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 x and y are integers, is xy + 1 divisible by 3 ? (1) When x is divided by 3, the remainder is 1. (2) When y is divided by 9,
If x and y are integers, is xy + 1 divisible by 3 ? (1) When x is divided by 3, the remainder is 1. (2) When y is divided by 9,
admin
2022-10-18
46
问题
If x and y are integers, is xy + 1 divisible by 3 ?
(1) When x is divided by 3, the remainder is 1.
(2) When y is divided by 9, the remainder is 8.
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
C
解析
Determine whether xy+ 1 is divisible by 3, where x and y are integers.
(1) It is given that the remainder is 1 when x is divided by 3. It follows that x = 3q + 1 for some integer q. So, xy + 1 = (3q + l)y + 1. If y = 2, then xy + 1 = 6q + 3, which is divisible by 3. However, if y = 1, then xy + 1 = 3q + 2, which is not divisible by 3; NOT sufficient.
(2) It is given that the remainder is 8 when y is divided by 9. It follows that y = 9r + 8 for some integer r. So, xy + 1 = (9r + 8)x + 1. If x = 1, then xy+1 = 9r+9, which is divisible by 3. However, if x = 2, then xy + 1 = 18r + 17, which is not divisible by 3; NOT sufficient.
Taking (1) and (2) together gives x = 3q + 1 and y = 9r + 8, from which it follows that xy + 1 = (3q+l)(9r+8) + l = 27qr+9r+24q + 9 = 3(9qr + 3r +8q + 3), which is divisible by 3.
The correct answer is C;
both statements together are sufficient.
转载请注明原文地址:https://kaotiyun.com/show/dttO777K
本试题收录于:
GMAT QUANTITATIVE题库GMAT分类
0
GMAT QUANTITATIVE
GMAT
相关试题推荐
Spending50minuteswithacellphoneclosetoyourearisenoughtochangebraincellactivityinthepartofthebrainclosest
Thegovernmentplaced______onthenumbersofforeigncarsthatcouldbeimported.
Nooneknowshowmanlearnedtomakewords.Perhapshebeganbymakingsoundslikethosemadebyanimals.Perhapshegruntedlik
Alawyerfriendofminehasdevotedherselftotheserviceofhumanity.Herspecialareaiscalled"publicinterestlaw".Ma
Isawacarinthedistance,butIcouldn’t______whetheritwasredornot.
TheannualcampaigntomakeSingapore’sthreemillionpeoplemorepoliteendedyesterdayandwasimmediatelyfollowedbyanother
Itisnotprofitabletoprovidebusservicesindistrictswherethepopulationiswidely______.
Sometimeinthemiddleofthe15thcentury,awell-to-domerchantfromLondonburiedmorethan6,700goldandsilvercoinsona
Inthecircularregionshownabove,sectionsAandBrepresent3/8and5/11,respectively,oftheareaofthecircularregion.S
Thefactsshowthatthefearofflyinginairplanesisnotrational.In1986alone,therewere46,000fatalitiesinhighwayacci
随机试题
患者男性,21岁。2周前出现尿频、尿急和排尿时疼痛,1周来出现左踝及足跟部肿痛,3天前出现双眼烧灼感,伴眼分泌物增多。下列哪项检查有助于诊断
依据民法总则的规定,法人成立的条件有()。
城市社会隔离表现在城市生活中最明显的是()。
3月15日,某交易者在国内市场卖出开仓50手9月份棕榈油期货合约,成交价格为8600元/吨。之后,该投机者D28670元/吨的价格将上述头寸全部平仓,若不计交易费用,其盈亏情况为()元。
关于中外合资经营企业财务与会计管理,下列说法中,正确的是()。
2013年东部地区专业技术人员的年平均工资约为东北地区的()。
改革要在________公平开放便利的市场环境上多下功夫,要在体恤民生上见真情。经济调整期,不能不顾小微企业实际承受能力,无节制地追求税收增长率。一项不期而至的小微企业普惠型免税政策,是炎炎烈日中吹来的清凉之风,是充满温情和体恤的善政,从这个意义上说,这项
下列关于秦朝法制的表述正确的是()。
有5封信随机投入4个信箱,设X为第2个信箱可能投入的信件数量,求EX.
Olderpeoplewhoholdtemporaryorpart-timejobsafterretirementenjoybetterphysicalandmentalhealththanthosewhostopw
最新回复
(
0
)