math GWD problems

董茜

Q2:

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

answer is B, why

Q14:

If 10⁵⁰ – 74 is written as an integer in base 10 notation, what is the sum of the digits in that integer?

 

A.      424

B.      433

C.      440

D.     449

E.      467

Answer: C ,how to caculate it

Q18:

 

x        x                 2 in          x                                                                                    x

 

 

 

 

 

 

 

 

 

 

                                        

                                    Note: Figure not drawn to scale.

 

The figure shows a square patio surrounded by a walkway of width x meters.  If the area of the walkway is 132 square meters and the width of the patio is 5 meters greater than the width of the walkway, what is the area of the patio, in square meters?

 

A.      56

B.      64

C.      68

D.     81

E.      100

Answer: B i don't know why

Q25:

A photographer
                        will arrange 6 people of 6 different heights for photograph by placing them in two rows of three so that each person in the first row is standing in front of someone in the second row.  The heights of the people within each row must increase from left to right, and each person in the second row must be taller than the person standing in front of him or her.  How many such arrangements of the 6 people are possible?

 

A.      5

B.      6

C.      9

D.     24

E.      36

Answer: A, why

thank you very much

董茜

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

ice_liu910

Q2.1*(1/3)*(1/3)=1/9 第一次随便找一辆就好 题目没规定 所以不计算概率或者为100%

后面2次同时选中一辆车则每次概率为1/3 相乘即得

Q14. 10^50是一个51位数 没错吧

当其减去74的时候 就还剩50位 那么前48位都为9 后2位为26 然后算....

48*9+2+6=440

Q18.没看明白...图不清楚...

Q28. 99-301之间有101个数 然后根据等差数列求和公式...(100+300)*101/2=20200

项数这里是这么算的300-100/2再加1否则就少算了一项

Q25.画图就能弄出来假设1,2,3,4,5,6从小到大排列 满足前面大于后面的排列方法 且必须满足从左到右依次增高那么就是这么些情况

123   124   125   134   135

456   356   346   256   256

没了 就这些了 下面是后排 上面是前排

董茜

sorry it's my mistake

the answer of Q2 is C

thanks

harry2006

For Q2, the first car (A or B or C) is 1/3 * 3; dont care.
              the second car  (B or C ) is 2/3 only
              the third car (C only)    is 1/3

So, it's  1/3 * 3 * 2/3 * 1/3 = 2/9