大家来讨论几道数学...

1.what is the greatest prime factor of 2^100-2^96?

key:5

2.A total of 30 percent of the geese included in a certain migration study were male. If some of the geese migrated during the study and 20 percent of the migrating geese were male, what was the ratio of geese to the migration rate for the female geese?

key:7/12

3.DS: S is a set of points in the plane. How many distincttriangles can be drawn that have three of the points in S as vertices?

(1)The number of distinct points in S is 5

(2)No three of the points in S are collinear

key:C

4.DS: For any positive interger x, the 2-height of x is defined to be the greatest nonnegative interger n such that 2^n is a factor of x. If k and m are positive intergers, is the 2-height of k greater than the 2-height of m?

(1)k>m

(2)k/m is an even interger

key:C

5.DS: A scientist recored the number of eggs in each of 10 birds'rests. What was the standard deviation of the numbers of eggs in the 10 nests?

(1)The average number of eggs for the 10 nests was 4

(2)Each of the 10 nests contained the same number of eggs.

key:B

6.Four extra-large sandwiches of exactly the same size were orded for m students, where m>4.Three of the sandwiches were evenly divided among the students.Since 4 students did not want any of the fourth sandwich, it was evenly divided among the remaining students. If Carl ate one piece from each of the four sandwiches, the amount of sandwich that she ate would be what fraction of a whole extra-large sandwich?

A.(m+4)/m(m-4)

B.2m-4/m(m-4)

C.4m-4/m(m-4)

D.4m-8/m(m-4)

E.4m-12/m(m-4)

key:E

1.what is the greatest prime factor of 2^100-2^96?

key:5

2^100-2^96 = 2^96 (2^4-1) = 2^96 (16-1)=2^96 * 3 * 5

So, the greatest prime factor is 5.

1.what is the greatest prime factor of 2^100-2^96?

key:5

对原式化简就得：2^96(2^4-1),后面减式为五，前面是2的指数，所以是个和数，15可分解为3和5，所以最小的质数为5。

2.A total of 30 percent of the geese included in a certain migration study were male. If some of the geese migrated during the study and 20 percent of the migrating geese were male, what was the ratio of geese to the migration rate for the female geese?

key:7/12

第二题，楼主是否敲掉了一小段，因为提干缺少the ratio of some of the geese migrated during the study。所以没有办法解出，不好意思，至少我凭这个条件解不出来。

3.DS: S is a set of points in the plane. How many distinct triangles can be drawn that have three of the points in S as vertices?

(1)The number of distinct points in S is 5

(2)No three of the points in S are collinear

key:C

条件一不能确定，因为这5个不同的点中的三个有可能在一条直线上；条件二没有给出具体的点数，所以无法确定；条件1和2合璧，则可以得出确定的值：C（3，5）

4.DS: For any positive interger x, the 2-height of x is defined to be the greatest nonnegative interger n such that 2^n is a factor of x. If k and m are positive intergers, is the 2-height of m?

(1)k>m

(2)k/m is an even interger

key:C

题目估计又敲错了，K表示什么？

5.DS: A scientist recored the number of eggs in each of 10 birds'rests. What was the standard deviation of the numbers of eggs in the 10 nests?

(1)The average number of eggs for the 10 nests was 4

(2)Each of the 10 nests contained the same number of eggs.

key:B

条件一只知均值，不知具体个案值，无法求SD；条件二说明所有的值都相同，则SD为零。故B

6.Four extra-large sandwiches of exactly the same size were orded for m students, where m>4.Three of the sandwiches were evenly divided among the students.Since 4 students did not want any of the fourth sandwich, it was evenly divided among the remaining students. If Carl ate one piece from each of the four sandwiches, the amount of sandwich that she ate would be what fraction of a whole extra-large sandwich?

A.(m+4)/m(m-4)

B.2m-4/m(m-4)

C.4m-4/m(m-4)

D.4m-8/m(m-4)

E.4m-12/m(m-4)

key:E

这题关键要读懂题意，由题意可得如下等式: Carl吃的所有的S有如下：3/m+(1/(m-4)),对该式简化就得E了。

marvelvaliant,第2题原题就是这样,所以我也很郁闷,求不出来,第4题我把题目打漏了一点,已经改正了,非常感谢你的帮忙!!^^