５）＾３就一定是integer吗？　如果n＝７呢？ 原题即为 2*3^2*5^2y=n^3, 因此可以推出 y一定等于2^2*3*5 才能满足(2*3*5)^3=n^3, 所以 2) y/3*2^2*5  一定是整数

能否请教我上面问的问题? n=7时,好象不成立!????   7^3=/=(3*2*5)^3  迷糊........

-----------------------------

--  作者：actionone --   ４３．A committee of three people is to be chosen from four married couples.  What is the number of different committees that can be chosen if two people who are married to each other cannot both serve on the committee?　　（Ｅ）   (A)  16　(B)  24　(C)  26(D)  30　(E)  32 C(3,4)*2^3=32

IT's C(4,3)*2^3 ??? 

 C(4,3) means choose three out four couple, while 2^3 means every chosen couple have 2 choice.

[此贴子已经被作者于2007-10-28 11:11:43编辑过]

huasing007

23.       1653-!-item-!-187;#058&000843

At
least 100 students at a certain high school study Japanese. If 4
percent of the students at the school who study French also study
Japanese, do more students at the school study French than
Japanese?　　（Ｂ）

 

(1)  16 students at the school study both French and Japanese.

 

(2)  10 percent of the students at the school who study Japanese also study Fren

how to answer this???

lisy

以下是引用ktj在2007-10-28 11:08:00的发言：

X=2时, X^2>1/X; 就这一条答案就都不符合,why????.

这题问的是could be ture, not must be ture.

--------------   162.If n and y are positive integers and 450y = n^3, which of the following must be an integer?  (2) 　  1) y/ 3^2*2*5^2     2)y/3*2^2*5    3)  y/ 3*2*5^2 我疑惑：代入后，（n／３＊２＊５）＾３就一定是integer吗？　如果n＝７呢？ 原题即为 2*3^2*5^2y=n^3, 因此可以推出 y一定等于2^2*3*5 才能满足(2*3*5)^3=n^3, 所以 2) y/3*2^2*5  一定是整数

能否请教我上面问的问题? n=7时,好象不成立!????   7^3=/=(3*2*5)^3  迷糊........

这题你这么理解，因为450Y是整数，而且是一个数的三次方，那么它本身的所有的指数必须都有三次方，450=3^2*2*5^2, 那么n^3=3^3*2^3*5^3*x^3(x可以是任何一个质数），所以450y =3^3*2^3*5^3*x^3

把450=3^2*2*5^2代入

得出Y=3*2^2*5*x^3

也就是y/3*2^2*5=x^3为整数

至于你说得N=7时候不成立，是因为N根本不可能等于7,N一定是2*3*5的倍数，最小是30

-----------------------------

--  作者：actionone --   ４３．A committee of three people is to be chosen from four married couples.  What is the number of different committees that can be chosen if two people who are married to each other cannot both serve on the committee?　　（Ｅ） (A)  16　(B)  24　(C)  26(D)  30　(E)  32 C(3,4)*2^3=32

IT's C(4,3)*2^3 ??? 

 C(4,3) means choose three out four couple, while 2^3 means every chosen couple have 2 choice.

我的做法是，先从8个人里面选一个，C(1,8)=8.然后7个人，但是只有6个选择，然后剩下5个人，只有4个选择，一共是8*6*4

但是选出的三个人可能是ABC,ACB,CBA....也就是说多排序了，所以要除以P(3,3)

[此贴子已经被作者于2007-10-28 14:28:46编辑过]

ktj

谢谢LISY! 这几道还没解决,哪位帮忙解释一下??

119.       12086-!-item-!-187;#058&008079

A contractor combined x tons of a gravel mixture that contained 10 percent gravel G, by weight, with y tons of a mixture that contained 2 percent gravel G, by weight, to produce z tons of a mixture that was 5 percent gravel G, by weight.  What is the value of x ?　　（Ｄ）

(1) y = 10　　　　　(2) z = 16

23.       1653-!-item-!-187;#058&000843

At least 100 students at a certain high school study Japanese. If 4 percent of the students at the school who study French also study Japanese, do more students at the school study French than Japanese?　　（Ｂ） 

(1)  16 students at the school study both French and Japanese.

(2)  10 percent of the students at the school who study Japanese also study French.

79.       6946-!-item-!-187;#058&005390

If the terms of a sequence are t1, t2, t3, . . . , tn, what is the value of n ?　　　（Ｃ）

(1)  The sum of the n terms is 3,124.

(2)  The average (arithmetic mean) of the n terms is 4.

lisy

以下是引用ktj在2007-10-28 19:52:00的发言：

谢谢LISY! 这几道还没解决,哪位帮忙解释一下??

119.       12086-!-item-!-187;#058&008079

A contractor combined x tons of a gravel mixture that contained 10 percent gravel G, by weight, with y tons of a mixture that contained 2 percent gravel G, by weight, to produce z tons of a mixture that was 5 percent gravel G, by weight.  What is the value of x ?　　（Ｄ）

(1) y = 10　　　　　(2) z = 16

由题干可以得出两个方程，都是含有x,y,z的，条件1知道y的值，就只剩下两个未知数，两个方程就可以解了，同理，2是，所以选D

23.       1653-!-item-!-187;#058&000843

At least 100 students at a certain high school study Japanese. If 4 percent of the students at the school who study French also study Japanese, do more students at the school study French than Japanese?　　（Ｂ） 

(1)  16 students at the school study both French and Japanese.

(2)  10 percent of the students at the school who study Japanese also study French.

因为是说at least，所以学日本的也许不止100人，由条件1，16人可以推出学法语的是400人，那就不能确定到底谁大谁小

条件2说了10%，那么就是说0.1学法语的=0.04学日语的，可以推出来学日语的多

79.       6946-!-item-!-187;#058&005390

If the terms of a sequence are t1, t2, t3, . . . , tn, what is the value of n ?　　　（Ｃ）

(1)  The sum of the n terms is 3,124.

(2)  The average (arithmetic mean) of the n terms is 4.

两个条件一起肯定能解决的，我不知道你不明白的是哪里，sum=t1+t2+t3+.....+tn,average=sum/n，知道了average和sum，n肯定就解出来了