小學(xué)奧數(shù)思維訓(xùn)練100題及詳解

1、romoting the construction of rule of law, but also the most basic development environment. Despite my good social order in General, but there are law-abiding consciousness, social order is not standard, regardless of faith, Twining visit visit and other outstanding problems. We want to actively prom

2、ote the field of multi-level governance according to law, promote the continuous improvement of the social environment. To promote universal compliance. Actively foster the rule of law culture, carry out law publicity and education on honesty and trustworthiness, guide the masses and consciously abi

3、de by the law, failing to find method, problem-solving method, method of gradually changing the world, he is not looking for but someone unspoken rules, formed all law law, abide by the good atmosphere. To strengthen the comprehensive management of public security. Deepening peace xingan constructio

4、n, strongly against violence crime, mafia and serious criminal offences, to protect the legitimate rights and interests of citizens, legal persons, carry out criminal policy of temper justice with mercy, the maximum stimulating social vitality, and earnestly safeguard social harmony and stability. T

5、o resolve social conflicts by law. To further smooth channels of reporting social conditions and public opinion, improving regulation, arbitration, as wellrelationship between Government and business. The two sessions, General Secretary of Pro, clear the word succinctly summarized the new relationsh

6、ip between Government and business, as pure politics, reshaping the political relationship specified in the direction. District leaders in handling political and business relations, engage in trading power for money, and finally stumbled, we a lesson, always keep in mind that Pro, clean practicing P

7、ro, clear. Pro is to open a sincere engagement with private enterprise to help solve practical difficulties; Clear is to clarify the Division of power, exercised in accordance with, private entrepreneurs with innocent purity, not abusing power for personal gain, not to engage in trading power for mo

8、ney. Third, in order to maintain fairness and justice. Fairness and justice is the lifeline of the rule of law, is the best development environment. Currently, lax law enforcement and the judicial sector in our region also exist to varying degrees, law enforcement departments and individual window u

9、nits power for personal gains and bribes, thick friends, relations, human cases, money cases in which seriously infringe on the legitimate rights and interests of enterprises and people. Especially some law enforcement and inspection for profit purposes, deliberately looking for corporate loopholes,

10、 found directly under the ticket does not give business improvement opportunities. We recruit a company doesnt easily, cultivating a business more difficult, never for personal gain, systematic harassment, card, last checked to check to get the enterprise collapsed. To guarantee the legitimate right

11、s and interests. Always proceed from the overall situation of reform and development of services, fully consider the characteristics of production and management in non-public enterprises and social benefits, an accurate grasp of legal limits, protect the enthusiasm of entrepreneurs and practitioner

12、s in innovation and entrepreneurship, enhancing expectations and confidence. To promote strict enforcement. Strengthening law enforcement procedures, improve law enforcement performance evaluation, strengthening the supervision of law enforcement, exploration and practice of risk control mechanism o

13、f law enforcement to further standardize the social security, urban management, road traffic administrative law enforcement, effectively free, extensive law-enforcement and lax enforcement of law enforcement and other issues. To uphold justice. Justice is the last line of Defense to safeguard fairne

14、ss and justice, to unequivocally support the courts and procuratorates independently exercise level . Judicial activities were rampant, must not be allowed to run, favors, money, must not be allowed to knowingly violate the miscarriage, violations of the legitimate rights and interests of the masses

15、 must not be allowed to abuse of power, to make forest mass can be felt in every judicial cases in equity and justice. Four to deepen grass-roots governance according to lawchain do long, and put scale big. To serve the development of enterprises. Duocuo simultaneously improving service efficiency,

16、build better public services platform, enhance work efficiency, initiative to help businesses solve the project procedures, financing loans, issues such as land-use approval, reduce operating costs, business travel light and enhance the confidence to overcome all kinds of difficulties and the Founda

17、tion, real entrepreneurial passion play entrepreneurship, enhance the internal vitality and creativity. SI XING an construction, promoting the rule of law, tries to make the transformation of forest development XI General Secretary stressed, to reinvigorate Northeast China, optimized development env

18、ironment is very important. Environment of rule of law most gather Moss, the most conducive to development. Improving the leading cadres using the method of thought and the rule of law Administration work, problem-solving, the ability to promote the development, is the key to promoting the rule of l

