接着发问题吧！

Drakedirect · 发表于 2007-8-24 02:45:00

在牛牛们的帮助下，今天模考数学终于有点进步了，第一次得了５０分，大家见笑了，呵呵！
不过还是有些疑问。GMATPre上面的，多谢大家帮忙！

1. The points A, B, C, and D are on a number line, not necessarily in that order. If the distance between A and B is 18 and the distance between C and D is 8, what is the distance between B and D?
(1) The distance between C and A is the same as the distance between C and B
(2) A is to the left of D on the number line

Key:E
我选了A，估计是落掉了一些情况，请赐教！

2. If Z^n =1, what is the value of z?
(1) n is a nonzero integer
(2) z>0
key: C 我选了A, 感觉即便是Z<0,如果要Z^n =1，z也只能等于1吧？还能等于别的？？不解

3. if x>y^2>z^4, which of the following statements could be true?
I. x>y>z
II. z>y>x
III. x>z>y
A. I only
B. I and II only
C. I and III only
D. II and III only
E. I, II, and III
key: E
做这种题我通常是带入一些数，但是经常会漏掉一些情况，所以这种题对我很头疼。我选了Ｂ不知道大家又没有什么好的办法来做这种题？谢了！

3. Henry purchased 3 items during a sale. He received a 20 percent discount off the regular price of the most expensive item and a 10 percent discount off the regular price of each of the other 2 items. Was the total amount of the 3 discounts greater than 15 percent of the sum of the regular prices of the 3 items?
(1) the regular price of the most expensive item was $50, and the regualr price of the next most expensive item was $20.
(2) the regular price of the least expensive item was $15
key: A
我的方程式：(20%*A+10%*B+10%*c)/(a+b+c),看了答案，突然想起来可以用＄２０来代替ｃ，接出来的值好像比１５％大，可是问题是分子分母都还有Ｃ，怎么确定最后的值比这个大还是小呢？

yedeanboy · 发表于 2007-8-24 02:55:00

1. The points A, B, C, and D are on a number line, not necessarily in
that order. If the distance between A and B is 18 and the distance
between C and D is 8, what is the distance between B and D?
(1) The distance between C and A is the same as the distance between C and B
(2) A is to the left of D on the number line

Key:E
(1)只能说明C是A和B的中点（假设A和B不能是同一点），并且C到两者的距离各为9。那么D可以在C左边或者右边，距离C为8。无法确定BD的距离
(2)不能退出任何有用的结论
（1）和（2）结合也无法推出任何结论，因为CD=8而CA=9，所以只要A在C的左侧，都满足A在D的左侧，这时D可以在C左侧或者右侧，无法确定BD

不知道说清楚没有？

yedeanboy · 发表于 2007-8-24 02:58:00

2. If Z^n =1, what is the value of z?
(1) n is a nonzero integer
(2) z>0
key: C

(1)无法推出z的值，因为当n为偶数时，z可以等于1或者-1
（2）z大于0单独自然也无法推出z的值
两者合并得到，z>0 并且z=1或者-1，所以z必然等于1

yedeanboy · 发表于 2007-8-24 03:01:00

3. if x>y^2>z^4, which of the following statements could be true?
I. x>y>z
II. z>y>x
III. x>z>y
A. I only
B. I and II only
C. I and III only
D. II and III only
E. I, II, and III
key: E

一般分析y和z大于1或者小于1大于0的情况，因为平方或者4次方会放大大于1的数而减小小于1的数
这类题确实很麻烦，很容易错。

yedeanboy · 发表于 2007-8-24 03:07:00

3. Henry purchased 3 items during a sale. He received a 20 percent
discount off the regular price of the most expensive item and a 10
percent discount off the regular price of each of the other 2 items.
Was the total amount of the 3 discounts greater than 15 percent of the
sum of the regular prices of the 3 items?
(1) the regular price of the most expensive item was $50, and the regualr price of the next most expensive item was $20.
(2) the regular price of the least expensive item was $15
key: A

题目问是否能确定总折扣大于15%，所以你只要确定折扣最小时能大于15%就可以了
（1）折扣最小时发生在最便宜的物品价格也是20时。总折扣为（20%*50+10%*40）/90=14/90=15.6%
所以（1）可以

（2）仅仅给出最便宜的物品的价格无法确定总折扣。可以举极端的例子。比如3个商品价格一样，则小于15%，最贵的那个商品价格为1000，则必然大于15%

所以选A

Drakedirect · 发表于 2007-8-24 03:12:00

yedeanboy，第一题的思路果然清晰，我做的时候画了半天，费了好多时间，还是做错了，按照你讲很容易就选Ｅ了。每次看到这种题目，脑子就乱了，不知道从哪里下手！

Drakedirect · 发表于 2007-8-24 03:12:00

第二题，是我忘记了－１的情况．．．哎，总是丢三落四的．．．多谢

Drakedirect · 发表于 2007-8-24 03:17:00

第三题找到一个：25>9^1/2>16^1/4, x>z>y,其实这样的例子还很多，可是考试时一有时间的压力，脑子就想不出来了，多谢yedeanboy提醒

Drakedirect · 发表于 2007-8-24 03:23:00

3. Henry purchased 3 items during a sale. He received a 20 percent
discount off the regular price of the most expensive item and a 10
percent discount off the regular price of each of the other 2 items.
Was the total amount of the 3 discounts greater than 15 percent of the
sum of the regular prices of the 3 items?
(1) the regular price of the most expensive item was $50, and the regualr price of the next most expensive item was $20.
(2) the regular price of the least expensive item was $15
key: A

题目问是否能确定总折扣大于15%，所以你只要确定折扣最小时能大于15%就可以了
（1）折扣最小时发生在最便宜的物品价格也是20时。总折扣为（20%*50+10%*40）/90=14/90=15.6%
所以（1）可以

（2）仅仅给出最便宜的物品的价格无法确定总折扣。可以举极端的例子。比如3个商品价格一样，则小于15%，最贵的那个商品价格为1000，则必然大于15%

所以选A
——————————————————————————————————————————————————————————————
还是有疑问，20不是最便宜的商品阿？所以用２０来代替最便宜的商品的出的折扣应该是最大的，所以实际的折扣应该小于１５．６％，怎么可能确定与１５％的关系呢？

yedeanboy · 发表于 2007-8-24 03:27:00

Drakedirect，你对这道题的理解不对。这道题其实说白了是数学里加权平均的概念。是20%和两个10%的加权平均。权重为商品价格。当10%的折扣的商品，商品价格最大时，可能得到的折扣最低。所以当最便宜的商品价格最高（即20）时，得到的折扣最低。
如果还是不明白，你可以带个极端的数字进去，比如最便宜的商品价格0元，可以得到的折扣肯定高于15.6%

接着发问题吧！

接着发问题吧！

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