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
80
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
Concerningmoneyoranythingelse,conflictsbetweenhusbandandwifeusuallyreflectapowerstruggle.Conflictsbetweenparent
HarrietBeecherStowehadpouredherheartintoheranti-slaverybook,"UncleTom’sCabin".Butneithershenorherfirstpubl
Alltheusefulenergyatthesurfaceoftheearthcomesfromtheactivityofthesun.Thesunheatsandfeedscreaturesandmank
Acompletelynewsituationislikelyto______whentheschoolleavingageisraisedto16.
Tom______theshopkeeperwithovercharginghimforthearticleshehadbought.
______fromthemoon,theearthwithwater______seventypercentofitssurface.
Whenwetalkaboutintelligence,wedonotmeantheabilitytogetgoodscoresoncertainkindsoftestsoreventheabilityto
Sheismakingherselfillwith______overherson’sfuture.
Thechairmanofthedepartment,togetherwithsomeotherteachers,______aconferenceforthepurposeoflayingdowncertainreg
AsTheplanecircledovertheairport,everyonesensedthatsomethingwaswrong.Theplanewasmovingunsteadilythroughtheair
随机试题
A.麻风病B.狂犬病C.风疹D.鼠疫E.流行性腮腺炎上述各项,属于乙类传染病的是()
会计核算软件主要是替代了手工会计的()等工作。
下列商业银行的理财顾问服务流程的环节中,顺序存“建立投资组合”之后的是()
房地产开发企业计算土地增值税时,所销售的房产对应的下列费用中,准予按照实际发生额从收入总额中扣除的有()。
在签署审计业务约定书前,会计师事务所应当评价自身的专业胜任能力,包括( )。在签署审计业务约定书之前,注册会计师应当对被审计单位的基本情况进行了解,其内容包括( )。
儿歌是以低幼儿童为主要对象的文学作品,试简述儿歌的特点。
3岁孩子拿着画笔认真画画时,不仅是手动,身体的动作、面部的动作也来帮忙。这体现了儿童动作发展的()。
在关系数据库中,用来表示实体间联系的是
Agoodbookmaydrawourattentionsocompletelythatweforgetoursurroundingsandevenouridentityforthetimebeing.
A、 B、 C、 A叙述将来的事情的陈述句→将来时态的否定回答
最新回复
(
0
)