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 Whitney wrote the decimal representations for the first 300 positive integer multiples of 5 and did not write any other numbe
If Whitney wrote the decimal representations for the first 300 positive integer multiples of 5 and did not write any other numbe
admin
2022-10-18
67
问题
If Whitney wrote the decimal representations for the first 300 positive integer multiples of 5 and did not write any other numbers,how many times would she have written the digit 5?
选项
A、150
B、185
C、186
D、200
E、201
答案
E
解析
The number of times the digit 5 would be written is the number of times the digit 5 will appear in the units place plus the number of times the digit 5 will appear in the tens place plus the number of times the digit 5 will appear in the hundreds place.
Number of times the digit 5 will appear in the units place: This will be the number of terms in the sequence 5,15,25,35,..., 1485,1495. Adding 5 to each member of this sequence does not change the number of terms, and doing this gives the sequence 10,20,30,40,..., 1490,1500, which clearly has 150 terms (dividing the terms by 10 gives 1,2,3,4,..., 149,150).Thus, the digit 5 appears 150 times in the units place.
Number of times the digit 5 will appear in the tens place: This will be the number of terms in the sequence 50,55,150,155,250,255,..., 1450, 1455. The digit 5 appears in the tens place twice for each consecutive change in the hundreds digit. Thus, the digit 5 appears 2(15) = 30 times in the tens place.
Number of times the digit 5 will appear in the hundreds place: This will be the number of terms in the sequence 500,505,510,515,...,590,595, 1500. Thus, the digit 5 appears 20 + 1 = 21 times in the hundreds place.
Therefore, the number of times the digit 5 would be written is 150 + 30 + 21 = 201.
Alternatively, in the 2-digit multiples of 5, namely the multiples of 5 in the interval 5-95, there are twelve occurrences of the digit 5. The same number of occurrences of the digit 5 appear in the multiples of 5 in each of the intervals 100-195,200-295,300-395, and 400-495. For the multiples of 5 in the interval 500-595, there are the same corresponding twelve occurrences of the digit 5 plus twenty more for the digit in hundreds place for each of the twenty multiples of 5 in 500-595, for a total of thirty-two occurrences of the digit 5. For the multiples of 5 in each of the intervals 600-695, 700-795, 800-895,900-995,1,000-1,095,1,100-1,195, 1,200-1,295,1,300-1,395, and 1,400-1,495, there are twelve occurrences of the digit 5. Finally, there is one occurrence of the digit 5 in 1,500. Therefore, the total number of occurrences of the digit 5 in the first 300 multiples of 5 is 14(12)+ 32+ 1 = 201.
The correct answer is E.
转载请注明原文地址:https://kaotiyun.com/show/KktO777K
本试题收录于:
GMAT QUANTITATIVE题库GMAT分类
0
GMAT QUANTITATIVE
GMAT
相关试题推荐
Hespendsmoneylikewater.Infact,hisexpensesonfoodandclothesareratherhigh______hisincome.
Itwasacoldwinterday.AwomandroveuptotheRainbowBridgetollbooth(收费站)."I’mpayingformyself,andforthesixcarsb
Aspecialresearchteamfromthelocalmedicalcenter【C1】______experimentsoncompletelyblindbabies.Thebabiestobetestedo
Thewaypeopleholdtothebeliefthatafunfilled,painfreelifeequalshappinessactuallyreducestheirchancesofeveratta
如果M和N被6除得到的余数分别为3和5,那么下面哪一个不可能为M+N的值?
6个相同的球放在1,2,3,4四个杯中,要求每个杯中至少放一个,一共有多少种不同的放法?
某一个公司的所有电话分机都是偶数.如果每一个分机号都是由5个数字1,3,4,5,6组成,那么这个公司最多能够有多少个五位分机号码?
Agivenstreetmedianisplantedwithtrees.Ofthe30treesinthemedian,3arelindens,one-fifthareoaks,12arecedars,an
写出将函数f(x)=(x+1)2按以下方式平移后的表达式。(1)向上平移2个单位。(2)向右平移1个单位。
在一个由20个连续整数组成的递增数列中,前面10个整数的和为380,求数列中所有整数的和?
随机试题
从细菌中分离质粒DNA的方法都包括的基本步骤是
适合治疗阴偏衰的治法是
不良贷款率是衡量()的最重要指标。
关于产品需求对劳动力需求的影响的说法,正确的是()。
Whyisitthatthemoreconnectedweget,themoredisconnectedwefelt?Everyadvanceincommunicationstechnologyisasetback
中国共产党同一切剥削阶级政党的根本区别是全心全意为人民服务,立党为公,执政为民。()
【掌衡派】北京大学2002年中国通史真题;河北师范大学2013年中国史真题;南京大学2015年中国近现代史基础真题;南京大学2016年中国近现代史基础真题
共享性是操作系统的特征之一,计算机中的各类设备在操作系统管理下实现共享,那么下列哪种设备可以同时共享?()
给定程序中,函数fun的功能是:用函数指针指向要调用的函数,并进行调用。规定在【2】处使f指向函数f1,在【3】处使f指向函数f2。当调用正确时,程序输出:x1=5.000000,x2=3.000000,x1*x1+x1*x2=40.0000
Wouldyoumindkeepinga(n)______onthehouseforuswhileweareaway?
最新回复
(
0
)