19、aw. The law may affect the efficiency of out of the path of development will be more smooth, won development gains will be sustained, and end with greater efficiency. Leading cadres at all levels should take the lead in respect of law law, abide by, and actively foster Socialist culture, actively pr

20、omoting the field of multi-level governance according to law, guide the masses and consciously abide by the law, failing to find law, solve the problem by law, in accordance with the law prevail. XXX administration by law of leading cadres do not exist on the rule of law, law enforcement, casual, an

21、d vow not to investors, the new scores and other turmoil. These important expositions on my district create good development environment with highly targeted and guidance, especially the General Secretary pointed out that the chaos in my area also exists to varying degrees, some even quite serious.

22、Leading cadres at all levels must improve the development environment of rule of law as a fundamental task, adhere to the problem oriented, solid and solve the problems in the construction of rule of law, to rule the new effect for development environment improvements. To hold key minority. Leaders

23、of this group, although few in number, but the effect is critical. If a local leaders take the lead right according to law, in accordance with the law, the local CPPCC fresh, pragmatic and efficient development environment. Conversely, if a local leaders of ignoring the law, impunity, not only the p

24、olitical environment will be destroyed, will have serious implications for the development environment. Now, some leading cadres lack of awareness on the importance of learning, that learn or not does not matter. Think efficiency is too low too much, act according to the procedure, than an executive

25、 order getting along with. In dealing with complex issues, often speak of settling and done; on the issue of handling letters and visits, like to spend money and buy stop and stable, but disregard the law administration, in accordance with the law, the rulechain do long, and put scale big. To serve

26、the development of enterprises. Duocuo simultaneously improving service efficiency, build better public services platform, enhance work efficiency, initiative to help businesses solve the project procedures, financing loans, issues such as land-use approval, reduce operating costs, business travel l

27、ight and enhance the confidence to overcome all kinds of difficulties and the Foundation, real entrepreneurial passion play entrepreneurship, enhance the internal vitality and creativity. SI XING an construction, promoting the rule of law, tries to make the transformation of forest development XI Ge

28、neral Secretary stressed, to reinvigorate Northeast China, optimized development environment is very important. Environment of rule of law most gather Moss, the most conducive to development. Improving the leading cadres using the method of thought and the rule of law Administration work, problem-so

29、lving, the ability to promote the development, is the key to promoting the rule of law. The law may affect the efficiency of out of the path of development will be more smooth, won development gains will be sustained, and end with greater efficiency. Leading cadres at all levels should take the lead

30、 in respect of law law, abide by, and actively foster Socialist culture, actively promoting the field of multi-level governance according to law, guide the masses and consciously abide by the law, failing to find law, solve the problem by law, in accordance with the law prevail. XXX administration b

31、y law of leading cadres do not exist on the rule of law, law enforcement, casual, and vow not to investors, the new scores and other turmoil. These important expositions on my district create good development environment with highly targeted and guidance, especially the General Secretary pointed out

32、 that the chaos in my area also exists to varying degrees, some even quite serious. Leading cadres at all levels must improve the development environment of rule of law as a fundamental task, adhere to the problem oriented, solid and solve the problems in the construction of rule of law, to rule the

33、 new effect for development environment improvements. To hold key minority. Leaders of this group, although few in number, but the effect is critical. If a local leaders take the lead right according to law, in accordance with the law, the local CPPCC fresh, pragmatic and efficient development envir

34、onment. Conversely, if a local leaders of ignoring the law, impunity, not only the political environment will be destroyed, will have serious implications for the development environment. Now, some leading cadres lack of awareness on the importance of learning, that learn or not does not matter. Thi

35、nk efficiency is too low too much, act according to the procedure, than an executive order getting along with. In dealing with complex issues, often speak of settling and done; on the issue of handling letters and visits, like to spend money and buy stop and stable, but disregard the law administrat

36、ion, in accordance with the law, the rule找家教，到 陽光家教網(wǎng) 全國最大家教平臺(tái) 1. 7652132776532727解：原式=76527(213+327)= 76527540=76520=153002. (999999979001)-(13999)解：原式=（9999-999）+（9997-997）+（9995-995）+(9001-1) =9000+9000+.+9000 (500個(gè)9000) =3-解：（+1）- =-+ =- =100004(873477-198)(476874199)解：873477-198=476874199 因此原式=1

