请帮忙解答下几道DS题

liptontea

1. S is a set of integers such that
i) if a is in S, then -a is in S, and
ii) if each of a and b is in S, then ab is in S.
Is -4 in S?

(1) 1 is in S.
(2) 2 is in S.

2. What was Bill's average (arithmetic mean) grade for all of his courses?
(1) His grade in social studies was 75, and his grade in science was 75.
(2) His grade in mathematics was 95.
(我觉得应该是C)

3. If x^2-y=w (x的平方), what is the value of x?
(1) w+y=4
(2) y=1
(我也觉得应该是C）

4. One kilogram of a certain coffee blend consists of x kilogram of type I coffee and y kilogram of type II coffee. The cost of the blend is C dollors per kilogram, where C=6.5x+8.5y. Is x<0.8?
(1) y>0.15
(2) C>=7.30

5. If x and y are positive integers and x is a multiple of y, is y=2?
(1) y=/1
(2) x+2 is a multiple of y

6. If @ denotes a mathematical operation, does x@y=y@x for all x and y?
(1) For all x and y, x@y=2(x^2+y^2)
(2) For all y, 0@y=2y^2

the keys: 1.B, 2.E, 3.E, 4.B, 5.C 6.A

多谢帮忙解答！

nioni

第一题
1>知道1在s里面，只能知道-1在s里面，不能推出-4在s里面
2>知道2在s里面，那么-2也在s里面，-2*2=-4也在s里面
因此选B

第二题
选项一二没有告诉Bill一共有多少门课

第三题
即使条件1，2一起也无法得出x是多少
因为x可能为2或者是-2，无法确定，因而不充分

第四题
由题目可知x+y=1
1> y>0.15,即1—x>0.15，得x<0.85,不能得出x<0.8
2>c>=7.3,即6.5x+8.5*（1—x)>=7.3,得x<0.6,可以推出x<0.8

nioni

第五题选项1有问题吧，是不是掉东西了？

liptontea

多谢解答！

第一题：那么说-a=b? 我没有想到呦。

能否一起解答一下第五、第六题？谢谢！

liptontea

多谢解答！

第一题：那么说-a=b? 我没有想到呦。

能否一起解答一下第五、第六题？谢谢！

liptontea

第五题核对过了，没掉东西，题目是这样的。

nioni

y=/1
=====
这个有点不对吧，是不是分子应该有一个啊？

nioni

第六题
1>对于x and y, x@y=2(x^2+y^2)，那么y@x=2（y^2+x^2),所以对于所有的x，y，x@y=y@x
2> 对于所有的y, 0@y=2y^2，不能得出x@y怎样，因为0只是一个特殊值，所以推不出来

uibe2005sunusa

5. If x and y are positive integers and x is a multiple of y, is y=2?
(1) y=/1
(2) x+2 is a multiple of y

solution：from the prerequisite we can deduce that x=ay, and a is a positive integer.
(1)&(2)=>x+2=by, b is a positive integer=>2=(a-b)y=>2*1=(a-b)y
because y is not 1,so y must be 2. the choice is C

多谢帮忙解答！

-- by 会员 liptontea (2010/8/23 21:27:04)

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liptontea

对第五题statement (1) 说明：y不等于1

Thank you very much for the solution, uib2005sunusa!