[数学讨论稿1]伊尔越二室屋日起 书学讨论稿第1-100题亥猪版 20日23点更新

JessicaOu

还有2题
32. DS What is the probability that event E or event F or both will occur?
(1) The probability that event E will occur is 0.6
(2)The probability that event F will occur is 0.4

QX: If the probability is 0.54 that Stock A will increase in value during the next month and the probability is 0.68 that Stock B will increase in value during the next month, what is the greatest possible value for the probability that neither of these two events will occur?
A. 0.22 B. 0.32 C.0.37 D.0.46 E. 0.63

sdcar2010

26. How many different 6-letter sequences are there that consist of 1 A, 2 B's, and 3 C's? A. 6 B. 60 C. 120 D. 360 E. 720

1) Treat all letters as different.  You get 6! = 720.
2) But B and B are the same in the final words.  So we counted the same setup 2! times.  720/2 = 360.
3) And C and C and C are the same in the final words.  So we counted the same setup 3! times.  360/6 = 60

B is the answer.

sdcar2010

6. The function f is defined for each positive three-digit integer n by f(n)=2^x3^y5^z, where x, y and z are the hundreds, tens, and units digits fo n, respectively. If m and v are three-digit positive integers such that f(m)=9f(v), then m-v=
A. 8 B.9 C. 18 D. 20 E.80

If f(m) = 9*f(v), then 2^x(m)*3^y(m)*5^z(m) = 9* 2^x(v)*3^y(v)*5^z(v) = 2^x(v)*3^[y(v)+2]*5^z(v)

So x(m)=x(v); y(m) = y(v) + 2; z(m)=z(v).  Basicly, the difference between m and v is at the ten digit place, in which the m has 2 more than v.  That's a difference of 20.

D

sdcar2010

22. DS If -2x>3y, is x negative?
(1)y>0 (2)2x+5y-20=0

From -2x>3y, we know that if y>=0, then x has to be negative. In addition, we know that 3y + 2x < 0.

1) y>0. Sufficient.
2) 2x+5y-20=0.  Then  20 - 2y = 3y +2 x < 0.  So 20<2y and y>0.  Sufficient.

Choose D.

sdcar2010

24. The positive numbers w, x, y, and z are such that x is 20 percent greater than y, y is 20 percent greater than z, and w is 20 percent less than x. What percent greater than z is w?
A. 15.2% B. 16.0% C.20.0% D. 23.2% E. 24.8%

x=1.2y; y=1.2z; w=0.8x

So z=(1/1.2)*y =(1/1.2)*(1/1.2)*x = (1/1.44)*x

percent greater than z is w = (w-z)/z=[0.8-1/1.44]/[1/1.44] = 1.44*0.8 -1 = 0.152

A

sdcar2010

36. DS  If x and y are integers, is y an even integer?
(1) 2y-x=x^2-y^2 (2) x is an odd integer

1) rearrange the equation to get y = x^2-y^2 +(x-y) = (x-y)(x+y+1)
   If x and y are both odd or both even, x-y = even.  y is even because one of its factors is even.
   If x and y are one odd and one even, then x+y+1 = even. y is evven because one of its factors is even.
  Sufficient.
2) insufficient.

Choose A

sdcar2010

32. DS What is the probability that event E or event F or both will occur?
(1) The probability that event E will occur is 0.6
(2)The probability that event F will occur is 0.4

1) insufficient.
2) insufficient.

1) and 2) together still insufficient.

Because we do not know if events E and F are mutually exclusive or if not mutually exclusive, what is the probability that one will happen in the absence of the other.

sdcar2010

QX: If the probability is 0.54 that Stock A will increase in value during the next month and the probability is 0.68 that Stock B will increase in value during the next month, what is the greatest possible value for the probability that neither of these two events will occur?
A. 0.22 B. 0.32 C.0.37 D.0.46 E. 0.63

This is simple.  Just use your common sense.  Because we want the greatest possible chance for neither of them to occur, then when B is not increasing, we let A not increasing NEITHER!  That will give us 1-0.68 =0.32 probability
So B.

JessicaOu

26题
2) But B and B are the same in the final words.  So we counted the same setup 2! times.  720/2 = 360.
3) And C and C and C are the same in the final words.  So we counted the same setup 3! times.  360/6 = 60

这2部分还是不懂

JessicaOu

32. DS Does the decimal equivalent of p/q, where p and q are positive integers, contain only a finite number of nonzero digits?
(1)p>q (2)q=8

11. DS If [x]<1?
(1)[x+1]=2[x-1] (2)[x-3]no equal to 0
notice:[]means绝对值

28. DS A school administrator will assign each student in a group of n students to one of m classrooms. If 3<m<13<n, is it possible to assign each of the n students to one of the m classrooms so that classroom has the same number of students assigned to it?
(1) It is possible to assign each of 3n students to one of m classrooms so that each classroom has the same students assigned to it.
(2)It is possible to assign of 13n students to one of m classrooms so that each classroom has the same number of students assinged to it.