37、520001999-1999199819981997-1997199621解：原式1999（20001998）1997（19981996）3（42）21（1999199731）2。6297293289209解：（209+297）*23/2=58197計(jì)算：解：原式=（3/2）*（4/3）*（5/4）*(100/99)*(1/2)*(2/3)*(3/4)*(98/99) =50*(1/99)=50/998.解：原式=（1*2*3）/(2*3*4)=1/49. 有7個(gè)數(shù)，它們的平均數(shù)是18。去掉一個(gè)數(shù)后，剩下6個(gè)數(shù)的平均數(shù)是19；再去掉一個(gè)數(shù)后，剩下的5個(gè)數(shù)的平均數(shù)是20。求去掉的兩個(gè)數(shù)的乘積。解

38、： 7*18-6*19=126-114=12 6*19-5*20=114-100=14 去掉的兩個(gè)數(shù)是12和14它們的乘積是12*14=16810. 有七個(gè)排成一列的數(shù)，它們的平均數(shù)是 30，前三個(gè)數(shù)的平均數(shù)是28，后五個(gè)數(shù)的平均數(shù)是33。求第三個(gè)數(shù)。解：283335-307=39。11. 有兩組數(shù)，第一組9個(gè)數(shù)的和是63，第二組的平均數(shù)是11，兩個(gè)組中所有數(shù)的平均數(shù)是8。問：第二組有多少個(gè)數(shù)？解：設(shè)第二組有x個(gè)數(shù)，則6311x=8（9+x），解得x=3。12小明參加了六次測(cè)驗(yàn)，第三、第四次的平均分比前兩次的平均分多2分，比后兩次的平均分少2分。如果后三次平均分比前三次平均分多3分，那么第四次

39、比第三次多得幾分？解：第三、四次的成績(jī)和比前兩次的成績(jī)和多4分，比后兩次的成績(jī)和少4分，推知后兩次的成績(jī)和比前兩次的成績(jī)和多8分。因?yàn)楹笕蔚某煽?jī)和比前三次的成績(jī)和多9分，所以第四次比第三次多98=1（分）。13. 媽媽每4天要去一次副食商店，每 5天要去一次百貨商店。媽媽平均每星期去這兩個(gè)商店幾次？(用小數(shù)表示)解：每20天去9次，9207=3.15（次）。14. 乙、丙兩數(shù)的平均數(shù)與甲數(shù)之比是137，求甲、乙、丙三數(shù)的平均數(shù)與甲數(shù)之比。解：以甲數(shù)為7份，則乙、丙兩數(shù)共13226（份）所以甲乙丙的平均數(shù)是（26+7）/3=11（份）因此甲乙丙三數(shù)的平均數(shù)與甲數(shù)之比是11：7。15. 五年級(jí)同

40、學(xué)參加校辦工廠糊紙盒勞動(dòng)，平均每人糊了76個(gè)。已知每人至少糊了70個(gè)，并且其中有一個(gè)同學(xué)糊了88個(gè)，如果不把這個(gè)同學(xué)計(jì)算在內(nèi)，那么平均每人糊74個(gè)。糊得最快的同學(xué)最多糊了多少個(gè)？解：當(dāng)把糊了88個(gè)紙盒的同學(xué)計(jì)算在內(nèi)時(shí)，因?yàn)樗绕溆嗤瑢W(xué)的平均數(shù)多88-7414（個(gè)），而使大家的平均數(shù)增加了7674=2（個(gè)），說明總?cè)藬?shù)是1427（人）。因此糊得最快的同學(xué)最多糊了746-70594（個(gè)）。16. 甲、乙兩班進(jìn)行越野行軍比賽，甲班以4.5千米時(shí)的速度走了路程的一半，又以5.5千米時(shí)的速度走完了另一半；乙班在比賽過程中，一半時(shí)間以4.5千米時(shí)的速度行進(jìn)，另一半時(shí)間以5.5千米時(shí)的速度行進(jìn)。問：甲、乙兩

