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
2024-01-13
45
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/3360112.html
相关试题推荐
Jim’sjobistokeephisboss______ofthelatestdevelopmentofthatproductin
Purchasingthenewproductionlinewillbea______dealforthecompany.A、profi
Thebirthrateinacity______tofallasitsgrossdomesticproduct(GDP)rises
JardenZincProducts,alargezincplantafewmilesoutsideGreeneville,Ten
JardenZincProducts,alargezincplantafewmilesoutsideGreeneville,Ten
JardenZincProducts,alargezincplantafewmilesoutsideGreeneville,Ten
JardenZincProducts,alargezincplantafewmilesoutsideGreeneville,
Howmanypositivefactorsdo180and96haveincommon?A、6B、12C、16D、18E、24
Howmanydifferentpositiveintegersarefactorsof342?A、9B、11C、12D、20E、22
Ifthesumoffiveconsecutiveoddintegersis5,whichofthefollowingcouldb
随机试题
[originaltext]W:John,doyouliketogoswimmingatthepoolwithmetoday?I’
王某将其集成电路布图设计申请登记,关于集成电路布图设计的申请程序,以下选项正确的
A.组织面 B.磨光面 C.咬合面 D.组织面-磨光面 E.组织面-磨光
商业银行开始向客户提供专业化投资顾问和个人外汇理财服务是我国个人理财业务的萌芽阶
十进制数+37的补码为00100101,其相反数的补码应为()。A.1101
在亚硝酸钠滴定法中,KBr的作用是A.增加重氮盐的稳定性B.防止副反应发生C.加
培训资源中培训空间的充分利用,对学习者空间位置的不同设计可以有( )等。A.U
古代埃及教育的一大特征是“以()为师”、“以()为师”。
下列焊接工艺评定说法中,不符合规定的是()。A.当改变任何一个重要因素时,
节能分部工程的验收可以由( )主持。A.政府监督部门 B.总监理工程师 C
最新回复
(
0
)