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标题: 明天就考了，prep数学竟然错了好几道……求助几道数学 [打印本页]
作者: 五月的天 时间: 2009-10-27 16:54
标题: 明天就考了，prep数学竟然错了好几道……求助几道数学
if n is a multiple of 5 and n=p^2q, where p and q are prime numbers, which of the following must be a multiple
of 25
A p^2 B q^2 C pq D p^2q^2 E P^3q^3
a company plans to assign identification numbers to its employees. each number is to consist of four different
digits from 0 to 9, inclusive, except that the first digit cannot be 0. How many different identification
numbers are possible?
A 3024 B 4536 C 5040 D 9000 E 10000
the
positive integer k has exactly two positive prme factors, 3 and 7 if k
has a total of 6 positive factors, including 1 and k, what is the value
of k?
1. 3^2 is a factor of k
2. 7^2 is not a factor of k
are at least 10 percent of the people in country X who are 65 years old or older employed?
1. in country x 11.3 percent of the population is 65 years old or older.
2. in country x of the population 65 years old or older, 20 percent of the men and 10 percent of the women are employed.
of the 1400 college teachers surveyed, 42 percent said they considered engaging in research an essential goal.
How many of the college teachers surveyed were women?
1.
in the survey, 36 percent of the men and 50 percent of the women said
that they considered engaging in research an essential goal.
2. in the survey, 288 men said that they considered engaging in research an essential goal.
作者: juange1014 时间: 2009-12-10 18:28
没有人回复。。。我刚才做了一遍，将我的思路整理如下,不对请指正
1.if n is a multiple of 5 and n=p^2q, where p and q are prime numbers, which of the following must be a multiple
of 25
A p^2 B q^2 C pq D p^2q^2 E P^3q^3 （should be P^3q)
Answer: D
n is a multiple of 5 and n=p^2q, where p and q are prime numbers==> p=5 or q=5
so, only p^2q^2 is certainly a multiple of 25
2. a company plans to assign identification numbers to its employees. each number is to consist of four different digits from 0 to 9, inclusive, except that the first digit cannot be 0. How many different identification numbers are possible?
A 3024 B 4536 C 5040 D 9000 E 10000
Answer: B
let abcd represent the 4 digit number, then
a is one of 1 to 9
b is one of 0-9 but exluding a
c is one of 0-9 but exluding a, b
d is one of 0-9 but exluding a, b, c
then the possibles are 9*(10-1)(10-2)(10-3)=4536
3.the positive integer k has exactly two positive prme factors, 3 and 7 if k has a total of 6 positive factors, including 1 and k, what is the value of k?
1. 3^2 is a factor of k
2. 7^2 is not a factor of k
Answer: D
K=3^n*7^n', because k has total 6 positive factors, n=2, n'=1(case 1), or n=1, n'=2(case 2)
1)3^2 is a factor of k ===> case 1, sufficient
2. 7^2 is not a factor of k ====> case 2, sufficient
4. are at least 10 percent of the people in country X who are 65 years old or older employed?
1. in country x 11.3 percent of the population is 65 years old or older.
2. in country x of the population 65 years old or older, 20 percent of the men and 10 percent of the women are employed.
Answer: B
1) not sufficient
2) the x, y represent number of Men and Women 65+ years old
then to check whether (0.2x+0.1y)/(x+y)>0.1?
(0.2x+0.1y)/(x+y)=(0.2x+0.2y-0.1y))/(x+y)=0.2-0.1y/(x+y)
since y/(x+y)<1, then 0.1y/(x+y)<0.1, while 0.2-0.1y/(x+y)>0.1, the 2) sufficient!
5. of the 1400 college teachers surveyed, 42 percent said they considered engaging in research an essential goal. How many of the college teachers surveyed were women?
1. in the survey, 36 percent of the men and 50 percent of the women said
that they considered engaging in research an essential goal.
2. in the survey, 288 men said that they considered engaging in research an essential goal.
1) total male x, women y, x+y=1400, then 0.36x+0.5y=0.42*1400, two equations can let us know the solusion of x and y, the number of college teachers surveyed were women is 0.5 y will be know. Sufficient
2) insufficient
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