41、班誰將獲勝？解：快速行走的路程越長，所用時(shí)間越短。甲班快、慢速行走的路程相同，乙班快速行走的路程比慢速行走的路程長，所以乙班獲勝。17. 輪船從A城到B城需行3天，而從B城到A城需行4天。從A城放一個(gè)無動(dòng)力的木筏，它漂到B城需多少天？解：輪船順流用3天，逆流用4天，說明輪船在靜水中行431（天），等于水流347（天），即船速是流速的7倍。所以輪船順流行3天的路程等于水流33724（天）的路程，即木筏從A城漂到B城需24天。18. 小紅和小強(qiáng)同時(shí)從家里出發(fā)相向而行。小紅每分走52米，小強(qiáng)每分走70米，二人在途中的A處相遇。若小紅提前4分出發(fā)，且速度不變，小強(qiáng)每分走90米，則兩人仍在A處相遇。小紅

42、和小強(qiáng)兩人的家相距多少米？解：因?yàn)樾〖t的速度不變，相遇地點(diǎn)不變，所以小紅兩次從出發(fā)到相遇的時(shí)間相同。也就是說，小強(qiáng)第二次比第一次少走4分。由（704）（9070）14（分）可知，小強(qiáng)第二次走了14分，推知第一次走了18分，兩人的家相距（5270）182196（米）。 19. 小明和小軍分別從甲、乙兩地同時(shí)出發(fā)，相向而行。若兩人按原定速度前進(jìn)，則4時(shí)相遇；若兩人各自都比原定速度多1千米時(shí)，則3時(shí)相遇。甲、乙兩地相距多少千米？解：每時(shí)多走1千米，兩人3時(shí)共多走6千米，這6千米相當(dāng)于兩人按原定速度1時(shí)走的距離。所以甲、乙兩地相距6424（千米）20. 甲、乙兩人沿400米環(huán)形跑道練習(xí)跑步，兩人同時(shí)從

43、跑道的同一地點(diǎn)向相反方向跑去。相遇后甲比原來速度增加2米秒，乙比原來速度減少2米秒，結(jié)果都用24秒同時(shí)回到原地。求甲原來的速度。解：因?yàn)橄嘤銮昂蠹?、乙兩人的速度和不變，相遇后兩人合跑一圈?4秒，所以相遇前兩人合跑一圈也用24秒，即24秒時(shí)兩人相遇。設(shè)甲原來每秒跑x米，則相遇后每秒跑（x2）米。因?yàn)榧自谙嘤銮昂蟾髋芰?4秒，共跑400米，所以有24x24（x2）400，解得x=7又1/3米。21. 甲、乙兩車分別沿公路從A，B兩站同時(shí)相向而行，已知甲車的速度是乙車的1.5倍，甲、乙兩車到達(dá)途中C站的時(shí)刻分別為5：00和16：00，兩車相遇是什么時(shí)刻？解：924。解：甲車到達(dá)C站時(shí)，乙車還需16

44、-511（時(shí)）才能到達(dá)C站。乙車行11時(shí)的路程，兩車相遇需11（11.5）4.4（時(shí)）4時(shí)24分，所以相遇時(shí)刻是924。22. 一列快車和一列慢車相向而行，快車的車長是280米，慢車的車長是385米。坐在快車上的人看見慢車駛過的時(shí)間是11秒，那么坐在慢車上的人看見快車駛過的時(shí)間是多少秒？解：快車上的人看見慢車的速度與慢車上的人看見快車的速度相同，所以兩車的車長比等于兩車經(jīng)過對(duì)方的時(shí)間比，故所求時(shí)間為1123. 甲、乙二人練習(xí)跑步，若甲讓乙先跑10米，則甲跑5秒可追上乙；若乙比甲先跑2秒，則甲跑4秒能追上乙。問：兩人每秒各跑多少米？解：甲乙速度差為10/5=2速度比為（4+2）：4=6：4所以甲

45、每秒跑6米，乙每秒跑4米。24甲、乙、丙三人同時(shí)從A向B跑，當(dāng)甲跑到B時(shí)，乙離B還有20米，丙離B還有40米；當(dāng)乙跑到B時(shí)，丙離B還有24米。問：（1） A， B相距多少米？（2）如果丙從A跑到B用24秒，那么甲的速度是多少？解：解：（1）乙跑最后20米時(shí)，丙跑了40-2416（米），丙的速度25. 在一條馬路上，小明騎車與小光同向而行，小明騎車速度是小光速度的3倍，每隔10分有一輛公共汽車超過小光，每隔20分有一輛公共汽車超過小明。已知公共汽車從始發(fā)站每次間隔同樣的時(shí)間發(fā)一輛車，問：相鄰兩車間隔幾分？解：設(shè)車速為a，小光的速度為b，則小明騎車的速度為3b。根據(jù)追及問題“追及時(shí)間速度差追及距離

