首页
外语
计算机
考研
公务员
职业资格
财经
工程
司法
医学
专升本
自考
实用职业技能
登录
外语
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.
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.
admin
2022-10-18
54
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://kaotiyun.com/show/ZttO777K
本试题收录于:
GMAT QUANTITATIVE题库GMAT分类
0
GMAT QUANTITATIVE
GMAT
相关试题推荐
TheChinesehaveusedamethodcalledacupuncture(针灸)toperform,operationsforabout4,000yearswithoutputtingthepatientto
Anotherthinganastronauthastolearnaboutiseatinginspace.Foodisweightless,justasmenare.Foodforspacehasto
Televisionhaschangedthelifestyleofpeopleineveryindustrializedcountryintheworld.IntheUnitedStates,wheresociolo
Inasecondhandbookshop,Billycameacrossabookwhichhethoughtwascertainlya______edition.
TheannualcampaigntomakeSingapore’sthreemillionpeoplemorepoliteendedyesterdayandwasimmediatelyfollowedbyanother
Nomatterwhoyouareorwhereyoucomefrom,onethingiscertain:youareacquaintedwiththemosquito(蚊子)—althoughyouprobab
Itwassuggestedthat________bigeventliketheYearofRussiainChinashouldcertainlybenefit________relationshipbetweenth
SpeakerA:IhaveanadmirationforChineseKungFu.BruceLee,JetLiandJackieChanareverypopularinmoviescircle.Speake
Ifforallintegersxandy;then(-5)×2=
ThefirstpeopletoinhabitNorthAmericacamefromAsia.Scientistshadhypothesizedthatthesepeopletraveledacrossanow-su
随机试题
Janehad(agreatdealof)trouble(toconcentrateon)herstudy(because)ofthenoisein(thenextroom).
100张病床以下医院感染发病率应低于()
建设工程投资具有“层次繁多”的特点,在计算建设工程投资时,按()顺序计算,并逐层汇总。
下列项目中属于流动负债项目的是( )。
宏观经济分析中的经济指标有()。
下列关于管理游戏的表述,不正确的是()。
Forseveralyears,Americanshaveenjoyedteleshopping—watchingTVandbuyingthingsbyphone.NowteleshoppingisstartinginE
在互联网上,每一个网民都是平等的个体,大家具有平等的话语权。任谁想借助现实世界的身份在网络上继续高人一等、威风八面,都是________。这似乎是一个领袖失势的时代,________的时代已然逝去,取而代之的是众声喧哗,甚至,关于领袖、成功的定义本身也__
王某是某市人民医院财务科科长,经举报查证有以下违法犯罪事实:(1)利用职务之便,侵吞公款8000元;(2)利用公款10万元用于个人炒股,且超过5个月未还;(3)任财务科科长期间,向市卫生局领导送礼达2万元;(4)王某
在苏俄新经济政策的内容中,最能体现多种所有制成分的是()。
最新回复
(
0
)