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
The cardinality of a finite set is the number of elements in the set.What is the cardinality of set A? (1) 2 is the cardinality
The cardinality of a finite set is the number of elements in the set.What is the cardinality of set A? (1) 2 is the cardinality
admin
2022-10-18
40
问题
The cardinality of a finite set is the number of elements in the set.What is the cardinality of set A?
(1) 2 is the cardinality of exactly 6 subsets of set A.
(2) Set A has a total of 16 subsets.including the empty set and set A itself.
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
D
解析
Let n be the cardinality of the finite set A. What is the value of n ?
(1) The number of 2-element subsets of A is equal to the number of unordered selections without replacement of 2 objects from a collection of n distinct objects, or "n choose 2."Therefore, we have
or equivalently, n
2
- n - 12 = 0. Because this is a quadratic equation that may have two solutions, we need to investigate further to determine whether there is a unique value of n. Factoring leads to (n - 4)(n + 3) = 0, and thus n = 4 or n = -3. Since n must be a nonnegative integer, we discard the solution n = -3. Therefore, n = 4; SUFFICIENT.
(2) The number of subsets of set A is 2
n
, because each subset of A corresponds to a unique sequence of answers to yes-no questions about membership in the subset (one question for each of the n elements). For example, let A = {1 2, 3, 4, 5}, let Y represent "yes," and let N represent "no." Then the sequence NYNNN corresponds to the subset {2}, since the answers to "is 1 in the subset," "is 2 in the subset," "is 3 in the subset," etc. are "no," "yes," "no," etc. Also, the subset {1, 3, 4} of A corresponds to the 5-letter sequence YNYYN. Since the number of 5-letter sequences such that each letter is either N or Y is 2
5
, it follows that there are 2
5
= 32 subsets of {1, 2, 3, 4, 5}. For Statement (2), we are given that 2
n
= 16, and hence n = 4; SUFFICIENT.
Alternatively, observe that {1} has two subsets, {1, 2} has four subsets, and each addition of a new element doubles the number of subsets, because the subsets after adding the new element will consist of all the previous subsets along with the new element included in each of the previous subsets. Thus, {1, 2, 3} has 2(4) = 8 subsets, [1, 2, 3, 4} has 2(8) = 16 subsets, {1, 2, 3, 4, 5} has 2(16) = 32 subsets, etc.
The correct answer is D;
each statement alone is sufficient.
转载请注明原文地址:https://kaotiyun.com/show/gktO777K
本试题收录于:
GMAT QUANTITATIVE题库GMAT分类
0
GMAT QUANTITATIVE
GMAT
相关试题推荐
Youcan’thearwhatI’msaying______youstoptalking.
AccordingtotheAmericanfederalgovernment,residentsofHawaiihavethelongestlife
Inasecondhandbookshop,Billycameacrossabookwhichhethoughtwascertainlya______edition.
IntimeoftroubleCharliecouldalways______asolution.
Mancannotgoonincreasinghisnumberatthepresentrate.Inthenext30yearsmanwillfaceaperiodofcrisis.Someexperts
Ourpreferencesforcertaincolorsare______accordingtothepassage.Whichofthefollowingcouldbethemostsuitabletitle
Doyouknowwhataresolutionis?It’sapromise.Mostpromisesaremade【C1】______otherpeople("Mom,IpromiseI’lltidymyr
今天早上我没有赶上公共汽车。
Solvetheproblemandindicatethebestoftheanswerchoicesgiven.NUMBERS:Allnumbersusedarerealnumbers.FIGURES:
三角形的两条边分别是4和6QuantityA:三角形的面积SQuantityB:13
随机试题
简述全连接端口扫描的原理和工作过程。
具有Vitali反应的药物是
1名12岁儿童由饮水含氟量0.3ppm地区迁居饮水含氟量1.2ppm地区,氟牙症发生的可能性为
有关左心衰竭病理生理及临床表现的描述,下列哪项不正确
不应计入招标所要求的到位资金的是()。
融资租赁的特点有()。
在我国封建社会时期,行政决策体制的类型属于()
Thedoctorhadalmostlosthopeatonepoint,butthepatientfinally______.
A、ItisinconvenienttotakethebaggageontoitB、Itisdifficulttosparetheroomforwheelchairs.C、Itisdangeroustogeti
A、Teamakespeoplemorehealthy.B、Teahasalonghistory.C、Frequentteadrinkersenjoyalongerlifespan.D、Teahasmorenutr
最新回复
(
0
)