46、”，可列方程10（ab）20（a3b），解得a5b，即車速是小光速度的5倍。小光走10分相當(dāng)于車行2分，由每隔10分有一輛車超過小光知，每隔8分發(fā)一輛車。26. 一只野兔逃出80步后獵狗才追它，野兔跑 8步的路程獵狗只需跑3步，獵狗跑4步的時(shí)間兔子能跑9步。獵狗至少要跑多少步才能追上野兔？解：狗跑12步的路程等于兔跑32步的路程，狗跑12步的時(shí)間等于兔跑27步的時(shí)間。所以兔每跑27步，狗追上5步（兔步），狗要追上80步（兔步）需跑27（805）8083192（步）。27. 甲、乙兩人在鐵路旁邊以同樣的速度沿鐵路方向相向而行，恰好有一列火車開來，整個(gè)火車經(jīng)過甲身邊用了18秒，2分后又用15秒從乙

47、身邊開過。問：（1）火車速度是甲的速度的幾倍？（2）火車經(jīng)過乙身邊后，甲、乙二人還需要多少時(shí)間才能相遇？ 解：（1）設(shè)火車速度為a米秒，行人速度為b米秒，則由火車的是行人速度的11倍；（2）從車尾經(jīng)過甲到車尾經(jīng)過乙，火車走了135秒，此段路程一人走需135011=1485（秒），因?yàn)榧滓呀?jīng)走了135秒，所以剩下的路程兩人走還需（1485135）2675（秒）。 28. 輛車從甲地開往乙地，如果把車速提高20，那么可以比原定時(shí)間提前1時(shí)到達(dá)；如果以原速行駛100千米后再將車速提高30，那么也比原定時(shí)間提前1時(shí)到達(dá)。求甲、乙兩地的距離。 29. 完成一件工作，需要甲干5天、乙干 6天，或者甲干 7

48、天、乙干2天。問：甲、乙單獨(dú)干這件工作各需多少天？解：甲需要(7*3-5)/2=8(天)乙需要(6*7-2*5)/2=16（天）30一水池裝有一個(gè)放水管和一個(gè)排水管，單開放水管5時(shí)可將空池灌滿，單開排水管7時(shí)可將滿池水排完。如果放水管開了2時(shí)后再打開排水管，那么再過多長時(shí)間池內(nèi)將積有半池水？31小松讀一本書，已讀與未讀的頁數(shù)之比是34，后來又讀了33頁，已讀與未讀的頁數(shù)之比變?yōu)?3。這本書共有多少頁？解：開始讀了3/7 后來總共讀了5/833/(5/8-3/7)=33/(11/56)=56*3=168頁32一件工作甲做6時(shí)、乙做12時(shí)可完成，甲做8時(shí)、乙做6時(shí)也可以完成。如果甲做3時(shí)后由乙接著

49、做，那么還需多少時(shí)間才能完成？解：甲做2小時(shí)的等于乙做6小時(shí)的，所以乙單獨(dú)做需要6*3+12=30（小時(shí)） 甲單獨(dú)做需要10小時(shí)因此乙還需要(1-3/10)/(1/30)=21天才可以完成。33. 有一批待加工的零件，甲單獨(dú)做需4天，乙單獨(dú)做需5天，如果兩人合作，那么完成任務(wù)時(shí)甲比乙多做了20個(gè)零件。這批零件共有多少個(gè)？解：甲和乙的工作時(shí)間比為4：5，所以工作效率比是5：4工作量的比也5：4，把甲做的看作5份，乙做的看作4份那么甲比乙多1份，就是20個(gè)。因此9份就是180個(gè)所以這批零件共180個(gè)34.挖一條水渠，甲、乙兩隊(duì)合挖要6天完成。甲隊(duì)先挖3天，乙隊(duì)接著解：根據(jù)條件，甲挖6天乙挖2天可挖

