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
60
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
[originaltext]WefirmlybelievethatanagentformarketingyourproductsinSh
嗜血杆菌药敏在M-H琼脂中加入A.Ca、Ⅴ因子 B.Ⅱ、Ⅴ因子 C.Ⅲ、Ⅹ因
A.两条相交的直线 B.两条异面直线 C.两条平行但不重合的直线 D.两条
左心衰竭最早出现的症状是A.夜间阵发性呼吸困难 B.端坐呼吸 C.劳力
我国法律规定的夫妻财产约定制的三种类型不包括()。A:部分共同制 B:完全共同
后遗效应是指A.大剂量下出现的不良反应B.血药浓度已降至最低有效浓度以下,仍残存
患儿,2岁。近1个月低热、咳嗽,夜间多汗,消瘦,胸片可见“哑铃状”双极阴影,结核
左边给定的是纸盒外表面的展开图,下面哪一项能由它折叠而成?请把它找出来。 A.
老刘和老张觉得人民调解员老王的调解效果不好,决定向人民法院起诉解决纠纷。老王仍然
某项永久性扶贫基金拟在每年年初发放80万元扶贫款,年利率为4%,则该基金需要在第
最新回复
(
0
)