首页
登录
职称英语
A $10 bill (1,000 cents) was replaced with 50 coins having the same total value.
A $10 bill (1,000 cents) was replaced with 50 coins having the same total value.
游客
2024-01-13
45
管理
问题
A $10 bill (1,000 cents) was replaced with 50 coins having the same total value. The only coins used were 5-cent coins, 10-cent coins, 25-cent coins, and 50-cent coins. How many 5-cent coins were used?
(1) Exactly 10 of the coins were 25-cent coins and exactly 10 of the coins were 50-cent coins.
(2) The number of 10-cent coins was twice the number of 5-cent coins.
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
Let a b, c, and d be the number, respectively, of 5-cent, 10-cent, 25-cent, and 50-cent coins. We are given that a + b + c+d= 50 and Sa + 10b + 25c + 50d = 1,000, or a + 2b + 5 c + 10d= 200. Determine the value of a.
a + b + c+d=50
a + 2b + 5c+10d=200
(1) We are given that c = 10 and d = 10. Substituting c = 10 and d=10 into the two equations displayed above and combining terms gives a + b = 30 and a + 2b = 50. Subtracting these last two equations gives b = 20, and hence it follows that a = 10; SUFFICIENT.
(2) We are given that b = 2a. Substituting b -2a into the two equations displayed above and combining terms gives a +2a+ c+d= 50 and a + 4a + 5c + 10d= 200, which are equivalent to the following two equations.
3a + c + d=50
a + c + 2d=40
Subtracting these two equations gives 2a — d= 10, or 2a = d + 10. Since 2a is an even integer, d must be an even integer. At this point it is probably simplest to choose various nonnegative even integers for d to determine whether solutions for a, b, c, and d exist that have different values for a. Note that it is not enough to find different nonnegative integer solutions to 2a = d+ 10, since we must also ensure that c and d are nonnegative integers. If d= 8, then 2a = 8 + 10 = 18, and we have a = 9, b= 18, c= 15, and d=8. However, if d= 10, then 2a = 10 + 10 = 20, and we have a =10,6 = 20, c = 10, and d= 10; NOT sufficient.
The correct answer is A;
statement 1 alone is sufficient.
转载请注明原文地址:https://tihaiku.com/zcyy/3360180.html
相关试题推荐
Ispenthalfanhour()thisdifficultmathproblem.A、havingworkedonB、towork
Thenewpowerplantisreported______withinthreeyears.A、havingbeencompleted
Hisfriends______himofhavingbrokerhiswords.A、denouncedB、complainedC、accus
______,theinhabitantsfled.A、ThecitytakenB、ThecityhavingbeentakenC、Hav
Havingsaidhewouldmendtheclock,hediscoveredthathehadnotbroughtthe_
______,heworksverylateatnigh.A、HavingbeenchoosingdirectorB、Choosingd
John,______thebet,hadtopayforthedinner.A、lostB、havinglostC、losingD、h
Though______,manylawsofnatureexist.A、nothavingbeendiscoveredB、havingno
Havingbeenfoundguilty,themanwasgivenasevere_______bythejudge.A、servic
Havingbeenpraisedbytheteacher,thelittlegirlranbackhome,________.A、ha
随机试题
Moresurprising,perhaps,astraditionalmarriagethedifficultyisthefacttha
Migrationisusuallydefinedas"permanentorsemipermanentchangeofresiden
Whatwillfuturehistoriansrememberabouttheimpactofscience【C1】______
Peoplethinkingabouttheoriginoflanguageforthefirsttimeusuallyarr
企业标准化的一般概念中以先进的科学、技术和生产实践经验的综合成果为()。A.目
我国把青岛市外的黄海海平面作为零点所测定的高度尺寸称为()。A.绝对标高 B
5岁小儿,两下肢(不包括臀部)烧伤,其烧伤面积为()A.34% B.
急性肺水肿最具特征性的临床表现是( )。A.端坐呼吸 B.咳粉红色泡沫痰
商业银行不得销售()的理财计划。A:收益率测算为负值B:收益率测算为正值C:
关于国债期货合约的特点,下列说法正确的有()。A.期货合约交易与标的国债的
最新回复
(
0
)