首页
登录
职称英语
If m and n are positive integers, is n even?(1) m(m + 2) + 1 = mn(2) m(m + n)
If m and n are positive integers, is n even?(1) m(m + 2) + 1 = mn(2) m(m + n)
游客
2025-02-27
9
管理
问题
If m and n are positive integers, is n even?
(1) m(m + 2) + 1 = mn
(2) m(m + n) is odd.
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
D
解析
(1) Given that m(m + 2) + 1 = mn, then m cannot be even, since if m were even, then we would have an odd integer, namely m(m + 2) + 1, equal to an even integer, namely mn. Therefore, m is odd. Hence, m(m + 2) is odd, being the product of two odd integers, and thus m(m + 2) + 1 is even. Since m(m + 2) + 1 = mn, it follows that mn is even, and since m is odd, it follows that n is even; SUFFICIENT.
Alternatively, the table below shows that m(m + 2) + 1 = mn is only possible when m is odd and n is even.
(2) Since m(m + n) is odd, it follows that m is odd and m + n is odd. Therefore, n = (m + n) - m is a difference of two odd integers and hence n is even; SUFFICIENT.
The correct answer is D;
each statement alone is sufficient.
转载请注明原文地址:https://tihaiku.com/zcyy/3974664.html
相关试题推荐
Ifmandnarepositiveintegers,isneven?(1)m(m+2)+1=mn(2)m(m+n)
GivenapositivenumberN,whenNisroundedbyacertainmethod(forconvenienc
Ifxandzareintegers,isx+z2odd?(1)xisoddandziseven.(2)x-zis
Foreachpositiveintegerk,letak=[img]2022m10x/ct_ve01204002j_0043_221018[/img
Iftheproductoftheintegersw,x,yandzis770,andif1<w<x<y<z.whatisthev
Fiveintegersbetween10and99,inclusive,aretobeformedbyusingeachofthe
Whichofthefollowingdescribesthesetofallpossiblevaluesofthepositive
Thedifference942—249isapositivemultipleof7.Ifa,b,andcarenonzerodi
Themedianof21differentintegersis17.Whichofthefollowingistheleastp
Ifx,yarepositiveintegers,isxydivisibleby4?(1)y+2isdivisibleby4.(
随机试题
Statusesaremarveloushumaninventionsthatenableustogetalongwithone
NotthatJohndoesn’twanttohelpyou,_____________(而是非他能力可及).butthatit’sbe
关于妊娠滋养细胞疾病,下列哪项是错误的A、胎盘部位滋养细胞肿瘤是一种特殊细胞形态
石质路堑钻爆开挖的方法有()。A、薄层开挖 B、分层开挖 C、全断面一次开挖
某35KV地下变电站,设有自动灭火系统。根据现行国家标准《火力发电厂与变电站设计
实行物业服务费用包干制的,物业服务费的构成包括()。 A.物业服务成
下列费用项目中,应列入制造费用的是()。A.直接材料费 B.直接人工费 C.
何首乌炮制的目的是A便于贮藏 B便于制剂 C改变性能 D引药入经
某公司员工甲在工作中发生轻伤,休工一年后又回到原工作岗位继续工作。根据《生产经营
下列关于基坑开挖的说法,正确的是()。A.场地开挖一般采取由上而下、分块分段分层
最新回复
(
0
)