请教几道PS

VICTOR_JZG

19. Each of the integers from 0 to 9, inclusive, is written on a separate slip of blank paper and the ten slips are dropped into a hat. If the slips are then drawn one at a time without replacement, how many must be drawn to ensure that the numbers on two of the slips drawn will have a sum of 10?
(A) Three  (B) Four (C) Five
(D) Six  (E) Seven

Ans:E

题目意思好象不是很明了.
是否可以这样理解:
如果取了0,1,2,3,4,5的话,这6个数中,任意两个数的和都不可能为10.那么,再取第7个数,不管是6,或7,或8,或9, 都有两个数的和为10.所以选7.
欢迎讨论.

VICTOR_JZG

20. In a certain formula, p is directly proportional to s and inversely proportional to r. If p =1 when r = 0.5 and s = 2, what is the value of p in terms of r, and s?
(A) s/r  (B)r/4s
(C) s/4r  (D) r/s
(E) 4r/s
ans:C

因为,根据题目意思将数值带入可以得出:C.

VICTOR_JZG

19. If w, x, y, and z are on-negative integers, each less than 3, and w(33) + x(32) + y(3) + z = 34, then w+z=
(A) 0
(B) 1
(C) 2
(D) 3
(E) 4
Ans;C

应该是w*33 + x*32 + y*3 + z = 34吧.
w, x, y, and z are on-negative integers, each less than 3,那么w, x, y, and z只能在0,1,2中取值.
带入方程,可以得出:w=0,z=2或 w=1,z=1.故选C.

joywzy

20，不对啊，将数学代入，发现C/E皆可，下一步不知该怎么办？

19，对不起，19题粘贴时有误，应是这样的。
If w, x, y, and z are on-negative integers, each less than 3, and w(3^3) + x(3^2) + y(3) + z = 34, then w+z=
(A) 0
(B) 1
(C) 2
(D) 3
(E) 4
Ans;C
on-negative integers是什么意思？非负整数？

joywzy

19. Each of the integers from 0 to 9, inclusive, is written on a separate slip of blank paper and the ten slips are dropped into a hat. If the slips are then drawn one at a time without replacement, how many must be drawn to ensure that the numbers on two of the slips drawn will have a sum of 10?
(A) Three          (B) Four        (C) Five
(D) Six          (E) Seven

Ans:E

20. In a certain formula, p is directly proportional to s and inversely proportional to r. If p =1 when r = 0.5 and s = 2, what is the value of p in terms of r, and s?
(A)  s/r                (B)r/4s  
(C)   s/4r                (D) r/s
(E) 4r/s
ans:C

19. If w, x, y, and z are on-negative integers, each less than 3, and w(33) + x(32) + y(3) + z = 34, then w+z=
(A) 0
(B) 1
(C) 2
(D) 3
(E) 4
Ans;C


6. Coins are to be put into 7 pockets so that each pocket contains at least one coin. At most 3 of the pockets are to contain the same number of coins, and no two of the remaining pockets are to contain an equal number of coins. What is the least possible number of coins needed for the pockets?
(A) 7
(B) 13
(C) 17
(D) 22
(E) 28
Ans: C

19. A certain clock marks every hour by striking a number of times equal to the hour and the time required for a stroke is exactly equal to the time interval between strokes. At 6:00 the time lapse between the beginning of the first stroke and the end of the last stroke is 22 seconds. At 12:00, how many seconds elapse between the beginning of the first stroke and the end of the last stroke?
(A) 72
(B) 50
(C) 48
(D) 46
(E) 44
Ans


18. In a certain class consisting of 36 students, some boys and some girls, exactly   of the boys and exactly   of the girls walk to school. What is the greatest possible number of students in this class who walk to school?
(A) 9
(B) 10
(C) 11
(D) 12
(E) 13
Ans: C


13. In the table above, what is the least number of table entries that are needed to show the mileage between each city and each of the other five cities?
(A) 15
(B) 21
(C) 25
(D) 30
(E) 36

Ans: A

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sherry

一(19).分3堆 (1)：0 5 (2)：1 2 3 4 (3)：9 8 7 6 最多的可能性是取(1)的全部，(2)或(3)的全部，及另一组的任意一个，所以是7 二(20).p与s正比，与r反比，所以 p.r=x.s, p=1, r=1/2, s=2 得 x=1/4, 得 p=s/4r 三(19).w,x,y,z各在0，1，2里，27w+9x+3y+z=34 （则w.x<1）。w+z=34-(26w+9x+3y)，(1)w=0, z=34-(9x+3y), 无解，(2)w=1,x=0, z=8-3y, 所以z=1 w+z=2 四(6). 有三个口袋硬币数一样：3m 剩下的都不一样，则最小的可能性为：n,n+1,n+2,n+3 (n>=1) 最多三个口袋一样，所以m不等于n,...,n+3 求 3m+n+(n+1)+(n+2)+(n+3)的最小值，m=1,n=2时最小，为17 五(19). 敲击时间y=xa+(x-1)a, x=marked hour, a=敲一下的时间, x=6,y=22/60, 所以a=1/30, 所以y=1/15*x-1/30, 当x=12, y=46/60 hour 六、七.不太明白题目

joywzy

A certain clock marks every hour by striking a number of times equal to the hour and the time required for a stroke is exactly equal to the time interval between strokes.
=> 敲击时间y=xa+(x-1)a, x=marked hour, a=敲一下的时间

这一步能否能详细讲讲?尤其是(x-1)a,是怎么回事?我还是不太明白.

其它题目已理解,非常感谢!

sherry

joywzy, 不用谢!

the time lapse between the beginning of the first stroke and the end of the last stroke
interval的次数比敲的次数少一次(x-1)，interval一次的时间与敲一下的时间(a)一样，所以(x-1)a 是指intervals的时间。

joywzy

sherry:我明白了，非常感谢！