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
What is the length of the hypotenuse of △ABC? (1) The lengths of the three sides of △ABC are consecutive even integers. (2) The
What is the length of the hypotenuse of △ABC? (1) The lengths of the three sides of △ABC are consecutive even integers. (2) The
admin
2022-10-18
80
问题
What is the length of the hypotenuse of △ABC?
(1) The lengths of the three sides of △ABC are consecutive even integers.
(2) The hypotenuse of AABC is 4 units longer than the shorter leg.
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
A
解析
(1) Let n,n + 2, and n + 4 be the consecutive even integers. Using the Pythagorean theorem, we have n
2
+ (n + 1)
2
= (n + 4)
2
. Because this is a quadratic equation that may have two solutions, we need to investigate further to determine whether there is a unique hypotenuse length.
n
2
+ (n + 2)
2
=(n+4)
2
= (n + 4)
2
n
2
+ n
2
+ 4n + 4=n
2
+8n+16
n2 - 4n - 12 = 0
(n-6)(n + 2) = 0
Therefore, n = 6 or n = -2. Since n = -2 corresponds to side lengths of-2,0, and 2, we discard n = -2. Therefore n = 6, the hypotenuse has length n + 4 = 10; SUFFICIENT.
(2) Let the side lengths be a, b, and a + 4. Using the Pythagorean theorem, we have a
2
+ b
2
= (a + 4)
2
. Expanding and solving for b in terms of a will facilitate our search for multiple hypotenuse length possibilities.
a
2
+ b
2
= (a + 4)
2
a
2
+ b
2
= a
2
+ 8a+16
b
2
= 8a+16
b =
When a = 1, we obtain side lengths 1 and
, and hypotenuse length 5. When a = 2, we obtain
side lengths 2 and
, and hypotenuse length 6; NOT sufficient.
The correct answer is A;
statement 1 alone is sufficient.
转载请注明原文地址:https://kaotiyun.com/show/5ttO777K
本试题收录于:
GMAT QUANTITATIVE题库GMAT分类
0
GMAT QUANTITATIVE
GMAT
相关试题推荐
Weallknowthatitispossibleforordinarypeopletomaketheirhomesontheequator(赤道),althoughoftentheymayfeeluncomfor
WhatdowemeanbyaperfectEnglishpronunciation?Inone【C1】______therearemanydifferentkindsofEnglishastherearespeak
Onlyresidentshereenjoythe______ofusingthisparkinglot.
Whenwetalkaboutintelligence,wedonotmeantheabilitytogetgoodscoresoncertainkindsoftestsoreventheabilityto
TheChinesehaveusedamethodcalledacupuncture(针炙)toperformoperationsforabout4,000yearswithoutputtingthepatientto
Thankstothemeansofmoderntransportationandcommunication,theworldisgettingsmaller.Thewholeworldcommunityappears
Inanoldtownlivedamerchant.Heearnedhugeprofitsbyfairmeansandfoul(恶劣的).Withmoreprofitsflowingin,hebecamemor
Frankfurt,Germany,isoneofthemost______populatedregionsinWesternEurope.
Ifx,y,andzarepositiveintegers,and4x=5y=6z,thentheleastpossiblevalueofx+y+zis
Althoughmanynovelistswriteforartisticreasons,othersareluredbythemoney,becausepopularsuccessinwritingcanbeso_
随机试题
流行性乙型脑炎的病变部位主要是在
撤销权在性质上属于()。
假设某股份有限公司成立于2013年9月10日,发起人甲认购公司股份200万股,为公司的小股东,2017年12月15日公司向社会公开发行A股10000万股,2018年1月5日,公司股票在证券交易所上市交易。下列关于公司上市后甲在公司成立时认购的股份转让的表述
根据增值税法律制度的规定,下列各项中,以1个季度为纳税期限的有()。
在社会主义市场经济条件下,我国宏观经济调控的主要手段是行政手段。()
入部10年后,你在北京还没有房子,有家私企出比外交部薪水高20倍的薪资挖你,你怎么办?
基于以下描述:有关系模式R(S,T,C,D,G),根据语义有如下函数依赖集:F={(S,C)→T,C→D,(S,C)→G,T→C}。关系模式R的规范化程度最高达到()。A)1NFB)2NFC)3NFD)4NF
Thefamousathleteexpressedhisregretatthefailureoftherunningrace.
A、TheauthormakesfunofthePresident.B、Theauthorthinkshighlyofthefilm.C、TheauthorisafanofHollywoodcomedies.D、
A、Hewasdoingshopping.B、Hewaswatchingafilm.C、Hewasmakingaphonecall.D、Hewastalkingtoapoliceman.A短文开头就说约翰“那时正在
最新回复
(
0
)