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标题: XY13-02-math 32,33,37 + 机井一道 [打印本页]

作者: suochuanghan 时间: 2008-1-18 04:28
标题: XY13-02-math 32,33,37 + 机井一道

各位XDJM

正在做XY13

这几道题想不明白

黄色是我做的结果

红色是答案

想不明白

还请NN指教，虚心向学。

Q32:

If x³y⁴
= 5,000, is y = 5?

(1) y
is a positive integer.

(2) x
is an integer.

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. （因为5000=（2*5 )^3* 5 = (xy)^3 *5，我以为显然。。。不过我大概错了）

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

Q33:

	Favorable	Unfavorable	Not Sure
Candidate M	40	20	40
Candidate N	30	35	35

The table above shows the results of a survey of 100 voters
each responded “favorable” or “unfavorable” or “not sure” when asked about
their impressions of candidate M and of candidate N. What was the number of voters who responded
“favorable” for both candidates?

(1) The number of voters who
did not respond “favorable” for either candidate was 40.

(2) The
number of voters who responded “unfavorable” for both candidates was 10.

A. Statement (1) ALONE is sufficient, but statement
(2) alone is not sufficient. 　　（死活想不明白）

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.

Q37:

How many different factors does the integer
n have?

(1) n = a⁴b³, where a and
b are different positive prime numbers.

(2) The only positive prime numbers that are
factors of n are 5 and 7.

A. Statement (1) ALONE is sufficient, but
statement (2) alone is not sufficient.　（至今不明白，　ｆａｃｔｏｒ是因数的意思吧，如果仅有条件1，因为a,b可以又很多种取法，那么，因数应该是无穷的 -- 由此想到机井一道，N=5个质数得乘积（其中2个完全相同），问得factor的个数（包括N和1）
有些JJ给的答案是8, 也想不明白，还请NN赐教，急等答案，谢谢）

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.

作者: ikoeisntekde 时间: 2008-1-18 04:49

32题如果不是整数两个分数也很容易凑成5000的

还有就是y必须正因为y=-5怎么办

作者: ikoeisntekde 时间: 2008-1-18 04:56

33题画个图就明白了， did not respond “favorable” 取非就是总共选择favorable的人，也就是100-40是总共选择了favorable的人

这60人里30选N，40选M。所以重合部分是10。

作者: ikoeisntekde 时间: 2008-1-18 05:01
37题 A，B不能是无穷的因为题目中说的是prime factor 是质因数既然是质因数就不能进一步分解了

作者: ikoeisntekde 时间: 2008-1-18 05:14

N=5个质数得乘积（其中2个完全相同），问得factor的个数（包括N和1）

这个机经题答案挺奇怪我觉得不是8。但是自己排列组合不好，也不太会。既然算了就贴上来和大家讨论吧，要是错了别拍我...

我们设5个质数是aabcd.然后我们先把abcd中取2个组合，取3个组合，取4个组合，等于6+4+1=11

然后再把aa拴在一起代替a和bcd排一次和上面一样11种组合最后abcd单独各是一种可能再加上1和本身是22+4+1+1=28

作者: suochuanghan 时间: 2008-1-18 06:23
谢谢楼上
32，33 明白了
37 -- a, b 不能分解了，但是a,b 的取法无穷，如果没有条件2，比如，a = 2,b=5, 因数好几种可能；a=3,b=7,因数又有好几种可能。。。除非，按照条件1，每次取不同质因数时得到的可能数也都是一样的，这样好像是想得通的

那道机井，我硬排的，也是的楼上的答案，谢谢哦

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