50、這條水渠的3/5所以乙挖4天能挖2/5因此乙1天能挖1/10，即乙單獨(dú)挖需要10天。甲單獨(dú)挖需要1/（1/6-1/10）=15天。35. 修一段公路，甲隊(duì)獨(dú)做要用40天，乙隊(duì)獨(dú)做要用24天。現(xiàn)在兩隊(duì)同時(shí)從兩端開工，結(jié)果在距中點(diǎn)750米處相遇。這段公路長多少米？36. 有一批工人完成某項(xiàng)工程，如果能增加 8個(gè)人，則 10天就能完成；如果能增加3個(gè)人，就要20天才能完成。現(xiàn)在只能增加2個(gè)人，那么完成這項(xiàng)工程需要多少天？解：將1人1天完成的工作量稱為1份。調(diào)來3人與調(diào)來8人相比，10天少完成（8-3）10=50（份）。這50份還需調(diào)來3人干10天，所以原來有工人501032（人），全部工程有（2+8

51、）10=100（份）。調(diào)來2人需100（2+2）=25（天）。37. 解：三角形AOB和三角形DOC的面積和為長方形的50%所以三角形AOB占32%1632%=5038. 解：1/2*1/3=1/6 所以三角形ABC的面積是三角形AED面積的6倍。 39.下面9個(gè)圖中，大正方形的面積分別相等，小正方形的面積分別相等。問：哪幾個(gè)圖中的陰影部分與圖（1）陰影部分面積相等？ 解：（2） （4） （7） （8） （9） 40. 觀察下列各串?dāng)?shù)的規(guī)律，在括號(hào)中填入適當(dāng)?shù)臄?shù)2，5，11，23，47，（ ），解：括號(hào)內(nèi)填95規(guī)律：數(shù)列里地每一項(xiàng)都等于它前面一項(xiàng)的2倍減141. 在下面的數(shù)表中，上、下兩行都是

52、等差數(shù)列。上、下對(duì)應(yīng)的兩個(gè)數(shù)字中，大數(shù)減小數(shù)的差最小是幾？解：1000-1=999997-995=992每次減少7，999/7=1425所以下面減上面最小是51333-1=1332 1332/7=1902所以上面減下面最小是2因此這個(gè)差最小是2。42. 如果四位數(shù)68能被73整除，那么商是多少？解：估計(jì)這個(gè)商的十位應(yīng)該是8，看個(gè)位可以知道是6因此這個(gè)商是86。43. 求各位數(shù)字都是 7，并能被63整除的最小自然數(shù)。解：63=7*9所以至少要9個(gè)7才行（因?yàn)楦魑粩?shù)字之和必須是9的倍數(shù)）44. 12315能否被 9009整除？解：能。將9009分解質(zhì)因數(shù)9009=3*3*7*11*1345. 能否

53、用1， 2， 3， 4， 5， 6六個(gè)數(shù)碼組成一個(gè)沒有重復(fù)數(shù)字，且能被11整除的六位數(shù)？為什么？解：不能。因?yàn)?2345621，如果能組成被11整除的六位數(shù)，那么奇數(shù)位的數(shù)字和與偶數(shù)位的數(shù)字和一個(gè)為16，一個(gè)為5，而最小的三個(gè)數(shù)字之和12365，所以不可能組成。46. 有一個(gè)自然數(shù)，它的最小的兩個(gè)約數(shù)之和是4，最大的兩個(gè)約數(shù)之和是100，求這個(gè)自然數(shù)。解：最小的兩個(gè)約數(shù)是1和3，最大的兩個(gè)約數(shù)一個(gè)是這個(gè)自然數(shù)本身，另一個(gè)是這個(gè)自然數(shù)除以3的商。最大的約數(shù)與第二大47.100以內(nèi)約數(shù)個(gè)數(shù)最多的自然數(shù)有五個(gè)，它們分別是幾？解：如果恰有一個(gè)質(zhì)因數(shù)，那么約數(shù)最多的是26=64，有7個(gè)約數(shù)；如果恰有兩個(gè)

