首页
登录
职称英语
If b is the product of three consecutive positive integers c, c + 1, and c + 2,
If b is the product of three consecutive positive integers c, c + 1, and c + 2,
游客
2025-02-27
9
管理
问题
If b is the product of three consecutive positive integers c, c + 1, and c + 2, is b a multiple of 24?
(1) b is a multiple of 8.
(2) c 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
A
解析
Since 24 = 23 x 3, and 1 is the only common factor of 2 and 3, any positive integer that is a multiple of 24 must be a multiple of both 23 = 8 and 3. Furthermore, the product of any three consecutive positive integers is a multiple of 3 This can be shown as follows. In b = c(c + 1) (c + 2), when the positive integer c is divided by 3, the remainder must be 0,1, or 2. If the remainder is 0, then c itself is a multiple of 3.
If the remainder is 1, then c = 3q + 1 for some positive integer q and c + 2 = 3q + 3 = 3(q + 1) is a multiple of 3. If the remainder is 2, then c = 3r + 2 for some positive integer r and c+1 = 3r+ 3 = 3(r+ 1) is a multiple of 3.In all cases, b - c(c + 1)(c + 2) is a multiple of 3.
(1) It is given that b is a multiple of 8. It was shown above that b is a multiple of 3, so b is a multiple of 24; SUFFICIENT.
(2) It is given that c is odd. If c - 3, then b = (3)(4)(5) = 60, which is not a multiple of 24. If c = 7, then b = (7)(8)(9) = (24)(7)(3), which is a multiple of 24; NOT sufficient.
The correct answer is A;
statement 1 alone is sufficient.
转载请注明原文地址:https://tihaiku.com/zcyy/3974674.html
相关试题推荐
Thebirthrateinacity______tofallasitsgrossdomesticproduct(GDP)rises
JardenZincProducts,alargezincplantafewmilesoutsideGreeneville,Ten
JardenZincProducts,alargezincplantafewmilesoutsideGreeneville,Ten
JardenZincProducts,alargezincplantafewmilesoutsideGreeneville,Ten
JardenZincProducts,alargezincplantafewmilesoutsideGreeneville,
JardenZincProducts,alargezincplantafewmilesoutsideGreeneville,
Howmanydifferentpositiveintegersarefactorsof342?A、9B、11C、12D、20E、22
Ifthesumoffiveconsecutiveoddintegersis5,whichofthefollowingcouldb
Ifrisnegativeandsispositive,whichofthefollowingmustbenegative?A、|r
Ifxandyareoddintegers,whichofthefollowingmustalwaysbeanon-integer
随机试题
Inthe1920sdemandforAmericanfarmproductsfell,asEuropeancountriesb
BasketballOrganizedbasketball【T1】______twoteamsoffiveplayerseach.
[originaltext]DemonstratorsfromalloverItalygatheredinaRomesquareSat
We【C1】______upacamerafortheveryfirsttime.Wesnapsomepictures.【C2
Whydoesthewomantellthemanthestory?[br][originaltext]W:Iseeyouare
LeviStrausswasborninGermany,and【C1】______toAmericawhenyoung.In185
组织建立和实施质量管理体系的方法步骤包括()。A.确定和提供实现质量目标必需
患者男性,50岁,因胆道感染入院保守治疗,治疗过程中突然出现神志淡漠,嗜睡,皮肤
张老师将多媒体技术与自己的学科教学紧密结合起来,编制的计算机辅助教学课件操作方便
某房地产开发公司购买一宗土地进行住宅开发,地价为1200万元,一次性付清。预计建
最新回复
(
0
)