建议使用官方纸质指南,查看对照完整题目
【OG20-P181-229题】
Of the 150 houses in a certain development, 60 percent have air-conditioning, 50 percent have a sunporch, and 30 percent have a swimming pool. If 5 of the houses have all three of these amenities and 5 have none of them, how many of the houses haveexactly two of these amenities?
-
xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
-
xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
-
xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
-
xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
-
xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx

【答案】D
【解析】设X=exactly two(4+5+6)
A∪B∪C=150-5=145
A+B+C=150×(60%+50%+30%)=210,A∩B∩C=5
A∪B∪C=A+B+C-X-2×(A∩B∩C),即145=210-x-10
x=55
【知识补充】
三个集合中
A∪B∪C=A+B+C-(A∩B)-(B∩C)-(A∩C)+(A∩B∩C)
A∪B∪C=A+B+C-只属于两个集合的部分-2×(A∩B∩C)
题目讨论 (10条评论)

-
Crystal8
又做错了,这次是忘记减去三者都不的情况了
0
0 回复 2021-11-23 13:14:17
-
304245sbzg
几何题:三个圆重叠,三个圆相加等于总面积+a+b+c+三叠部分*2
0
0 回复 2021-11-11 16:17:23
-
你这只猪
要熟记文氏图公式以及它的变体
0
0 回复 2020-07-07 16:13:35
-
1289311ww
有且只有2個的分别为 m,n,r(不包括同時有三個的)所求 同時有3個的 x 其他的不包括以上的 y 所以2m+2n+2r+3x+y=90+75+45 又m+n+r+x+y=150-5=145 又x=5 聯立得m+n+r=55
1
0 回复 2019-12-22 18:53:12
-
212629sr
为什么(number with all three things)要*2呢?
0
0 回复 2019-12-06 02:34:10
-
赤木青帝回复212629sr
同问……看了好久没看懂这个
0
0 回复 2019-12-09 20:54:11
-
Stanley想去荷兰回复212629sr
因为中间重合部分被三个圆圈重复计算了3次,所以减掉两次
1
0 回复 2019-12-30 09:03:14
-
-
Thomasgo
Total houses = number with air conditioning + number with sunporch + number with pool - number with only two of the three things - 2(number with all three things) + number with none of the three things 150
0
0 回复 2019-09-20 11:50:54
-
EscapeFromFate
Total houses = number with air conditioning + number with sunporch + number with pool - number with only two of the three things - 2(number with all three things) + number with none of the three things 150 = 0.6(150) + 0.5(150) + 0.3(150) - D - 2(5) + 5 150 = 90 + 75 + 45 - D - 10 + 5 150 = 205 - D D = 55
2
0 回复 2019-04-18 23:00:21
-
棋王回复EscapeFromFate
很详细,谢谢
0
0 回复 2019-06-25 15:27:37
-
-
贝熊猫
画三个互相交叉起来的圆,所求部分为x,有90+75+45-x-2*5=150-5得x为55
2
0 回复 2019-03-05 22:11:25
-
乔治8198
韦恩图公式很重要
0
0 回复 2018-12-12 20:28:22
-
hecmelo
air=150*0.6=90 sun=150*0.5=75 swim=150*0.3=45
Total=air+sun+swim-1*two amenities-2*three amenities+none=90+75+45-1*two amenities-10+5=205-two amenities
205-two amenities=150
so two amenities=55
0
0 回复 2017-12-24 00:25:34
-
lxra回复hecmelo
请问这是什么公式啊?
0
0 回复 2018-05-15 10:42:45
-
180687pkqh回复hecmelo
A∪B∪C=A+B+C-A∩B-B∩C-A∩C+A∪B∪C =A+B+C-只属于2个集合-2A∩B∩C
0
0 回复 2022-03-03 17:07:10
-
180687pkqh回复hecmelo
A∪B∪C=A+B+C-A∩B-B∩C-A∩C+A∩B∩C =A+B+C-只属于2个集合-2A∩B∩C
0
0 回复 2022-03-03 17:13:57
-