54、不同質(zhì)因數(shù)，那么約數(shù)最多的是233272和25396，各有12個(gè)約數(shù)；如果恰有三個(gè)不同質(zhì)因數(shù)，那么約數(shù)最多的是223560，223784和2325=90，各有12個(gè)約數(shù)。所以100以內(nèi)約數(shù)最多的自然數(shù)是60，72，84，90和96。48. 寫出三個(gè)小于20的自然數(shù)，使它們的最大公約數(shù)是1，但兩兩均不互質(zhì)。解：6，10，1549. 有336個(gè)蘋果、 252個(gè)桔子、 210個(gè)梨，用這些果品最多可分成多少份同樣的禮物？在每份禮物中，三樣水果各多少？解：42份；每份有蘋果8個(gè)，桔子6個(gè)，梨5個(gè)。50. 三個(gè)連續(xù)自然數(shù)的最小公倍數(shù)是168，求這三個(gè)數(shù)。解：6，7，8。 提示：相鄰兩個(gè)自然數(shù)必互質(zhì)，其最小

55、公倍數(shù)就等于這兩個(gè)數(shù)的乘積。而相鄰三個(gè)自然數(shù)，若其中只有一個(gè)偶數(shù)，則其最小公倍數(shù)等于這三個(gè)數(shù)的乘積；若其中有兩個(gè)偶數(shù)，則其最小公倍數(shù)等于這三個(gè)數(shù)乘積的一半。51. 一副撲克牌共54張，最上面的一張是紅桃K。如果每次把最上面的12張牌移到最下面而不改變它們的順序及朝向，那么，至少經(jīng)過多少次移動(dòng)，紅桃K才會(huì)又出現(xiàn)在最上面？解：因?yàn)?4，12=108，所以每移動(dòng)108張牌，又回到原來的狀況。又因?yàn)槊看我苿?dòng)12張牌，所以至少移動(dòng)10812=9（次）。52. 爺爺對(duì)小明說：“我現(xiàn)在的年齡是你的7倍，過幾年是你的6倍，再過若干年就分別是你的5倍、4倍、3倍、2倍。”你知道爺爺和小明現(xiàn)在的年齡嗎？解：爺爺7

56、0歲，小明10歲。提示：爺爺和小明的年齡差是6，5，4，3，2的公倍數(shù)，又考慮到年齡的實(shí)際情況，取公倍數(shù)中最小的。（60歲）53. 某質(zhì)數(shù)加6或減6得到的數(shù)仍是質(zhì)數(shù)，在50以內(nèi)你能找出幾個(gè)這樣的質(zhì)數(shù)？并將它們寫出來。解：11，13，17，23，37，47。54. 在放暑假的8月份，小明有五天是在姥姥家過的。這五天的日期除一天是合數(shù)外，其它四天的日期都是質(zhì)數(shù)。這四個(gè)質(zhì)數(shù)分別是這個(gè)合數(shù)減去1，這個(gè)合數(shù)加上1，這個(gè)合數(shù)乘上2減去1，這個(gè)合數(shù)乘上2加上1。問：小明是哪幾天在姥姥家住的？解：設(shè)這個(gè)合數(shù)為a，則四個(gè)質(zhì)數(shù)分別為（a1），（a1），（2a1），（2a1）。因?yàn)椋╝1）與（a1）是相差2的質(zhì)數(shù)，

57、在131中有五組：3，5；5，7；11，13；17，19；21，31。經(jīng)試算，只有當(dāng)a6時(shí)，滿足題意，所以這五天是8月5，6，7，11，13日。55. 有兩個(gè)整數(shù)，它們的和恰好是兩個(gè)數(shù)字相同的兩位數(shù)，它們的乘積恰好是三個(gè)數(shù)字相同的三位數(shù)。求這兩個(gè)整數(shù)。解：3，74；18，37。提示：三個(gè)數(shù)字相同的三位數(shù)必有因數(shù)111。因?yàn)?11337，所以這兩個(gè)整數(shù)中有一個(gè)是37的倍數(shù)（只能是37或74），另一個(gè)是3的倍數(shù)。56. 在一根100厘米長的木棍上，從左至右每隔6厘米染一個(gè)紅點(diǎn)，同時(shí)從右至左每隔5厘米也染一個(gè)紅點(diǎn)，然后沿紅點(diǎn)處將木棍逐段鋸開。問：長度是1厘米的短木棍有多少根？解：因?yàn)?00能被5整除，所以可以看做都是自左向右染色。因?yàn)?與5的最小公倍數(shù)是30，即在30厘米處同時(shí)染上紅點(diǎn)，