GWD的几道数学题，求牛人解答~~~十万分感谢！！！

jessica_yuan

求牛牛解答以下的GWD数学题，本人百思不得其解~~~~~~十万分感谢！！！！！！！！！！！

每题后的答案为正确答案，谢谢！！

GWD 01

Q10:

A set of numbers has the property that for any number t in the set, t + 2 is in the set.  If –1 is in the set, which of the following must also be in the set?

I.                    -3

II.                 1

III.               5

A.    I only

B.    II only

C.    I and II only

D.    II and III only

E.    I, II, and III

Answer: D

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为什么-3不在set 中，而5在set中？

Q28:

For any positive integer n, the sum of the first n positive integers equals [n(n+1)]/2.  What is the sum of all the even integers between 99 and 301?

 

 

A.      10,100

B.      20,200

C.      22,650

D.     40,200

E.      45,150

Answer: B

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Q30:

Joanna bought only $0.15 stamps and $0.29 stamps.  How many $0.15 stamps did she buy?

(1)     She bought $4.40 worth of stamps.

(2)     She bought an equal number of $0.15 stamps and $0.29 stamps.

                  

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.

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

Answer: D

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 我觉得但是B条件不可以，因为只要数量相等，随便买多少都可以~~~~~~ 

 我觉得但是B条件不可以，因为只要数量相等，随便买多少都可以~~~~~~ 

GWD 03

Q18:

Last year the price per share of Stock X increased by k percent and the earnings per share of Stock X increased by m percent, where k is greater than m.  By what percent did the ratio of price per share to earnings per share increase, in terms of k and m?

 

 

A.      k/m %

B.      (k-m) %

C.      [100(k-m)]/(100+k) %

D.     [100(k-m)]/(100+m) %

E.      [100(k-m)]/(100+k+m) %

Answer: D

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GWD 06

GWD 06

Q6:

If a, b, k, and m are positive integers, is a^k
    a factor of b^m?

(1)     a is a factor of b.

(2)     k ≤ m

                  

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.

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

Answer: C

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Q26:

K is a set of integers such that if the integer r is in K, then r + 1 is also in K.  Is 100 in K?

(1)     50 is in K.

(2)     150 is in K.

                  

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.

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

Answer: A

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GWD 08

Q9:

If an integer n is to be chosen at random from the integers 1 to 96, inclusive, what is the probability that n(n + 1)(n + 2) will be divisible by 8?

 

 

A.      1/4

B.    3/8

C.    1/2

D.  5/8    

E.    3/4

Answer: D

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GWD 09

Q10:

What is the value of (x - y)⁴?

(1)     The product of x and y is 7.

(2)     x and y are integers.

                  

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.

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

Answer: C

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GWD 10

Q8:

An equilateral triangle that has an area of 9 √3 is inscribed in a circle.  What is the area of the circle?

 

 

A.      6派

B.9派     

C.12派     

D.  9派   √3

E. 18派√3    

Answer: C

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GWD 11

Q7:

Before a certain tire is used, 40 percent of its total weight consists of tread.  If during a lifetime of use, 50 percent, by weight, of the tire’s tread is lost and no other parts of the tire is lost, what per cent of the tire’s total remaining weight consists of the remaining tread?

 

 

A.   55%

B.   20%

C.   25%

D.       30%

E.        35%

Answer: C

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我解到是20%~~~~~~~~~~

Q21:

A certain circle in the xy-plane has its center at the origin.  If P is a point on the circle, what is the sum of the squares of the coordinates of P?

(1)      The radius of the circle is 4.

(2)      The sum of the coordinates of P is 0.

                  

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.

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

                                                          Answer: A

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题目有点多，真的十分十分感谢！！！！！！！！！！！！！！！

题目有点多，真的十分十分感谢！！！！！！！！！！！！！！！

[此贴子已经被作者于2008-3-26 20:18:04编辑过]

jessica_yuan

麻烦哪位高人指点一下迷津啊~~~~~~~~~~

不一定全部解答，可以只解答其中几题，CD 上人多力量大啊~~~~~~~~~~~~~~~~~~

lisimba

http://forum.chasedream.com/dispbbs.asp?boardID=22&ID=58619

GWD数学讨论帖汇总，MM研究一下这个吧

zacharyzhang

以下是引用jessica_yuan在2008-3-26 0:21:00的发言：

求牛牛解答以下的GWD数学题，本人百思不得其解~~~~~~十万分感谢！！！！！！！！！！！

每题后的答案为正确答案，谢谢！！

GWD 01

Q10:

A set of numbers has the property that for any number t in the set, t + 2 is in the set.  If –1 is in the set, which of the following must also be in the set?

