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
31
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
thespaceshuttleDiscoverycompleteda______missionuponitsreturntoKennedy
TheUniversityBookstoreisaself-supportinguniversity-ownedorganization,
宋朝始于960年,一直延续到1279年。这一时期,中国经济大幅增长,成为世界上最先进的经济体,科学、技术、哲学和数学蓬勃发展。宋代中国是世界历史上首先发
与HTTP相比,HTTPS协议将传输的内容进行加密,更加安全。HTTP
前列腺增生病人早期最常见的症状是( )A.排尿困难 B.尿频 C.尿急
利率期限结构理论中,市场分割理论的假设条件有( )。 Ⅰ投资者和借款人喜欢
下列关于城市停车设施规划的表述,正确的是()。(2012年真题)A.城市出
(2017年真题)“在关键事件法的基础上发展起来,与行为锚定法大体相近,只是在量
下列选项中属于工程寿命周期成本的有()。A.工程寿命周期经济成本 B.工
施工成本管理的原则包括()。A.领导者推动 B.以人为本,全员参与 C
最新回复
(
0
)