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
2024-01-13
17
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/3360102.html
相关试题推荐
Howmanypositivefactorsdo180and96haveincommon?A、6B、12C、16D、18E、24
Ifthesumoffiveconsecutiveoddintegersis5,whichofthefollowingcouldb
Ifrisnegativeandsispositive,whichofthefollowingmustbenegative?A、|r
Ifxandyareoddintegers,whichofthefollowingmustalwaysbeanon-integer
Whichofthefollowingisequaltox24forallpositivevaluesofx?A、x12+x12B、
Whichofthefollowingcannotbethemedianoffivepositiveintegersa,b,c,d
Foranynumberswandz,w·z=w3z(8-w2).Ifbothzandw·zarepositivenumbers,
Thesquarerootof636isbetweenwhichsetofintegers?A、24and25B、25and26
Foranynumbersaandb,ab=ab(3-b).Ifaandabbothrepresentpositivenumbers
If[img]2011q3/ct_egmatqm_egmatqchoose_0381_201121[/img]forallintegersxand
随机试题
Traditionally,theAmericanfarmerhasalwaysbeenindependentandhard-wor
下面你将听到的是一位中国官员在世界经济论坛年会上的一段讲话。主席先生,女士们、先生们:目前,国际形势正处于深刻变化之中。和平与发展仍然是当今时代的
Hemingway’sstylecanbebestexplainedwithhis______.A、useofvernacularB、ice
下列存储设备中,存取速度最快的是()。A.主存 B.辅存 C.寄存器
对一位小脑损伤患者进行协调功能评定,常用的评定方法不包括A.指指试验 B.指鼻
某女,42岁,务农,已婚,经济生活拮据,平时缺乏体力活动,肥胖,饮酒多年,每次饮
患者,女,39岁,主诉有接触性阴道流血,偶有血性排液,有腥臭味。既往体健。经各项
“金边债券”是指()。A.政府债券 B.公司债券 C.金融债券 D.实物
电流互感器二次绕组所接负荷应在()所规定的负荷范围内。额定容量$;$准确等级$;
医生刘某看药品经营能挣钱,便与院领导拉关系。请假离岗搞药品销售,时间近3年。并借
最新回复
(
0
)