首页
登录
职称英语
The difference 942—249 is a positive multiple of 7. If a,b,and c are nonzero di
The difference 942—249 is a positive multiple of 7. If a,b,and c are nonzero di
游客
2025-02-27
9
管理
问题
The difference 942—249 is a positive multiple of 7. If a,b,and c are nonzero digits,how many 3-digit numbers abc are possible such that the difference abc—cba is a positive multiple of 7?
选项
A、142
B、71
C、99
D、20
E、18
答案
E
解析
Since abc is numerically equal to 100a + 10b + c and cba is numerically equal to 100a + 10b + a, it follows that abc - cba is numerically equal to (100 - 1)a + (10 - 10)b + (1 - 100)c = 99(a - c). Because 7 and 99 are relatively prime, 99(a - c) will be divisible by 7 if and only if a - c is divisible by 7. This leads to two choices for the nonzero digits a and c,namely a = 9, c = 2 and a =8,c=1. For each of these two choices for a and c, b can be any one of the nine nonzero digits. Therefore, there is a total of 2(9) = 18 possible 3-digit numbers abc.
The correct answer is E.
转载请注明原文地址:https://tihaiku.com/zcyy/3974609.html
相关试题推荐
Whichofthefollowingdescribesthesetofallpossiblevaluesofthepositive
Thedifference942—249isapositivemultipleof7.Ifa,b,andcarenonzerodi
IfWhitneywrotethedecimalrepresentationsforthefirst300positiveinteger
Howmanypositiveintegersnhavethepropertythatboth3nandn/3are4-digit
Ifx,yarepositiveintegers,isxydivisibleby4?(1)y+2isdivisibleby4.(
X,FarepositiveintegersandX+2Y=16.What’sthevalueofX?(1)X>Y(2)X>4,Y>4
Whatisthegreatestcommondivisorofpositiveintegersmandn?(1)misaprim
Whatistheunitsdigitofpositiveintegerx?(1)xdividedby9hasaremainder
Ifx,y,andzarepositiveintegersand2x=3y=5z=7w,thentheleastpossibleva
Ifxisaprimenumber,whatisthevalueofx?(1)41<x<48(2)x+1isamultiple
随机试题
BuildYourSelf-confidence1.【T1】______fearSelf-confidence≠【T2】______Fea
AresearchpresentedtotheAAASmeetinginSanDiegosuggeststhatmuchof
When_______,thebridgeconnectingtheislandtothecontinentwillbeopento
吴茱萸汤中包含的药物组是A.吴茱萸、人参、白术 B.人参、大枣、生姜 C.吴
1.变电运维室(分部)和班组应每()对计划执行情况进行检查,提高运维
()对人际接触和交往频繁的工作岗位尤其重要。A:结果性效标 B:特征性效标
五年一班全体学生42人开展第二课堂活动,他们从学校大队部借来图书222本,规定每
关于固定资产清查,下列说法中不正确的是()。A.盘盈固定资产应作为前期差错处理
某市为了科学准确地分析本市的安全生产状况,组织各生产经营单位开展生产安全事故统计
阻塞性肺气肿支气管炎型的临床表现,下列哪项是正确的() A.发病年龄较轻 B
最新回复
(
0
)