Question

提问几道GRE数学！急！！！

都是绿皮上的，本人数学不大好，请尽可能详细解释，谢谢！
180.36
If 2/3 of the number of women attending a
certain dance is equal to 1/2 the number of men attending, what fraction of
those attending are women?
A.2/5 B.3/7 C.5/7 D.3/4 E.5/6
答案B 我算得2/7?

The length of a rectangular floor is 16
feet and its width is 12 feet. If each dimension were reduced by s feet to make
the ratio of length to width 3 to 2, what would be the value of s?
A0 B2 C4 D6 E8
答案C 没太读懂题且不会算

223.9
A board of length L feet is cut into two
pieces such that the length of one piece is 1 foot more than twice the length
of the other piece. What is the length, in feet, of the longer piece?
答案(2L+1)/3 咋算？

223.13
A watch gains 7 minutes and 6 seconds every
6 days. If the rate of gain is constant, how much does the watch gain in one
day?
答案是1min 11sec 我算得1min 1sec？

232.10
One-kth of a circular pie has been served.
If the rest of the pie is divided into n equal servings, then each of these servings
is what fraction of the whole pie?
答案(k-1)/nk 我算得1/nk^2?

191.18
If x^2=68, which of the following could be
true?
答案-9<x<-8 为何不是-8<x<8?怎么算得？

230.16
If x is the number of the number line
between 5 and 15 that is twice as far from 5 as from 15, then x is?
答案35/3 题干什么意思？咋算？

265.7
If a and b are positive and 7a-5<=9 and
3-b>=2, what is the greatest possible value of ab?
答案10 咋算？

Answer 1

1. 设女的有x人，男的有y人，则2/3 * x = 1/2 * y，故4x=3y，即x=3/4 * y

   从而女的比例为x/(x+y)=3/4 / (3/4+1)=3/7

2. 长16宽12，都缩短s使得长宽比是3:2，故(16-s):(12-s)=3:2,求得s=6

3. 设长的那块为x，则x=2(L-x)+1，求得x=(2L+1)/3

4. 7分6秒=7*60+6=426秒，除以6，得71秒=1分11秒

5. 总的为1，1/k去掉，还有(1-1/k)，n等分，即为(1-1/k)/n=(k-1)/nk

6. x的平方是68，8的平方是64，9的平方是81，x的绝对值一定在8到9之间，所以8<x<9或-9<x<-8

7. x-5=2(15-x)，得x=35/3
   

8. 7a-5<=9，故a<=2；3-b>=2，故b<=1，a,b都是正数，所以ab的最大值应该为2*1=2，答案10应该不对

Answer 2

180.36
2/3 x = 1/2 * (1-x) => 7/6 x = 1/2 => x = 3/7

2. 矩形地面长16英尺宽12英尺，如果每边缩小S英尺以至于长宽比为3:2，S为何值？
将各选项代入，只有C成立， （16-4）：（12-4）=3:2

223.9 长的段为x，短的那段则为L-x。长的那段等于短的的两倍加1：
x = （L-x）*2 +1 => x = (2L +1)/3

223.13
(7*60 + 6) / 6 = 71(秒）= 1分11秒

232.10 1/k的馅饼被吃掉，剩下1-1/k，再平均分成n份，每份占整个馅饼的：
（1-1/k) / n = (k-1)/ nk

191.18 x = 正的或负的根号68，是正或负8点几的一个数（比如说正的或负的8.2），所以可以是-9<x<-8,或 8<x < 9

230.16 x是5到15之间的数字线上的数字，它到5的距离是到15的距离的两倍。
x-5 = 2*(15-x) => 3x = 35 => x = 35/3

265.7 7a-5 <=9 得出a <=2，a最大为2； 3-b>=-2 得出b <=5，b最大为5. ab最大为2*5=10