问数学题啊，高手指点下，谢谢

cckjenius

1，For a certain race, 3 teams were allowed to enter 3 members each.A team earned 6 – n points whenever one of its members fiFor a certain race, 3 teams were allowed to enter 3 members each.A team earned 6 – n points whenever one of its members finished in nth place, where 1 ≤ n ≤ 5.There were no ties, disqualifications, orwithdrawals.If no team earned more than 6 points, what is the least possible score a team could have earned? 选D


A.0
B.1
C.2
D.3

E.4

2，At a certain food stand, the price of each apple is ¢ 40 and the price of each orange is ¢ 60.Mary selects a total of 10 apples and oranges from the food stand, and the average (arithmetic mean) price of the 10 pieces of fruit is ¢ 56.How many oranges must Mary put back so that the average price of the pieces of fruit that she keeps is ¢ 52?


A.1
B.2
C.3
D.4

E.5

这题我感觉我会做，可是我的答案是2个，为什么答案说是E呢？

3，If a and b are integers, is b even?
(1)3a + 4b is even.
(2)3a + 5b is even.
我感觉选B呀，我的推导是条件2，a一定是双数，b也一定是要双数，否则加起来不会是EVEN啊，但是答案说选C，不解啊。


4，The area of square S is equal to the area of rectangle R.What is the perimeter of square S?
(1)The length of one of the sides of rectangle R is twice the length of a side of square S.
(2)The area of rectangle R is 36.
这题答案说选B，可是我选的C啊，条件2光知道个面积，怎么算的出周长啊，求解，是不是答案错啦？

最后一道，不好意思题目有点多
5，A certain list consists of 21 different numbers.If n is in the list and n is 4 times the average (arithmetic mean) of the other 20 numbers in the list, then n is what fraction of the sum of the 21 numbers in the list?


A.  1/20

B.  1/6
C.  1/5  
D. 4/21  
E. 5/21
答案选B，完全做不来，解释一下，谢谢拉
For a certain race, 3 teams were allowed to enter 3 members each.A team earned 6 – n points whenever one of its members finished in nth place, where 1 ≤ n ≤ 5.There were no ties, disqualifications, orwithdrawals.If no team earned more than 6 points, what is the least possible score a team could have earned? 选D


A.0
B.1
C.2
D.3

E.4

2，At a certain food stand, the price of each apple is ¢ 40 and the price of each orange is ¢ 60.Mary selects a total of 10 apples and oranges from the food stand, and the average (arithmetic mean) price of the 10 pieces of fruit is ¢ 56.How many oranges must Mary put back so that the average price of the pieces of fruit that she keeps is ¢ 52?


A.1
B.2
C.3
D.4

E.5

这题我感觉我会做，可是我的答案是2个，为什么答案说是E呢？

3，If a and b are integers, is b even?
(1)3a + 4b is even.
(2)3a + 5b is even.
我感觉选B呀，我的推导是条件2，a一定是双数，b也一定是要双数，否则加起来不会是EVEN啊，但是答案说选C，不解啊。


4，The area of square S is equal to the area of rectangle R.What is the perimeter of square S?
(1)The length of one of the sides of rectangle R is twice the length of a side of square S.
(2)The area of rectangle R is 36.
这题答案说选B，可是我选的C啊，条件2光知道个面积，怎么算的出周长啊，求解，是不是答案错啦？

最后一道，不好意思题目有点多
5，A certain list consists of 21 different numbers.If n is in the list and n is 4 times the average (arithmetic mean) of the other 20 numbers in the list, then n is what fraction of the sum of the 21 numbers in the list?


A.  1/20
B.  1/6
C.  1/5  
D. 4/21  
E. 5/21
答案选B，完全做不来，解释一下，谢谢拉

Nickyl90

At a certain food stand, the price of each apple is ¢ 40 and the price of each orange is ¢ 60.Mary selects a total of 10 apples and oranges from the food stand, and the average (arithmetic mean) price of the 10 pieces of fruit is ¢ 56.How many oranges must Mary put back so that the average price of the pieces of fruit that she keeps is ¢ 52

In this case, you thought to exchange an orange with an apple while the stimulus tells you to put back oranges WITHOUT taking any extra apples.

parispings

3，If a and b are integers, is b even?
(1)3a + 4b is even.
(2)3a + 5b is even.
我感觉选B呀，我的推导是条件2，a一定是双数，b也一定是要双数，否则加起来不会是EVEN啊，但是答案说选C，不解啊

