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
129
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://www.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
Icanhardly______thedifferencebetweenthesetwowords.
Thegovernmentplaced______onthenumbersofforeigncarsthatcouldbeimported.
Treesareusefultomaninthreeimportantways:theyprovidehimwithwoodandotherproducts:theygivehimshade:andtheyh
UsedtoTVshows,whereeverythingisquickandinteresting,theydonothavethepatiencetoreadanarticlewithoutpictures:
ABritishteenagerhasbecomeamulti-millionaireaftersellinganapplicationsoftwarehecreatedtowebgiantYahoo.Thedeal
AsTheplanecircledovertheairport,everyonesensedthatsomethingwaswrong.Theplanewasmovingunsteadilythroughtheair
Long-distancerunnersmayattimesworryabouttheirhearthealthwhiletakingpartintheevents.Butastudyfindsthatheats
Iffandgaredistinctprimenumberslessthan10,whichofthefollowingcannotbetheproductoffandg?
Whatisthesmallestintegerkforwhich64k>414?
Asthepriceofgasolinerises,whichmakessubstitutingalcoholdistilledfromcerealgrainattractive,thepriceofbreadand
随机试题
中国特色社会主义进入了新时代,中国的基本国情是()
哮病中痰哮治法为:哮证缓解期属肾虚者,治宜:
过敏性紫癜风热伤络证的首选方剂是
分析项目是否采取了技术上先进可行、经济上合理以及环境和社会上可以承受的措施。此为项目土地资源综合利用评价的基本内容中的()。
银行职业道德的基本原则是()。
某合伙企业解散时,在如何确定清算人的问题上,合伙人甲、乙、丙、丁各执一词。下列各合伙人的主张中,不符合合伙企业法律制度规定的有()。
某公司为建造一项固定资产于2004年1月1日发行5年期债券,面值为21000万元,票面年利率为6%,发行价格为20000万元,每年年末支付利息,到期还本,假定不考虑发行债券的辅助费用。建造工程于2004年1月1日开始,年末尚未完工。该建造工程2004年度
世界上最大的宫殿是()。
Everygrouphasaculture,howeveruncivilizeditmayseemtous.Totheprofessionalanthropologist,thereisnointrinsicsup
A、Acabdriver.B、Arepairman.C、Atrafficofficer.D、Anautomobilesalesman.A
最新回复
(
0
)