I.                    -3

II.                 1

III.               5

A.    I only
B.    II only

C.    I and II only
D.    II and III only
E.    I, II, and III

Answer: D

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为什么-3不在set 中，而5在set中？你自己仅用题目所给的条件尝试推导出-3来看看？然后我再根据你的推理指出其中破绽。

Q28:

For any positive integer n, the sum of the first n positive integers equals [n(n+1)]/2.  What is the sum of all the even integers between 99 and 301?

A.      10,100

B.      20,200

C.      22,650

D.     40,200

E.      45,150

Answer: B

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“sum of all the even integers between 99 and 301”=2*(sum of all integers from 50 to 150)，自己算吧。

Q30:

Joanna bought only $0.15 stamps and $0.29 stamps.  How many $0.15 stamps did she buy?

(1)     She bought $4.40 worth of stamps.

(2)     She bought an equal number of $0.15 stamps and $0.29 stamps.

                  

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.

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

Answer: D

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 我觉得但是B条件不可以，因为只要数量相等，随便买多少都可以~~~~~~

 我觉得但是B条件不可以，因为只要数量相等，随便买多少都可以~~~~~~

GWD 02

Q8:

The operation Ä is defined for all nonzero numbers a and b by a Ä b = a/b – b/a.  If x and y are nonzero numbers, which of the following statements must be true?

I.               x Ä xy = x(1 Ä y)

II.                  x Ä y = -(y Ä x)

III.               1/x Ä 1/y = y Ä x

A.    I only
B.    II only

C.    III only

D.    I and II
E.    II and III

  Answer: E

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我觉得 I,II,III都可以啊~~~~~~~~·I的左边是(1/y-y)，右边是x*(1/y-y)，除非x=1，否则怎么会“must be true”

我觉得 I,II,III都可以啊~~~~~~~~·I的左边是(1/y-y)，右边是x*(1/y-y)，除非x=1，否则怎么会“must be true”

GWD 03

GWD 03

Q14: 

How many seconds will it take for a car that is traveling at a constant rate of 45 miles per hour to travel a distance of 22 yards?  (1 mile = 1,160 yards)

A.      8

B.      9

C.      10

D.     11

E.      12

Answer: C

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这题貌似简单，但不知道为什么我算了好多遍得出结果都是1.5秒左右~~~~~

我的算法：22/(45*1160/3600)根据你所列出的题目，你的算法没错。要么题目数据有问题，要么题目要求抄得不对。实际上1mile = 1760 yards，另外题目可能是问220yards而非22yards

Q18:

Last year the price per share of Stock X increased by k percent and the earnings per share of Stock X increased by m percent, where k is greater than m.  By what percent did the ratio of price per share to earnings per share increase, in terms of k and m?

A.      k/m %

B.      (k-m) %

C.      [100(k-m)]/(100+k) %

D.     [100(k-m)]/(100+m) %

E.      [100(k-m)]/(100+k+m) %

Answer: D

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GWD 06

GWD 06

Q6:

If a, b, k, and m are positive integers, is a^k
    a factor of b^m?

(1)     a is a factor of b.

(2)     k ≤ m

                  

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.

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

Answer: C

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Q26:

K is a set of integers such that if the integer r is in K, then r + 1 is also in K.  Is 100 in K?

(1)     50 is in K.

(2)     150 is in K.

                  

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.

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

Answer: A

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GWD 08

GWD 08

Q9:

If an integer n is to be chosen at random from the integers 1 to 96, inclusive, what is the probability that n(n + 1)(n + 2) will be divisible by 8?

A.      1/4

B.    3/8

C.    1/2

D.  5/8    

E.    3/4

Answer: D

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对于所有偶数，n(n + 1)(n + 2)一定是8的倍数；奇数中除8余7的所有数字都能保证n(n + 1)(n + 2)能被8整除，这种数字每4个奇数中存在一个。这样一来共有1/2+1/4*1/2的数字符合要求。

GWD 09

Q10:

What is the value of (x - y)⁴?

(1)     The product of x and y is 7.

(2)     x and y are integers.

                  

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.

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

Answer: C

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The product of x and y is 7.意思是x*y=7。连同x,y都是整数的条件可得(1,7),(7,1),(-1,-7),(-7,-1)这4组(x,y)。无论哪一组，(x-y)的4次方都是1296

Q20:

	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.

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.

