請教幾題prep的數學

waigedet · 发表于 2010-6-16 03:29:17

1. The total of company C's assets in 1994 was 300 percent greater than the total in 1993, which in turn was 400 percent greater than the total in 1992, if the total of company C's assets in 1992 was N dollars, which of the following represent the total of company C's assets, in dollars, in 1994
(1)7N (2)8N (3)9N (4)12N (5)20N
---1994=1993*300% 1993=1992*400% 1994=12N.....請問這樣為什麼錯了??

2. Amy's grade was the 90th percentile of the 80% grades for her class, of the 100 frades from another class, 19 were higher than Amy's, and the rest were lower. If no other grade was the same as Amy's grades then Amy's grade was what percentile of the grades of the two classes combined?
(1)72nd (2)80th (3)81st (4)85th (5)92rd

3. The function f is defined for all integers n by the following rule: f(n) is the number of positive integers each of which is less than n and has no positive factor in common which n other than 1. If p is any prime number then f(p)=
(1)p-1 (2)p-2 (3)(p+1)/2 (4)(p-1)/2 (5)2
----可以告訴我要怎麼代換嗎??

4. Equal amounts of water were poured into two wmpty jars of different capacities, which mafe one jar 1/4 full and the other jar 1/3 full. If the water in jar with the lesser capacity is then poured into the jar with the greater capacity, what fraction of the larger jar will be filled with water?
(1)1/7 (2)2/7 (3)1/2 (4)7/12 (5) 2/3

5. Circle C and line K lie in the xy-plane. If circle C is centered of the origin and has radius 1, does line K intersect circle C?
(1) The x-intercept of line K is greater than 1
(2) The slope of line K in -1/10

ttt936 · 发表于 2010-6-16 04:13:00

1是20N吗。。。。93的资产是比92多400%，那么既是93-92=92*400%，同理得出93和94的关系，最后算出94是20N
4、我算是3/7。。你有个答案是不是打错了，有两一样的
5选c，第一个单独不充分，第二个设直线式y=ax+b从K=-a/b=-1//10只能知道直线在坐标轴的大概位置，对xy的取值无法确定范围。1+2知x取值大于1，那么y比大于1，所以直线与圆没有交点。。

waigedet · 发表于 2010-6-16 04:43:27

sorry忘了po上答案了
(1)5 (2)4 (3)1 (4)3 (5)忘了是C還是E...抱歉= =
第四題的答案我已更正~~

請問ttt936: 第一題可以說清楚一點嗎? 腦子有點轉不過來= =....謝謝你的幫忙了
第四題我是算7/12.....~~

ttt936 · 发表于 2010-6-16 05:44:25

第一题的意思是94年比93年多的是93的400%，而不是94年比93年多400%，93年和92年的关系一样。。。所以不能直接用93年的总量直接乘以400%得到94年的。。。

ttt936 · 发表于 2010-6-16 05:46:31

另外第四题就是用1/3+1/4吗。。。那我理解成倒入的占总的水的比例了。。。

wolfheulen · 发表于 2010-6-16 06:38:49

第一题：
“The total of company C's assets in 1994 was 300 percent greater than the total in 1993”
means
assets in 1994 is 400 percent of the asset in 1993.
you can interpret it as: assets in 1994 is assets in 1993 plus 300 percent of the assets in 1993.

similarly, assets in 1993 is 500 percent the assets in 1992

hence assets in 1994 is 5*4=20 times the assets in 1992, or 20N.

第二题：
第一句： “Amy's grade was the 90th percentile of the 80% grades for her class,”应该是“Amy's grade was the 90th percentile of the 80 grades for her class”
这样的话，可以知道在amy's class, 有80*90%=72人的分数小于或等于amy的分数。
在另一班，总共有100-19=81人的分数小于amy的分数。
两班总共180人，其中有81+72=153人的分数小于或等于amy的分数。所以amy的分数是153/180=0.85， or 85th percentile

第三题：
f(n)其实就是与n互质并且小于n的正整数，也就是所有小于n，并且和n的最大公约数是1的正整数。If n is a prime number, then every positive integer less than n has a common factor of 1. 所以总共有n-1个这样的数，f(n)=n-1

第四题：
two jars. the same amount of water fills 1/4 of jar A, but 1/3 of jar B. clearly, jar A is the bigger jar, because with the given amount, you have to pour 4 times to fill jar A, but you only need to pour 3 times to fill jar B.
now, jar B has the same amount of water as jar A, so pouring water from jar B into jar A doubles the amount of water in jar A. jar A already had 1/4 filled, doubling that amount will give jar A 1/2 filled.

第5题：
we know the location of the circle. we can determine whether a line will cross the circle if we know the exact formula for the line. clearly, only both conditions together will specify the location of the line. therefore, both conditions combined will allow you to draw a definitive conclusion.

waigedet · 发表于 2010-6-16 08:34:32

感謝各位的解答~~
我會好好研究的!!
第四題仍然有點迷惑啊...><
研究去!!

請教幾題prep的數學

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