二战 求助几道数学题

xiahuistacy

１　
　　

How many 4-digit positive integers are there in which all 4 digits are even?



A.    625

B.     600

C.     500

D.    400

E.     256

选Ｃ　　但是我不明白为什么这么选



２

What was the percent increase in the average (arithmetic mean) contribution per member of a certain public radio station from 1985 to 1995 ?

(1)   Total contributions by members increased from $505,210 in 1985 to $1,225,890 in
1995.


(2)     The number of members exactly doubled from 1985 to 1995.

                   

A. Statement (1) ALONE is sufficient, but statement (2) alone is not sufficient.

B. Statement (2) ALONE is sufficient, but statement (1) alone is not sufficient.

C. BOTH statements TOGETHER are sufficient, but NEITHER statement ALONE is sufficient.

D. EACH statement ALONE is sufficient.

E. Statements (1) and (2) TOGETHER are NOT sufficient.

还是选Ｃ　但是我依旧　　不知道怎么下手　　　

　

How many 4-digit positive integers are there in which all 4 digits are even?



A.    625

B.     600

C.     500

D.    400

E.     256

选Ｃ　　但是我不明白为什么这么选



２

What was the percent increase in the average (arithmetic mean) contribution per member of a certain public radio station from 1985 to 1995 ?

(1)   Total contributions by members increased from $505,210 in 1985 to $1,225,890 in
1995.


(2)     The number of members exactly doubled from 1985 to 1995.

                   

A. Statement (1) ALONE is sufficient, but statement (2) alone is not sufficient.

B. Statement (2) ALONE is sufficient, but statement (1) alone is not sufficient.

C. BOTH statements TOGETHER are sufficient, but NEITHER statement ALONE is sufficient.

D. EACH statement ALONE is sufficient.

E. Statements (1) and (2) TOGETHER are NOT sufficient.

还是选Ｃ　但是我依旧　　不知道怎么下手　　　

　

flyingbunny

How many 4-digit positive integers are there in which all 4 digits are even?

千位可以为10/2-1 个不同的偶数，其余各位为10/2个不同的偶数
4*5*5*5

a10285

1、 4位正数各位数均偶，
  首位不能为0，   0-9偶数数5， 4*5*5*5=500

2、      （1）Total增长1,225,890 /505,210
           （2）The number of members增长100%
 
公式average = Total/The number of members
（1）（2）结合可得出the percent increase in the average

flyingbunny

What was the percent increase in the average (arithmetic mean) contribution per member of a certain public radio station from 1985 to 1995 ?
(1)   Total contributions by members increased from $505,210 in 1985 to $1,225,890 in
1995
(2)     The number of members exactly doubled from 1985 to 1995.

From 1)
C1985=$505,210
C1995=$1,225,890
not sufficient

From 2)
M1995=2*M1985
not sufficient

Together,
Avg1985= C1985/M1985
Avg1995= C1995/M1995
(Avg1995-Avg1985)/Avg1985
Sufficient
Therefore C

xiahuistacy

但是第一题 为什么要4*5*5*5   从题目哪里可以看出是要乘？  我以为是问哪个数是偶数

wy215

但是第一题 为什么要4*5*5*5   从题目哪里可以看出是要乘？  我以为是问哪个数是偶数

-- by 会员 xiahuistacy (2009/12/25 10:33:20)

这个应该是排列组合那一块。如果这个四位数每一位都是偶数的话，那么首位有四种选择，其它三位都是5个选择，所以就是4*5*5*5啦

wy215

2）他问的是average的增长。那么如果能把两个average表示出来不就好了嘛。首先看1.他说total增加了多少，但是我们不知道Number,所以光靠1不行。再看2，他说number double了。好吧，我们假设第一个number是x.那么第二个就是2x.好的，现在来表示average.A1 = 505210/X      A2 = 1225890/2X . 问增长，就用(A2 - A1)/A1. 发现x 是可以约掉的。于是together有效。这个是最笨但也是最直接最简单的方法，LZ如果有时转不过来，不妨直接从最简单的定义出发。