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
39
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
_____salariesmaynotbehigh,workingasanursingassistantdoeshavesomeot
Thislatestoutbreakofviolenceisaclear______ofdiscontentinthecity.A、m
[originaltext]W:Hi,mynameisKathy.Nicetomeetyou!M:Nicetomeetyou,t
施工阶段的新砌体,砂浆尚未硬化时,砌体的抗压强度( )。A.按砂浆强度为零计算
患儿,6岁,出生后发绀,活动后加重,喜蹲踞,体格检查:发育不良,明显紫绀及杵状指
患儿男,4岁。间歇性呕吐2年,左胸疼痛1天住院。X线胸片检查发现有一巨大囊状物突
2×18年12月31日,甲公司在非同一控制下的企业合并业务中获得一批存货(100
2017年3月31日,某企业乙存货的实际成本为100万元,加工该存
硫酸镁治疗妊娠高血压疾病时,下述哪项不对A.血清镁离子浓度超过1mmol/L,可
类风湿关节炎的特点是A.多见于青年男性 B.基本病理改变是滑膜炎 C.多累及
最新回复
(
0
)