(中一級)有關數學問題 (super急*!!!)

[匿名]

2012-01-24 6:45 am

不好意思.以下有3條關於數學的問題麻煩各位高人除了提供答案之外,懇請大家给予公式..及一些簡單的解說拜託了各位MATHS高人`` 請替我解答以下關於MATH的問題Photo1(question is included): http://a5.sphotos.ak.fbcdn.net/hphotos-ak-ash4/394780_353192804693803_100000092605044_1439611_891647412_n.jpg Photo2(question is included) : http://a5.sphotos.ak.fbcdn.net/hphotos-ak-ash4/405182_353192078027209_100000092605044_1439605_540944172_n.jpg Question3 : number has 3 digits.When it is divided by 6 or 7 ,it leaves a remainder of1. When it is divided by 8 or 11,it leaves a remainder of 7.Q.What isthe largest such number?請各位盡快回覆><(super急*!!!) Thank you so much><

更新1:

Photo 1 's website : http://a5.sphotos.ak.fbcdn.net/hphotos-ak-ash4/394780_353192804693803_100000092605044_1439611_891647412_n.jpg

回答 (1)

用戶2053

2012-01-25 10:32 am

✔ 最佳答案

Photo 1 :

左層有 1 個 :
□
□■
□□

中層有 2 個 :
■□■

右層有 3 個 :
■■
□■

共 1 + 2 + 3 = 6 個 , Answer is B.

Photo 2 :

1 2 3 ------> 3 choices
4 5 6 ------> 3 choices
7 8 9 ------> 3 choices
...0... ------> 1 choice

Total 3 x 3 x 3 x 1 = 27 choices
而 4 個數有 4 x 3 x 2 x 1 = 24 種排列
所以有 27 x 24 = 648 possibilities bank numbers.

Question 3 :

Let x < 1000 be the number , then

x = 6a + 1 = 7b + 1 = 8c + 7 = 11d + 7 , (a , b , c , d are positive integers)

==>
x = 42m + 1 = 88n + 7 , (m , n are positive integers)

42m + 1 = 88n + 7
21m - 3 = 44n
3 (7m - 1) = 44n

So 3 is a factor of n since 44 is not divisible by 3.

88n + 7 = x < 1000
n < 993 / 88 = 11.28...

So n = 3 , 6 or 9.
When n = 9 , x = 88*9 + 7 = 799

42m + 1 = 799
m = 19

So 799 is the largest such number.

Verify :
799 = 6 * 133 + 1 = 7 * 144 + 1 = 8 * 99 + 7 = 11 * 72 + 7

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