首页
登录
职称英语
If x and y are integers, is xy + 1 divisible by 3 ?(1) When x is divided by 3,
If x and y are integers, is xy + 1 divisible by 3 ?(1) When x is divided by 3,
游客
2024-01-13
41
管理
问题
If x and y are integers, is xy + 1 divisible by 3 ?
(1) When x is divided by 3, the remainder is 1.
(2) When y is divided by 9, the remainder is 8.
选项
A、Statement (1) ALONE is sufficient, but statement (2) alone is not sufficient.
B、Statement (2) ALONE is sufficient, but statement (1) alone is not sufficient.
C、BOTH statements TOGETHER are sufficient, but NEITHER statement ALONE is sufficient.
D、EACH statement ALONE is sufficient.
E、Statements (1) and (2) TOGETHER are NOT sufficient.
答案
C
解析
Determine whether xy+ 1 is divisible by 3, where x and y are integers.
(1) It is given that the remainder is 1 when x is divided by 3. It follows that x = 3q + 1 for some integer q. So, xy + 1 = (3q + l)y + 1. If y = 2, then xy + 1 = 6q + 3, which is divisible by 3. However, if y = 1, then xy + 1 = 3q + 2, which is not divisible by 3; NOT sufficient.
(2) It is given that the remainder is 8 when y is divided by 9. It follows that y = 9r + 8 for some integer r. So, xy + 1 = (9r + 8)x + 1. If x = 1, then xy+1 = 9r+9, which is divisible by 3. However, if x = 2, then xy + 1 = 18r + 17, which is not divisible by 3; NOT sufficient.
Taking (1) and (2) together gives x = 3q + 1 and y = 9r + 8, from which it follows that xy + 1 = (3q+l)(9r+8) + l = 27qr+9r+24q + 9 = 3(9qr + 3r +8q + 3), which is divisible by 3.
The correct answer is C;
both statements together are sufficient.
转载请注明原文地址:https://tihaiku.com/zcyy/3360110.html
相关试题推荐
Ifthesouthhadwonthewar,whatisnowtheUnitedStates______dividedintose
Thesquarerootof800isbetweenwhichofthefollowingintegers?A、21and25B、
Ifathree-digitnumberisselectedatrandomfromtheintegers100to999,incl
Thesquarerootof636isbetweenwhichsetofintegers?A、24and25B、25and26
Ifx,y,andzarepositiveintegersandx2=y2+z2,whichofthefollowingmustb
Whatisthesmallestpossiblecommonmultipleoftwointegerswhicharebothgre
Whatisthegreatestpossiblecommondivisoroftwodifferentpositiveintegers
Themedianoffivedifferentpositiveintegersis12,whichofthefollowingis
Whatisthetotalnumberofdifferent5-digitintegersthatcontainallofthed
Howmanypositive4-digitintegersbegin(ontheleft)withallevendigitande
随机试题
GuyMoreno—ProfessionalFootballerFavouriteinterestatschool:
CompletethesummaryofthelasttwoparagraphsofReadingPassage2.ChooseNO
TheFutureofTallBuildingsArchitectsresponsibleforthe
[originaltext]W:CanIhelpyou?M:Well.I’mlookingforsomethingIsawata
开放系统互连参考模型OSI中,()管理数据的解密加密、数据转换、格式化和文
下列各项不属于违约责任的特征的是()。A、相对性B、补偿性C、意定性D、对
机关幼儿园所获财政补贴逐年提高,难免令公众质疑,这是不是在维护一种“特权”。相比
下列资本结构理论中,认为资本结构影响企业价值的有( )。A.最初的MM理论
甲公司录用许某并订立5年期劳动合同。该劳动合同中双方依法可约定的最长试用期期限为
治疗指数A.比值越大就越不安全 B.ED/LD C.ED/TD D.LD/
最新回复
(
0
)