几道数学题, 请教高手

fuchuan · 发表于 2012-8-20 15:33:25

1 A certain library accesses fines for overdue books as follows. On the first day taht a book is overdue, the
total fine is $0.10. For each additional day that the book is overdue, the total
fine is either increased by $0.30 or doubled, whichever reults in the lesser amount. What is the total fine
for a book on the fourth day it is overdue?
a $0.60
b $0.70
c $0.80
d $0.90
e $1.00

2 If x and y are positive integers such that x=8y+12, what is the greatest common
divisor of x and y?
1) x=12u, where u is an integer.
2) y=12z, where z is an integer.
A Statement 1) alone is sufficient, but statement 2) alone is not
B Statement 2) alone is sufficient, but statement 1) alone is not
C Both together
D Each statement Alone is sufficient.
E Together are not sufficient.

fuchuan · 发表于 2012-8-20 23:07:16

高手回一下啊？都沉了

fallwater · 发表于 2012-8-20 23:18:27

第一题自己耐心算一下就有了。答案选B。
除第一天外每天的罚金是前一天罚金加0.3或者前一天罚金乘以2的较小者。
四天罚金分别是0.1 0.2 0.4 0.7。

第二题题目没打清楚吧。x=8y = 12是啥意思?

tomatoshirt · 发表于 2012-8-20 23:21:36

Q1. 先 double, double, double 然后再加3 的最小的fine

Day 1   0.1
Day 2   0.2
Day 3   0.4
Day 4   0.7

Q 2 http://www.manhattangmat.com/forums/in-x-and-y-are-positive-integers-such-that-x-8y-12-t902.html

tomatoshirt · 发表于 2012-8-20 23:22:05

x = 8y + 12

他抄错了

hshbaby · 发表于 2012-8-20 23:23:33

楼上正解第二题我也没看懂

tomatoshirt · 发表于 2012-8-20 23:28:09

Q2
1) X = 8y + 12 -> x = 12U ... U 可以是任何数 4 (3u) = 4 (2y+3) 揭不开

2) y = 12z .... x = 8 (12z) + 12.... 12 是两项共除项. 所以可以揭

hshbaby · 发表于 2012-8-20 23:28:51

第二题B？

fallwater · 发表于 2012-8-20 23:38:22

2 If x and y are positive integers such that x=8y = 12, what is the greatest common
divisor of x and y?
1) x=12u, where u is an integer.
2) y=12z, where z is an integer.
A Statement 1) alone is sufficient, but statement 2) alone is not
B Statement 2) alone is sufficient, but statement 1) alone is not
C Both together
D Each statement Alone is sufficient.
E Together are not sufficient.

-- by 会员 fuchuan (2012/8/20 15:33:25)

根据正解x=8y+12,
条件1 不充分，例如u=5,y=6时，x=60，最大公因数是6. 但例如y=12，u=9,x=108时,最大公因数是12.不能推出一个确定的数。
条件2 x=8*12z+12，充分。此时x=12（8z+1)，而y=12z，易见有公因数12，又因为z和8z+1互质，所以x，y最大公因数就是12.

答案选B

fuchuan · 发表于 2012-8-21 00:05:10

明白了，谢谢watefall 和其他热心的朋友们

几道数学题, 请教高手

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