求助：GMAT Prep Data Sufficiency Questions

自由心证 · 发表于 2009-11-23 09:55:03

Hello,

以下是几道GMAT Prep上我做错的题。我的数学错了12个！而且1个礼拜后就开考了。希望CDer能够帮忙看看正确答案是什么，并且给我一点思路，谢谢。

3．Last month 15 homes were sold in Town X, the average (arithmetic mean) sale price of the homes was $ 150,000 and the median sale price was $ 130,000. Which of the following statements must be true?

I. At least one of the homes was sold for more than $ 165,000

II. At least one of the homes was sold for more than $ 130,000 and less than $ 150,000

III. At least one of the homes was sold for less than $ 130,000

A. I only

B. II only

C. III only

D. I and II

E. I and III

为什么答案不是E？

4．Linda put an amount of money into each of two new investments, A and B, that pay simple annual interest. If the annual interest rate of investment B is 1.5 times that of investment A, what amount did Linda put into investment A?

(1) The interest for 1 year is $ 50 for investment A and $ 150 for investment B

(2) The amount that Linda put into investment B is twice the amount that she put in investment A

为什么答案不是E？

5．How many odd integers are greater than the integer x and less than the integer y?

(1) There are 12 even integers greater than x and less than y.

(2) There are 24 integers greater than x and less than y.

为什么答案不是E?

6．Is z equal to the median of the three positive integers x, y and z?

(1) x< y+z

(2) y=z

为什么答案不是B?

7．Of the 1,400 college teachers surveyed, 2 percent said that they considered engaing in research an essential goal. How many of the college teachers surveyed were woman?

(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.

答案是不是C?

jane_wang00 · 发表于 2009-11-23 12:11:14

自己做的。请大家验证

3．Last month 15 homes were sold in Town X, the average (arithmetic mean) sale price of the homes was $ 150,000 and the median sale price was $ 130,000. Which of the following statements must be true?

I. At least one of the homes was sold for more than $ 165,000

II. At least one of the homes was sold for more than $ 130,000 and less than $ 150,000

III. At least one of the homes was sold for less than $ 130,000

Total price : 150，000×15＝2，250，000

Median sale price : 130,000.

I, if no one is sold for more than 165,000, then 130,000*8+(165,000-n)*7＝2195000－7n=2250000

(中数取8个是为了让大于中数的售价达到最大化，下同)

The value of n (2195000-2250000)7 is negative.

I must be true

II if no one was sold for more than 130,000 and less than 150,000, then

130,000*8+(150,000+n)7=2,090,000+7n

The value of n( 2,250000-2090000)/7 is positive , so ii is not necessary be true.

III, let’s assume none of the home was sold less than 130,000, then the least total price 130,000*8+(130,000+n)7=1,950,000+7n

The value of n= (2,250,000-1,950,000)/7 , is positive . so III is not necessary be true

Answer is A.

A. I only

B. II only

C. III only

D. I and II

E. I and III

自由心证 · 发表于 2009-11-23 13:12:35

谢谢jane_wang的热心解答。分析实在太棒了。

请问您对其余题目的看法是？

celineyo · 发表于 2009-11-23 16:50:58

你最好把正确答案给出来，让大家对自己做的有个验证，要不然没人敢百分百确定地告诉你怎么做……

jane_wang00 · 发表于 2009-11-23 17:50:46

楼主客气。

我才看到自己的回复有好多源代码，取消不了，看起来有点费劲。

第5题：

How many odd integers are greater than the integer x and less than the integer y?

(1) There are 12 even integers greater than x and less than y.

(2) There are 24 integers greater than x and less than y.

为什么答案不是E?
如果你不说答案不是E，我也会选E的。我觉得题目中再加上一个单词consecutive(连续的）就会比较明确。

按这种思路来求解：

要寻找的答案: Y ＞奇数集合中元数的数目＞ X

(1) Y ＞偶数集合、元数数目为12 ＞ X

设N为该集合中最小的偶数，则其他连续的偶数依次为N，N＋2，N＋4…，N＋22

要知道奇数集合中元数的数目，先要定义最小和最大的奇数，N＞X, 则奇数N＋1一定大于X，所以最小的奇数为N＋1；N＋22＜Y，则奇数N＋21一定小于Y，所以最大的奇数为N＋21. 从N＋1到N＋21，奇数为10个数。

（2）Y ＞连续整数集合、元数数目为24＞ X

有两种可能，连续整数集合中最小的是奇数或最小的是偶数。分别分析：

最小的是奇数N，则这些数依次为N, N＋1，N＋2…, N+23

其中奇数有N，N＋2…, N+22, 奇数共有12个；

第二种可能最小的是偶数N,则奇数有N＋1，N＋3… N+23,奇数共有12个。

所以不管哪种情况，根据条件2都能得出奇数元数的数目为12。

答案为D

自由心证 · 发表于 2009-11-23 23:44:42

你最好把正确答案给出来，让大家对自己做的有个验证，要不然没人敢百分百确定地告诉你怎么做……

-- by 会员 celineyo (2009/11/23 16:50:58)

Sorry la. 我也没有答案，所以才来这里和大家讨论嘚。

自由心证 · 发表于 2009-11-23 23:47:51

关于条件（1）

为什么最小的奇数不可以是N-1呢？同理为什么最大的奇数不可以是N+23?

这一点我还在犹豫。

关于条件（2）

我觉得你的解释是很到位的。

所以答案为 B?

xianxianwang · 发表于 2009-11-24 03:52:42

我对第五题的理解条件1：两个正整数之间整数的个数有两种情况第一x为偶数第二种情况为X为奇数，举个例子两个整数间有4个偶数：1（x）2，3，4，5，6，7，8，9(y) 2(x)3，4，5，6，7，8，9,10,11(y) 第一组有3个奇数，第二组有4个奇数。
条件2:参照条件1; 无论x是奇数还是偶数，x,y 之间的奇数和偶数的数量是相等的。

自由心证 · 发表于 2009-11-25 08:47:40

所以你的答案是B?

jane_wang00 · 发表于 2009-11-25 11:11:14

[quote]
关于条件（1）

为什么最小的奇数不可以是N-1呢？同理为什么最大的奇数不可以是N+23?

这一点我还在犹豫。

因为X是整数，而我的假定是N是集合中最小的偶数，那么N－1就一定比X小。N＋23同理

求助：GMAT Prep Data Sufficiency Questions

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