a*****g
发帖数: 1320 | 1 【 以下文字转载自 SanFrancisco 讨论区 】
发信人: ashuang (不要迷恋哥，哥只是个传说), 信区: SanFrancisco
标 题: mathscounts 数学题求助
发信站: BBS 未名空间站 (Fri Oct 29 00:35:22 2010, 美东)
1.WHAT IS THE PROBABILITY THAT A RANDOMLY SELECTED TWO -DIGIT POSITIVE
INTEGER IS A PERFECT SQUARE OR A PERFECT CUBE? EXPRESS YOUR ANSWER AS A
COMMON FRACTION.
2. A FIVE DIGIT NUMBER IS CREATED USING THE DIGITS 1-5 EACH ONCE.WHAT IS THE
PROBABILITY THAT THE NUMBER IS ODD? EXPRESS YOUR ANSWER AS A COMMON
FRACTION.
3.THE DIGITS 2,3, 4, 7 AND 8 ARE EACH USED ONCE TO FORM A FIVE DIGIT NUMBER
. WHAT IS THE PROBABILITY THAT THE TENS DIGIT IS ODD AND THE NUMBER IS
DIVISIBLE BY 4? EXPRESS YOUR ANSWER AS A COMMON FRACTION
4.THE SUM OF THE DIGITS OF A NUMBER IS 9.WHAT IS THE PROBABILITY THAT THE
NUMBER IS PRIME?
本人无力辅导儿子的数学竞赛，请好心人给出解题步骤，衷心感谢了。 | h******g
发帖数: 11250 | 2
6 two digit positive integers are perfect square (4^2 to 9^)
2 two digit positive integers are perfect cube (3^3 and 4^3)
so the probability is 8/90 (totally 90 two digit positive integers)
THE
3/5
3 odd numbers out of 1-5
NUMBER
to be divisible by 4, the first two digits (count from right) has to be
divisible by 4, so only xxx32, xxx72 meet this requirement, therefore. the
fraction is
2*P(3,3)/P(5,5)=2*3!/5!=1/10
need to think about it
【在 a*****g 的大作中提到】
: 【 以下文字转载自 SanFrancisco 讨论区 】
: 发信人: ashuang (不要迷恋哥，哥只是个传说), 信区: SanFrancisco
: 标 题: mathscounts 数学题求助
: 发信站: BBS 未名空间站 (Fri Oct 29 00:35:22 2010, 美东)
: 1.WHAT IS THE PROBABILITY THAT A RANDOMLY SELECTED TWO -DIGIT POSITIVE
: INTEGER IS A PERFECT SQUARE OR A PERFECT CUBE? EXPRESS YOUR ANSWER AS A
: COMMON FRACTION.
: 2. A FIVE DIGIT NUMBER IS CREATED USING THE DIGITS 1-5 EACH ONCE.WHAT IS THE
: PROBABILITY THAT THE NUMBER IS ODD? EXPRESS YOUR ANSWER AS A COMMON
: FRACTION.
| a*****g
发帖数: 1320 | 3 谢谢你！
【在 h******g 的大作中提到】
:
: 6 two digit positive integers are perfect square (4^2 to 9^)
: 2 two digit positive integers are perfect cube (3^3 and 4^3)
: so the probability is 8/90 (totally 90 two digit positive integers)
: THE
: 3/5
: 3 odd numbers out of 1-5
: NUMBER
: to be divisible by 4, the first two digits (count from right) has to be
: divisible by 4, so only xxx32, xxx72 meet this requirement, therefore. the
| a*****g
发帖数: 1320 | 4 可不可以给我再讲讲第三题？谢谢。
【在 h******g 的大作中提到】
:
: 6 two digit positive integers are perfect square (4^2 to 9^)
: 2 two digit positive integers are perfect cube (3^3 and 4^3)
: so the probability is 8/90 (totally 90 two digit positive integers)
: THE
: 3/5
: 3 odd numbers out of 1-5
: NUMBER
: to be divisible by 4, the first two digits (count from right) has to be
: divisible by 4, so only xxx32, xxx72 meet this requirement, therefore. the
| h******g
发帖数: 11250 | 5
0
there is a rule, if the sum of all digits of a number is 9, this number is
divisible by 9, therefore, it is not a prime.
the proof is following
suppose there is a n-digit number XnX(n-1)....X2X1, where Xi is a integer
between 0 and 9, then
XnX(n-1)....X2X1=sum(Xi*10^(i-1))=sum(Xi*(10^(i-1)-1))+sum(Xi), i=1,2,...,n
the first term is divisible by 9, if the second is divisible as well, the
number has to be divisible
【在 a*****g 的大作中提到】
: 【 以下文字转载自 SanFrancisco 讨论区 】
: 发信人: ashuang (不要迷恋哥，哥只是个传说), 信区: SanFrancisco
: 标 题: mathscounts 数学题求助
: 发信站: BBS 未名空间站 (Fri Oct 29 00:35:22 2010, 美东)
: 1.WHAT IS THE PROBABILITY THAT A RANDOMLY SELECTED TWO -DIGIT POSITIVE
: INTEGER IS A PERFECT SQUARE OR A PERFECT CUBE? EXPRESS YOUR ANSWER AS A
: COMMON FRACTION.
: 2. A FIVE DIGIT NUMBER IS CREATED USING THE DIGITS 1-5 EACH ONCE.WHAT IS THE
: PROBABILITY THAT THE NUMBER IS ODD? EXPRESS YOUR ANSWER AS A COMMON
: FRACTION.
| h******g
发帖数: 11250 | 6 对任意一个数字 XnX(n-1)....X1，其中Xi为0-9的整数
XnX(n-1)...X2X1=XnX(n-1)...X3*100+X2X1
第一项可被4整除，因为是100的倍数
所以只要第二项可比4整除，整个数字就可以被4整除
剩下的就排列组合而已
【在 a*****g 的大作中提到】
: 可不可以给我再讲讲第三题？谢谢。
| k*b
发帖数: 15 | 7 8^2=4^3, can not double count. so 7/90 then.
【在 h******g 的大作中提到】
: 对任意一个数字 XnX(n-1)....X1，其中Xi为0-9的整数
: XnX(n-1)...X2X1=XnX(n-1)...X3*100+X2X1
: 第一项可被4整除，因为是100的倍数
: 所以只要第二项可比4整除，整个数字就可以被4整除
: 剩下的就排列组合而已
| h******g
发帖数: 11250 | 8 you are right
【在 k*b 的大作中提到】
: 8^2=4^3, can not double count. so 7/90 then.
| d********a
发帖数: 3698 | 9
POSITIVE
A
IS THE
NUMBER
啊
【在 a*****g 的大作中提到】
: 可不可以给我再讲讲第三题？谢谢。
| n******r
发帖数: 718 | |
|
