Beyond GMAT免费公开课 GWD数学难题解析

主讲人：Robert

题号后面括号里面对应的是GWD31套，第一个数字是套题号，第二个数字是具体题号。

1.(20Q14)

Six cards numbered from 1 to 6 are placed in an empty bowl.  First one card is drawn and then put back into the bowl; then a second card is drawn.  If the cards are drawn at random and if the sum of the numbers on the cards is 8, what is the probability that one of the two cards drawn is numbered 5 ?

A.    1/6

B.     1/5

C.     1/3

D.    2/5

E.     2/3

用概率的定义去做 该事件发生的可能/所有事件发生的可能

该事件：其中一张卡片是5    (3,5) (5,3)

所有事件：两张卡片加起来和是8  (2,6) (6,2) (3,5) (5,3) (4,4)

（D）

2.(2Q22)

A construction company was paid a total of $500,000 for a construction project.  The company’s only costs for the project were for labor and materials.  Was the company’s profit for the project greater than $150,000?

(1)     The company’s total cost was three times its cost for materials.

(2)     The company’s profit was greater than its cost for labor.

P > 150000 ? 已知：S=500000 隐含条件： S=P+C

由(1)知 C = 3Cm ，无法判断

由(2)知 P > Cl ，无法判断

(1)+(2)知：

C=Cm+Cl => Cl=2Cm , P>2/3 C  => P>200000

（C）

3.(7Q12)

If r, s, and w are positive numbers such that w = 60r + 80s and r + s = 1, is w < 70?

(1)     r > 0.5

(2)     r > s

当r=s=0.5时，w=70

(1)和(2)是一个意思

（D）

4.(9Q36)

If x, y, and k are positive numbers such that (x/(x+y))(10) + (y/(x+y)

)(20) = k and if x < y, which of the following could be the value of k?

A.    10

B.     12

C.     15

D.    18

E.     30

推导并变形

（D）

5.(10Q4)

If S is the sum of the reciprocals of the consecutive integers from 91 to 100, inclusive, which of the following is less than S?

  I.  1/8

        II.  1/9

       III.  1/10

A.   None

B.   I only

C.   III only

D.   II and III only

E.    I, II, and III

(C)

6.(2Q6)

The figure above shows the dimensions of a semicircular cross section of a one-way tunnel.  The single traffic lane is 12 feet wide and is equidistant from the sides of the tunnel.  If vehicles must clear the top of the tunnel by at least ½ foot when they are inside the traffic lane, what should be the limit on the height of vehicles that are allowed to use the tunnel?

A.    5½ ft

B.     7½ ft

C.     8 ½ ft

D.    9½ ft

E.     10 ft

(B)

7.(1Q2)

A certain roller coaster has 3 cars, and a passenger is equally likely to ride in any 1 of the 3 cars each time that passenger rides the roller coaster.  If a certain passenger is to ride the roller coaster 3 times, what is the probability that the passenger will ride in each of the 3 cars?

A.      0

B.       1/9

C.       2/9

D.      1/3

E.       1

用概率的定义去做。

该事件：每次做不同的车P(3,3)

所有事件：3×3×3

(C)

8.(1Q9)

A gardener is going to plant 2 red rosebushes and 2 white rosebushes.  If the gardener is to select each of the bushes at random, one at a time, and plant them in a row, what is the probability that the 2 rosebushes in the middle of the row will be the red rosebushes?

A.    1/12

B.     1/6

C.     1/5

D.    1/3

E.     1/2

用概率的定义去做。

该事件：中间两个是红的。C(2,1)×C(2,1)

所有事件：P(4,4)

(B)

9.(2Q31)

There are 8 magazines lying on a table; 4 are fashion magazines and the other 4 are sports magazines.  If 3 magazines are to be selected at random from the 8 magazines, what is the probability that at least one of the fashion magazines will be selected?

A.    1/2

B.     2/3

C.     32/35

D.    11/12

E.     13/14

至少的题用减法去做。算出一本fashion magazine都没有的概率1/14。

所有可能是：1-1/14=13/14

(E)

10.(11Q30)

In a stack of cards, 9 cards are blue and the rest are red.  If 2 cards are to be chosen at random from the stack without replacement, the probability that the cards chosen will both be blue is 6/11.  What is the number of cards in the stack?

A.   10

B.   11

C.   12

D.   15

E.   18

用概率的定义去做

假设红色的有x张。

9×8/((9+x)(8+x))=6/11

该式子不要去算，分析一下x等于3或者2

(C)