Beyond GMAT免费公开课 GWD数学难题解析21-30

myice

转自robert征途空间：http://forum.topway.org/sns/spac ... ;do=blog&id=958

Beyond GMAT免费公开课 GWD数学难题解析
主讲人：Robert


21.(3Q2)

On Saturday morning, Malachi will begin a camping vacation and he will return home at the end of the first day on which it rains.  If on the first three days of the vacation the probability of rain on each day is 0.2, what is the probability that Malachi will return home at the end of the day on the following Monday?



A.    0.008

B.     0.128

C.     0.488

D.    0.512

E.     0.640

独立事件。0.8×0.8×0.2=0.128

(B)

myice

22.(9Q23)

When tossed, a certain coin has equal probability of landing on either side.  If the coin is tossed 3 times, what is the probability that it will land on the same side each time?



A.    1/6

B.     2/9

C.     6/11

D.    9/16

E.     3/4

独立事件。第一次概率为，第二次1/2,第三次1/2，一共是1×1/2×1/2=1/4

(B)

myice

23.(19Q37)

AB

     +BA

AAC

In the correctly worked addition problem shown, where

the sum of the two-digit positive integers AB and BA is

the three-digit integer AAC, and A, B, and C are different digits, what is the units digit of the integer AAC?

A.    9

B.     6

C.     3

D.    2

E.     0

分析一下。11(A+B)=110A+C，C必然为11的倍数，所以为0

(E)

myice

23.(19Q37)

AB

     +BA

AAC

In the correctly worked addition problem shown, where

the sum of the two-digit positive integers AB and BA is

the three-digit integer AAC, and A, B, and C are different digits, what is the units digit of the integer AAC?

A.    9

B.     6

C.     3

D.    2

E.     0

分析一下。11(A+B)=110A+C，C必然为11的倍数，所以为0

(E)

myice

24.(22Q29)

In the xy-plane, region R consists of all the points (x, y) such that 2x + 3y ≤ 6.  Is the point (r, s) in region R ?

(1)     3r + 2s = 6

(2)     r ≤ 3 and s ≤ 2

画图。

(E)

myice

25.(25Q27)

If M is a positive integer, then M^3 has how many digits?

(1) M has 3 digits.

(2) M^2 has 5 digits

进位问题

反例法：

条件1： M=100, M=300

条件2： M=100, M=300

(E)

myice

26.(1Q31)

A positive integer n is said to be “prime-saturated” if the product of all the different positive prime factors of n is less than the square root of n.  What is the greatest two-digit prime-saturated integer?



A.    99

B.     98

C.     97

D.    96

E.     95

所有不同质因子的乘积小余它的平方根

约数的个数＝因子的个数＝每个质因子的个数（即指数）加1的连乘积。

(D)

myice

27.(2Q26)

There are 8 books on a shelf, of which 2 are paperbacks and 6 are hardbacks.  How many possible selections of 4 books from this self include at least one paperback?



A.    40

B.     45

C.     50

D.    55

E.     60

用减法去做。

C(8,4)-C(6,4)=55

(D)

myice

28.(15Q18)

Departments A, B, and C have 10 employees each, and department D has 20 employees.  Departments A, B, C, and D have no employees in common.  A task force is to be formed by selecting 1 employee from each of departments A, B, and C and 2 employees from department D.  How many different task forces are possible?



A.      19,000

B.       40,000

C.     100,000

D.    190,000

E.     400,000

10×10×10×C(20,2)=190000

(D)

myice

29.(19Q6)

An analyst will recommend a combination of 3 industrial stocks, 2 transportation stocks, and 2 utility stocks.  If the analyst can choose from 5 industrial stocks, 4 transportation stocks, and 3 utility stocks, how many different combinations of 7 stocks are possible?



A.   12

B.   19

C.   60

D.   180

E.    720

C(5,3)×C(4,2)×C(3,2)=

(D)