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
Let’s be the set of all positive integers having at most 4 digits and such that each of the digits is 0 or 1．What is the greates
Let’s be the set of all positive integers having at most 4 digits and such that each of the digits is 0 or 1．What is the greates
admin
2022-10-18
63
问题
Let’s be the set of all positive integers having at most 4 digits and such that each of the digits is 0 or 1．What is the greatest prime factor of the sum of all the numbers in S?
选项
A、11
B、19
C、37
D、59
E、101
答案
E
解析
By writing down all the positive integers in S, their sum can be found.
The sum of these integers is 8,888. Since this sum is 8 × 1,111 = 2
3
× 11 × 101 (note that 1,111 = (11 × 100) +11), it follows that 101 is the largest prime factor of the sum.
Alternatively, we can simplify the description by letting the integers having fewer than four digits be represented by four-digit strings in which one or more of the initial digits is 0. For example, the two-digit number 10 can be written as 0010 = (0 × 10
3
) + (0 × 10
2
) + (1 × 10
1
) + (0 × 10
0
). Also, we can include 0 = 0000, since the inclusion of 0 will not affect the sum. With these changes, it follows from the Multiplication Principle that there are 2
4
= 16 integers to be added. Moreover, for each digit position (units place, tens place, etc.) exactly half of the integers will have a digit of 1 in that digit position. Therefore, the sum of the 16 integers will be (8 × 10
3
) + (8 × 10
2
) + (8 × 10
1
) + (8 × 10
0
), or 8,888. Note that this alternative method of finding the sum is much quicker than the other method if "at most four digits" had been "at most seven digits." In the case of "at most seven digits," there will be 2
7
= 128 integers altogether, and for each digit position, half of the integers will have a digit of 1 in that digit position and the other half will have a digit of 0 in that digit position. Thus, the sum will be (64 × 10
6
) + (64 × 10
5
) + ... + (64 × 10
0
) = 71,111,104. Incidentally, finding the greatest prime factor of 71,111,104 is not appropriate for a GMAT problem, but in this case a different question about the sum could have been asked.
The correct answer is E.
转载请注明原文地址:https://kaotiyun.com/show/dktO777K
本试题收录于：
GMAT QUANTITATIVE题库GMAT分类
0
GMAT QUANTITATIVE
GMAT
相关试题推荐
Doyouknowinsurance(保险)?Buyinginsuranceisameansbywhichpeoplecanprotectthemselves【C1】______largelosses.Protection
Ican’ttellthe______differencebetweenthetwinsisters.
A、 B、 C、 D、 C短语搭配错误，应改为justasmuch。as…as…“和……一样……，像……一样……”，用来表示同级比较，其否定形式是notso…as…。因该句是肯定句，所以用as…as…
W:Howannoying!Ican’tfigureoutasolutiontothisproblem.Canyouhelpme?M:______
Aspecialresearchteamfromthelocalmedicalcenter【C1】______experimentsoncompletelyblindbabies.Thebabiestobetestedo
Morecanbelearnedaboutaculturefromastudyofarthistorythangeneralhistorybecause______.Whichofthefollowingsta
李明正在看报纸。
圆心在原点、半径为5的圆上有多少个整数点?
已知在标准正态分布中，各部分概率如下：在大学的一门专业课考试中，学生的成绩近似服从于均值为75，标准差为5的正态分布，已知该课程共有400位同学参与考试。(1)有多少考生的成绩大于等于85分?(2)成绩70分位于第几个百分位数上?
数字2，3，4，5，6，7，0可以组成多少个两位数。
随机试题
毛泽东对实事求是的含义作了马克思主义界定的文章是()
在正常情况下，SaO2为0．90时，PO2的值约为
患儿，女，6岁，突然出现小便频数短赤，尿道灼热疼痛，尿液淋沥浑浊，小腹坠胀，腰部酸痛，伴有发热，烦躁口渴，甚有恶心呕吐，舌质红，苔黄腻，脉数有力。治疗首选方剂()
同年同月同日出生的刘某、项大和项二是某市D区楚汉中学的同班同学，刘某居住在该市A区，项大和项二都居住在B区，在一次班级活动中，三人都报名参加攀登C区的爬山比赛。在爬山过程中，项大和项二为争第一，故意将刘某推倒，导致刘某头部受伤。活动组织者立即将刘某送往医院
关于水泥混凝土面层用养护剂的说法正确的是()。
采用内部转移价格主要是为了考核、评价责任中心的业绩，并不强求各责任中心的转移价格完全一致，可分别采用对不同责任中心最有利的价格为计价的依据。()
突然，从窗外传来一阵急促的“的嘟”——“的嘟”——声，这声音犹如一块巨石落入平静的水面，教室里顿时喧闹起来。紧接着，像有谁下了一道命令：“向左看齐”，所有的学生都向左边看去。这是怎么回事，还没等老师喊出话来，坐在靠窗边的同学已经站起来，趴在窗台上向外张望，
公诉案件实行国家追诉制度，被害人不是原告人，但是他对人民检察院作出的不起诉决定有()。
Generallyspeaking,aBritishiswidelyregardedasaquiet,shyandconservativepersonwhois【B1】______onlyamongthosewith
Afterwardstherewasjustafeelingoflet-down.
最新回复
(
0
)
