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
26
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
A.solidB.madeupofC.equalD.fillsE.describingF.vaporG.there
[originaltext]TheInternetisaworldwidecommunicationnetworkthatlinks
WhichofthefollowingstatementsisTRUEaccordingtothepassage?[br][origi
Chinalauncheditssecondmannedspacemission.sendingtwoastronautsinto
下图所示的调制方式是( ),若载波频率为2400Hz,则码元速率为( )。
TherearedifferentwaystoperformIPb
关于血液的理化性质,错误的叙述是A.血浆渗量为290~310mOsm/kg·HO
椎管内麻醉平面过高,可致A.血压下降 B.呼吸抑制 C.恶心呕吐 D.头痛
关于中国的法律现代化,三位同学发表了一些看法。甲说:“中国社会转型对法律制度变革
(2021年真题)根据证券法律制度的规定,下列各项中,属于公开发行证券的交易场所
最新回复
(
0
)