Answer: A

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GWD 10

Q8:

An equilateral triangle that has an area of 9 √3 is inscribed in a circle.  What is the area of the circle?

A.      6派

B.9派     

C.12派     

D.  9派   √3

E. 18派√3    

Answer: C

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你试试看用圆半径r来表示内接正三角形的面积。

GWD 11

GWD 11

Q7:

Before a certain tire is used, 40 percent of its total weight consists of tread.  If during a lifetime of use, 50 percent, by weight, of the tire’s tread is lost and no other parts of the tire is lost, what per cent of the tire’s total remaining weight consists of the remaining tread?

A.   55%

B.   20%

C.   25%

D.       30%

E.        35%

Answer: C

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我解到是20%~~~~~~~~~~

Q21:

A certain circle in the xy-plane has its center at the origin.  If P is a point on the circle, what is the sum of the squares of the coordinates of P?

(1)      The radius of the circle is 4.

(2)      The sum of the coordinates of P is 0.

                  

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.

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

                                                          Answer: A

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题目有点多，真的十分十分感谢！！！！！！！！！！！！！！！

题目有点多，真的十分十分感谢！！！！！！！！！！！！！！！

问题好多，先随便解答几个。

jessica_yuan

GWD 01
     

Q10:

A set of numbers has the property that for any number t in the set, t + 2 is in the set.  If –1 is in the set, which of the following must also be in the set?

I.                    -3

II.                 1

III.               5

A.    I only
B.    II only

C.    I and II only
D.    II and III only
E.    I, II, and III
     

Answer: D

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为什么-3不在set 中，而5在set中？你自己仅用题目所给的条件尝试推导出-3来看看？然后我再根据你的推理指出其中破绽。

我认为1）如t=-1，则t+2= -1+2=1

             2）如t+2= -1，则t=-3，这种情况错在哪里？

             但是怎样推到5在set中？

谢谢！

[此贴子已经被作者于2008-3-26 20:22:27编辑过]

jessica_yuan

GWD 08
                    

Q9:

If an integer n is to be chosen at random from the integers 1 to 96, inclusive, what is the probability that n(n + 1)(n + 2) will be divisible by 8?

A.      1/4

B.    3/8

C.    1/2

D.  5/8    

E.    3/4

Answer: D

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对于所有偶数，n(n + 1)(n + 2)一定是8的倍数；奇数中除8余7的所有数字都能保证n(n + 1)(n + 2)能被8整除，这种数字每4个奇数中存在一个。这样一来共有1/2+1/4*1/2的数字符合要求。

谢谢zacharyzhang的解答，对于偶数的情况我明白了，感激！！！！！！！！

但是对于奇数的情况，我有点不明，举个例子：1、2、3        3、4、5        5、6、7        7、8、9        9、10、11

能被8整除的应该是每5个奇数中存在一个啊，而且碰到79、80、81，则这个又可以被整除了，而且按我的算法也不能得出正确答案，还请指教我的想法哪里出问题了~~~~~~

再次感谢~~~~~~~~~~~~~~~~~~~~

jessica_yuan

ding上去先

求各路大仙指点迷津！！！！！！！！！！

本人不胜感激~~~~~~~~~~~~~~~~~~

graysytl

以下是引用jessica_yuan在2008-3-26 20:22:00的发言：

GWD 01
     

Q10:

A set of numbers has the property that for any number t in the set, t + 2 is in the set.  If –1 is in the set, which of the following must also be in the set?

I.                    -3

II.                 1

III.               5

A.    I only
B.    II only

C.    I and II only
D.    II and III only
E.    I, II, and III
     

Answer: D

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为什么-3不在set 中，而5在set中？你自己仅用题目所给的条件尝试推导出-3来看看？然后我再根据你的推理指出其中破绽。

我认为1）如t=-1，则t+2= -1+2=1

             2）如t+2= -1，则t=-3，这种情况错在哪里？

             但是怎样推到5在set中？

谢谢！

先说后面那个，因为有-1，所以-1+2=1也在；当1在集合里面，那么3也在，因为1+2=3。如果3在，那么3+2=5也在。

你知道了这个集合里面的数字全部都是奇数，但并不表示全部奇数都在这个集合里面。条件说的是，如果t在集合里，t+2也在，但是没说如果t在，t-2也在。什么意思呢？如果-1是集合中最小的数字，那么剩下的数字是比-1大的所有奇数，在这种情况下就没有-3。所以总结起来，-3不一定出现，所以不选。

jessica_yuan

graysytl，明白了，谢谢！！