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
62
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
Muchunfriendlyfeelingtowardscomputershasbeenbasedonthefearofwidespreadunemploymentresultingfromtheirintroductio
Muchunfriendlyfeelingtowardscomputershasbeenbasedonthefearofwidespreadunemploymentresultingfromtheirintroductio
Treesareusefultomaninthreeimportantways:theyprovidehimwithwoodandotherproducts:theygivehimshade:andtheyhel
Studentsareexpectedto______theirclassesregularly.
Ahighercrimerateexistsincities______alargepercentageofunemployment.
Therearemanyolderpeopleintheworldandtherewillbemanymore.Alittle-knownfactisthatover60percentoftheolderp
Everythingweeatanddrinkcontainssomesalt;wecanmeetthebody’sneedforitfromnaturalsourceswithoutturning________
Belowisapictureshowingayoungwomanwhoworksathome.Writeanessayofabout120wordsmakingreferencetothefollowing
我会去火车站接你。
Oneofthebestpiecesofmedicalnewstoemergeoverthelastseveralyearsisthatchocolatemay【C1】______youlivelonger,pro
随机试题
急性链球菌感染后肾炎典型的临床表现是
A、dearB、heartC、earD、tearB
体内CO2分压最高的部位是
上颌骨骨折后骨折片移位方向一般是A.向后上B.向后内C.向后下D.向后外E.向内前
房地产的特性主要取决于土地的特性,它的基础是()。
起重机械失稳的主要原因有()。
进行火灾风险识别中,需判定火灾危险源。下列火灾危险源因素中,属于人为因素的是()。
甲公司和乙公司2013年度和2014年度发生的有关交易或事项如下:(1)2013年5月20日,乙公司的客户(丙公司)因产品质量问题向法院提起诉讼,请求法院裁定乙公司赔偿损失120万元。截止到2013年6月30日,法院尚未对上述案件作出判决,在向法院了解情
在一个复杂多变的世界里,我们不仅要努力工作,还要学习更灵捷地工作。更清楚、更快捷和更有创造性的能力是重要的,然而,许多人并没有意识到我们思维的局限性。问题在于,我们的思维定式束缚了我们思想中最灵捷的部分。本书诠释了思维创新的技巧,提出了一系列思考的工具和技
A、Becauseit’snotherjobtotakecareofthenoise.B、Becausethebigtenantmightposeathreattoher.C、Becauseshecan’tc
最新回复
(
0
)