What if both a and b are odd for condition 2 ?

parispings

4，The area of square S is equal to the area of rectangle R.What is the perimeter of square S?
(1)The length of one of the sides of rectangle R is twice the length of a side of square S.
(2)The area of rectangle R is 36.
这题答案说选B，可是我选的C啊，条件2光知道个面积，怎么算的出周长啊，求解，是不是答案错啦？

Well the area of the square S is 36, courtesy of rectangle R.  And the square root of 36 should be the length of the sides of that square.  So the answer is 24.

parispings

5，A certain list consists of 21 different numbers.If n is in the list and n is 4 times the average (arithmetic mean) of the other 20 numbers in the list, then n is what fraction of the sum of the 21 numbers in the list?

A.  1/20
B.  1/6
C.  1/5  
D. 4/21  
E. 5/21

Let's assume the average of the other 20 numbers is A.  Then the sum of that 20 numbers is 20 x A = 20A, while the value of the number n is 4 x A, or 4 A.  The sum of the 21 numbers = the sum of the value of number n and the other 20 numbers = 4A + 20A = 24A

The desired ratio = the value of number n / the sum of the 21 numbers = 4A / 24 A = 1/6

parispings

For a certain race, 3 teams were allowed to enter 3 members each.A team earned 6 – n points whenever one of its members fiFor a certain race, 3 teams were allowed to enter 3 members each.A team earned 6 – n points whenever one of its members finished in nth place, where 1 ≤ n ≤ 5.There were no ties, disqualifications, orwithdrawals.If no team earned more than 6 points, what is the least possible score a team could have earned? 选D


A.0
B.1
C.2
D.3

E.4


Basically, the only points each team can earn are from the pool of 5, 4, 3, 2, 1.  If  no team earned more than 6 points, then let two teams earn 6 points (1 and 5, 2 and 4).  Which available spot left for the third team? Only 3 points to earn.

seuhongkai

3，If a and b are integers, is b even?
(1)3a + 4b is even.
(2)3a + 5b is even.
我感觉选B呀，我的推 ...
parispings 发表于 2010-11-23 06:48

    奇数*奇数=奇数  奇数*偶数=偶数  奇数+奇数=偶数  奇数+偶数=奇数 偶数+偶数=偶数
Thus，from condition1,3a ,4b 同奇偶，4b是偶数 所以 3a是偶 推出a是偶数   不能确定 b 是 even
from condition 2 ，a，b同奇偶，单独不能确定 b 是偶
但from 1，a is even。 so b is even。  选c

yoyo9012

3，If a and b are integers, is b even?
(1)3a + 4b is even.
(2)3a + 5b is even.
我感觉选B呀，我的推 ...
parispings 发表于 2010-11-23 06:48

    这个 两个单独肯定都不能推出  两个在一起  你拿第二个等式减第一个等式得b   两个偶数相减肯定也是偶数啊   所以两个一起sufficient

zhongyaya

4，The area of square S is equal to the area of rectangle R.What is the perimeter of square S?
(1)The length of one of the sides of rectangle R is twice the length of a side of square S.
(2)The area of rectangle R is 36.
这题答案说选B，可是我选的C啊，条件2光知道个面积，怎么算的出周长啊，求解，是不是答案错啦？

最后一道，不好意思题目有点多
5，A certain list consists of 21 different numbers.If n is in the list and n is 4 times the average (arithmetic mean) of the other 20 numbers in the list, then n is what fraction of the sum of the 21 numbers in the list?


A.  1/20
B.  1/6
C.  1/5  
D. 4/21  
E. 5/21
答案选B，完全做不来，解释一下，谢谢拉
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4。 条件是S正方形，R是长方形，两个图形的面积相等。
      如果设S的边长是a, R的边长分别为 b,c。则可以得等式 a*a=b*c,那不是很明显B答案中 R的面积就可以求出S的边了吗~


5。设m为除了n意外20个数的和，根据条件得 n=4乘以 m/20，即m=5n,最后问的是 n和21个数之和的比是多少，很明显就是 1/6啦~
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给楼主的一点建议。
这两道题目不是难，就是要看清楚题目，切勿急躁。将题目信息整合成数字等式很很重要的，凭空乱想很容易错，也很容易思维混乱。
不知道楼主还有多少时间要考试。我觉得多做做GWD数学提高一下题感是很重要的，有题感才能有效的抓住题目主干和考点。

最后祝楼主成功~！

cckjenius

谢谢各位相助，数学实在太差啊。。见笑了。。