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
49
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
Thegovernmentplaced()onthenumbersofforeigncarsthatcouldbeimported.
______fromthemoon,theearthwithwater______seventypercentofitssurface.
Asmileisastrongsignofafriendlyandopenattitudeandawillingnesstocommunicate.Itisapositive,silentsignsentwi
Whatisthesmallestintegerkforwhich64k>414?
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。
现在有100个球,其中30个是白球,40个是红球,还有30个是蓝球,从中任意取出5个,其中至少4个是红球的概率?
一个矩形长宽分别为80,50,问两条边各增加多少时矩形面积是5400?
直线2y=6x+4的斜率和在x轴、y轴上的截距分别是多少?
从15个人中选择5个人,且有3个人不能同时选择,问有多少种选择方法?
一个正整数的映像可由颠倒其数字得到,比如321的映像是123,那么一个五位数字和其映像的差一定能够被下面哪一个整除?
随机试题
从事各种生产劳动,能引起劳动者职业性紧张的因素中,不包括
A.纤维素样血栓B.氮气栓塞C.羊水栓塞D.脂肪栓塞E.混合栓塞孕妇生产时出现的栓塞
某新生儿出生6小时,进行预防接种。接种乙肝疫苗的正确方法是
B公司代理A公司与C公司和下届商店签订合同的行为分别属于()。B公司代理A公司与C公司和下属商店签订买卖合同的行为属于()。
下列各种人力资源供需平衡的方法中,见效速度最快的是( )。
教育目的可以发挥()。
对于性格的特征差异,心理学家一般从以下方面进行分析()
()地方各级人民政府公安机关均设立督察机构。
现代微型计算机中所采用的电子器件是()。
Haveyoueveraskedyourselfwhychildrengotoschool?Youwillprobablysaythattheygotolearntheirownlanguageandother
最新回复
(
0
)