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
A bank account earned 2% annual interest, compounded daily, for as long as the balance was under $1,000, starting when the accou
A bank account earned 2% annual interest, compounded daily, for as long as the balance was under $1,000, starting when the accou
admin
2022-10-18
75
问题
A bank account earned 2% annual interest, compounded daily, for as long as the balance was under $1,000, starting when the account was opened. Once the balance reached $1,000, the account earned 2. 5% annual interest, compounded daily until the account was closed. No deposits or withdrawals were made. Was the total amount of interest earned at the 2% rate greater than the total amount earned at the 2. 5% rate?
(1) The account earned exactly $25 in interest at the 2. 5% rate.
(2) The account was open for exactly three years.
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
C
解析
Let P
0
, P
1
and P
2
be the initial balance, the balance after one year, and the balance after two years.
(1) Since $25 is the exact amount of interest earned in one year by an initial amount of $1,000 earning 2.5 percent annual interest, compounded yearly, it follows that $25 is the total amount of interest earned in slightly less than one year by an initial amount of $1,000 earning 2.5 percent annual interest, compounded daily. However, the total amount of interest earned at the 2 percent rate could be less than $25 (for example, if P
0
= $990, then the interest earned at the 2 percent rate is $10) and the total amount of interest earned at the 2 percent rate could be greater than $25 (for example, if P
0
= $900, then the interest earned at the 2 percent rate is $100); NOT sufficient.
(2) Given that the account was open for exactly three years, then the total amount of interest at the 2 percent rate could be less than the total amount of interest at the 2.5 percent rate (for example, if the balance reached $1,000 a few days after the account was open). On the other hand, the total amount of interest at the 2 percent rate could also be greater than the total amount of interest at the 2.5 percent rate (for example, if the balance reached $1,000 a few days before the account was closed); NOT sufficient.
Given (1) and (2), it follows that the account earned interest at the 2.5 percent rate for slightly less than one year and the account earned interest at the 2 percent rate for slightly more than two years. Therefore, the balances of P
1
and P
2
were reached while the account was earning interest at the 2 percent rate. Since P
0
(1.02) < P
1
and P
1
(1.02) < P
2
(compounding daily for one year produces a greater amount than compounding annually for one year), the values of P
0
, P
1
, and P
2
satisfy the following inequalities.
P
0
< P
0
(1.02) < P
1
< P
1
(1.02) < P
2
< 1,000
Note that the difference 1,000 - P
0
is the total amount of interest earned at the 2 percent rate. Thus, using (2), we wish to determine whether this difference is greater than 25. From P
0
(1.02) < P
1
it follows that P
0
(1.02)
2
< P
1
(1.02), and since P
1
(1.02) < 1,000, we have P
0
(1.02)
2
< 1,000. Therefore, P
0
< 1000/(1.02)
2
, from which we can conclude the following inequality.
1,000-P
0
> 1,000-1000/(1.02)
2
Since 1,000-1000/(1.02)
2
> 25 (see below), it follows that 1,000 - P
0
> 25 and hence the total amount of interest earned at the 2 percent rate is greater than the total amount of interest earned at the 2.5 percent rate.
One way to verify that 1,000 - 1000/(1.02)
2
> 25 is to verify that 1-1/(1.02)
2
>1/40, or equivalently, verify that 1/(1.02)
2
< 39/40, or 40 < 39(1.02)
2
.
Now note that we can obtain this last inequality from 40 < 39(1.04) (because 39 + 39(0.04) is greater than 39 + 1) and 1.04 < (1.02)
2
.
The correct answer is C;
both statements together are sufficient.
转载请注明原文地址:https://kaotiyun.com/show/2ktO777K
本试题收录于:
GMAT QUANTITATIVE题库GMAT分类
0
GMAT QUANTITATIVE
GMAT
相关试题推荐
Televisionhaschangedthelifestyleofpeopleineveryindustrializedcountryintheworld.IntheUnitedStates,wheresociolo
Atfirsttheinstituterefusedtopurchasethetelescope,butthisdecisionwas()revised.
Concerningmoneyoranythingelse,conflictsbetweenhusbandandwifeusuallyreflectapowerstruggle.Conflictsbetweenparen
Isawacarinthedistance,butIcouldn’t______whetheritwasredornot.
Whenwetalkaboutintelligence,wedonotmeantheabilitytogetgoodscoresoncertainkindsoftestsoreventheabilityto
Atfirsttheinstituterefusedtopurchasethetelescope,butthisdecisionwas______revised.
ABritishteenagerhasbecomeamulti-millionaireaftersellinganapplicationsoftwarehecreatedtowebgiantYahoo.Thedeal
Inanoldtownlivedamerchant.Heearnedhugeprofitsbyfairmeansandfoul(恶劣的).Withmoreprofitsflowingin,hebecamemor
Aspecialresearchteamfromthelocalmedicalcenter【C1】______experimentsoncompletelyblindbabies.Thebabiestobetestedo
Whenweplaytenniswehaveto______.Whatisofthegreatestimportancetoafootballteamis______.
随机试题
下列关于风险的说法,不正确的是()。
关于重症多形红斑,下列正确的是
处方炒三仙、焦三仙中,“三仙”的组成是()。
监理组织形式根据()情况而定。
根据《水工建筑物地下开挖工程施工技术规范》DL/T5099—1999,相向开挖的两个工作面相距()m或()倍洞径距离放炮时,双方人员均需撤离工作面。
预计资产负债表中现金科目的期末数不一定等于资金预算中的期末现金余额。()
对会议文件资料立卷归档的意义在于()。
下列典故利用了自然规律的有()。
若3号线在1月份的车票是红色的,则下面哪一句话一定正确?()下面哪一句话可能正确?()
Whydoestheprofessormentionhowwell-informedpeopleareaboutmedicalissuestoday?
最新回复
(
0
)