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
35
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
NinestatesandtheDistrictofColumbiaaredoingawaywiththesalestaxo
Thelasttwotornadoseasonshavebeenthedeadliestinadecade,with206
[originaltext]Goodmorning.TodayI’dliketotalkaboutelectroniccigaret
网络192.168.21.128/26的广播地址为(),可用主机地址数(请作答
银行信贷产品开发的目标不包括( )。A.提高现有市场的份额 B.吸引现有市场
具有独特发育周期的微生物是A:支原体B:衣原体C:立克次体D:螺旋体E:
肾单位由下列哪项组成A:肾小球和肾小囊 B:肾小体和集合管 C:肾小球和肾小
酸中毒时远曲小管的( )。A.K+分泌增多,Na+重吸收增多 B.K+分泌减
下列关于非货币性资产投资企业所得税政策的表述中,错误的是( )。 A.居民企
关于民事诉讼中数个证据对同一事实的证明力的说法,正确的是()。A.书证的证明
最新回复
(
0
)