首页
登录
职称英语
How many positive integers n have the property that both 3n and n/3 are 4-digit
How many positive integers n have the property that both 3n and n/3 are 4-digit
游客
2024-01-13
39
管理
问题
How many positive integers n have the property that both 3n and n/3 are 4-digit integers?
选项
A、111
B、112
C、333
D、334
E、1,134
答案
B
解析
If n is an integer, then 3n is always an integer. Also, 3n will be a 4-digit integer only when 1,000 ≤ 3n ≤ 9,999.Therefore, n is an integer such that
≤ n ≤ 3,333. Equivalently, n is an integer such that 334 ≤ n ≤ 3,333.
If n is an integer, then n/3 is an integer only when n is a multiple of 3. Also, n/3 will be a 4-digit integer only when 1,000 ≤ n/3 ≤ 9,999, or 3,000 ≤ n ≤ 29,997. Therefore, n is a multiple of 3 such that 3,000 ≤ n ≤ 29,997.
It follows that the values of n consist of all multiples of 3 between 3,000 = 3(1,000) and 3,333 = 3(1,111), inclusive. The number of such multiples of 3 is (1,111 - 1,000) + 1 = 112.
The correct answer is B.
转载请注明原文地址:https://tihaiku.com/zcyy/3360045.html
相关试题推荐
Howmanypositivefactorsdo180and96haveincommon?A、6B、12C、16D、18E、24
Ifthesumoffiveconsecutiveoddintegersis5,whichofthefollowingcouldb
Ifrisnegativeandsispositive,whichofthefollowingmustbenegative?A、|r
Whichofthefollowingisequaltox24forallpositivevaluesofx?A、x12+x12B、
Ifathree-digitnumberisselectedatrandomfromtheintegers100to999,incl
Whichofthefollowingcannotbethemedianoffivepositiveintegersa,b,c,d
Thesquarerootof636isbetweenwhichsetofintegers?A、24and25B、25and26
Foranynumbersaandb,ab=ab(3-b).Ifaandabbothrepresentpositivenumbers
Ifx,y,andzarepositiveintegersandx2=y2+z2,whichofthefollowingmustb
Whatisthegreatestpossiblecommondivisoroftwodifferentpositiveintegers
随机试题
Turningtocrimeisinthegenes,accordingtonewresearchcarriedoutint
Readthefollowingpassage.ChoosefromthesentencesA—Gtheonewhichbestfit
Alltoooften,peopleapproachtheirworkcareershaphazardly,waitingforo
自动化仪表工程施工程序中,仪表管道安装后的试验内容有()。A、仪表电源设备试验
地图管理条例规定,国家对向社会公开的地图实行()制度。A.审查 B.审核
属于阿片生物碱类药的是A:可待因 B:哌替啶 C:芬太尼 D:曲马朵 E
除甲、乙类生产车间外,人数不超过( )人且每道门的平均疏散人数不超过30人的房
(2020年真题)甲公司是一家医疗行业投资机构,拟对乙医院进行投资。乙医院是一家
矿业工程施工质量控制点设置,属于工程薄弱环节的有()。A.井壁壁座 B.井壁接
项目部对劳务分包单位协调管理的重点是( )。A.施工进度安排 B.质量安全制度
最新回复
(
0
)