STT

1400 BI TON TIU HCSTTCu hiLi gii, p n

1Cho mi ngi 21 qu bng trong c 20 qu nng bng nhau 1 qu th nh hn,ch bng cch cn hi s ln cn t nht c th tm ra c qu bng nh

2Mt nhm c 10 ngi.Trong 1 thng c 10 ci qun v 10 ci o :1 ci qun mang s 12 ci qun mang s 2....4 ci qun mang s 4v4 ci o mang s 13 ci o mang s 2....1 ci o mang s 4Mi ngi c chn cho mnh 1 b qun o.Hi c th tt c mi ngi mc khc nhau ko.Nu khng th ti a c ? ngi c th mc khc nhau

3Cho dy s 0,2,4,6,8,10... Hi s hng th 2012 l s no?

4Mt ngi mang cam i i ly to v l. C 9 qu cam th i c 2 qu to v 1 qu l, 5 qu to th i c 2 qu l. Nu ngi i ht s cam mang i th c 17 qu to v 13 qu l. Hi ngi mang i bao nhiu qu cam ?

5Cho 3 thnh ph A,B,C l 3 nh ca 1 tam gic u.2 xe X v Y xut pht t A->B->C->A (around)Bit xe X i trc xe Y 40 pht.xe X i t thnh ph ny n thnh ph kia mt 20 phtxe y i t thnh ph ny n thnh ph kia mt 30 phtHi 2 xe gp nhau ln th 2 sau khong thi gian bao lu?

6Trn mt con knh c 2 on thuyn chy ngc chiu, mi on gm 10 chic thuyn. Chiu rng ca con knh ch va cho 1 chic chy. Trn con knh ch c mt v tr A duy nht m va cho 2 chic thuyn trnh nhau ( chiu rng v chiu di ch cho 2 thuyn trnh nhau). Hi phi lm sao 2 on thuyn trnh c nhau?

7Mt on gm 46 hc sinh Gii ca trng tiu hc A i du lch cha Hng u nm. Khi xung thuyn qua bn c, th c hai loi thuyn, mt loi ch c 6 hc sinh/ chuyn, mt loi ch c 4 hc sinh/ chuyn. Khi cc em xung thuyn th xp va va 10 thuyn hai loi. Hi c my chic thuyn mi loi?

8Hy chia 10 nghn ng thnh 10 t, trong khng c dng t mnh gi 1 nghn ng.

9Mt m rung hnh ch nht c chiu di gp 3 ln chiu rng . Tnh chiu di v chiu rng m rung bit rng chu vi m rung l 48m3

10Nm nay cha 41 tui , con 9 tui :a - My nm na cha gp 5 ln tui con ?b - My nm na cha gp 3 ln tui con ?c - C khi no tui cha gp 4 ln tui con khng ?

11Cho phn s a/b . C a + b = 7525 v b - a = 903 .a) Tm a/ b rt gnb) Nu thm 42 vo MS ca phn s ti gin trn th phi thm t s ca phn s bao nhiu gi tr phn s khng i .4

121 thng cha y sa nng 50kg. Nu ly ra 1/4 s sa v thay bng nc lc th thy thng ch cn nng 49,7kg. Bit 1l sa nng 1,03kg ; 1l nc nng 1kg. Hi thng cha bao nhiu lt sa ?

13C 4 qu trng vt v 2 qu trng g. C 1 ci xoong mi ln ch un c ti a 4 qu trng. Bit rng thi gian luc chn trng vt l 6 pht v trng g l 2 pht. Trnh by cch luc chn 6 qu trng trn trong thi gian t nht c th. (gi s s gin on trong khi luc khng nh hng n qu trnh chn ca trng, ch cn thi gian luc l trng chn)

14Hnh thoi ABCD c di 2 ng cho AC = 30 cm v BD = 12 cm,c cnh AD = 10 cm.tnh chiu cao BH ?

151/a+1/b+1/c+1/d=1Hi c th tm c cc s a, b, c, d l l tho mn iu kin trn ko?Ta c 1/a+1/b+1/c+1/d = 1,Tng ng bcd+acd+abd+abc = abcd.Trong tp hp s t nhin N c 1 s tnh cht sau y: Tng ca 2 s l l 1 s chn; tng ca 1 s l v 1 s chn l s l; tch ca 2 s l l 1 s l; tch ca 2 s chn l 1 s chn; tch ca 1 s chn v 1 s l l 1 s chn.T cc tnh cht trn ta thy: Gi s a, b, c, d u l th lc ta c: abcd l, bcd l, acd l, abd l, abc l, bcd+acd+abd+abc chn. Vy suy ra a, b, c, d khng th cng l

16Mt ngi em ban da hu ,ln th nht ban c 1/2 s da va cng thm na qua ,ln th 2 ban 1/2 s da con lai cung cng thm na qua ,ln th 3 th 4 va th 5 cung nh vy va ban n ln th 6 thi ht s da. Hoi ngi o a ban tt ca bao nhiu qua da ?Nu nh ln th 6 bn ht th r rng sau ln th 5 s da cn li l 1 qu. Do ln th 6 bn ht qu da cng na qu na tc l bn ht 1 qu( ht lun)T suy ngc li sau ln 4 cn 3 qu, sau ln 3 cn 7 qu, sau ln 2 cn 15 qu, sau ln 1 cn 31 qu.Vy s da lc u ( bn) l 63 qu

17Cho tam gic ABC.Bit AM=1/2MB, BN=1/2NC, CP=1/2 PA.MC ct AN ti im E, AN ct BP ti im F,MC ct BP ti im R, din tch hnh MAE=PRC=BNF=2cm vung.Tnh din tch hnh ERF6 cm2

18Hai cy nn c cng chiu di v lm bng hai cht liu khc nhau, mt cy chy ht vi tc u trong 3 gi, trong khi cy kia chy ht trong 4 gi. Hi phi bt u t nn lc my gi n 4 gi chiu, cy nn ny c di gp i cy nn kia?1 gi 36 pht

19Mt t chy t A n B vi vn tc 40 km/h v chy t B v A vi vn tc 20 km/h. Hi vn tc trung bnh ca t trn on ng AB?vn tc trung bnh=1: ( 1/40+1/20):2=80/3 ( km/h)

20Nu chiu di v chiu rng ca hnh ch nht c tng 10% th din tch ca n tng bao nhiu %?" khi chiu rng tng ln bao nhiu n v th s s tng tng ng mt s bng tch ca s n v tng ca chiu rng x chiu di. Khi tng chiu di cng tng t. C th:Tng chiu rng 10% th s tng: 0.1x a x bTng chiu di 10% th s tng 0.1x b x 1.1aTng tng l 0.21 x a x b= 21 % din tch c.Chiu rng tng 10%, chiu di tng 10%, din tch tng 21%.

21bi ton lp 4: t s ca 2 s l 3:7.Tm 2 s bit nu s b tng 76 n v th c s ln (v s ) ?S ln l 7 phn th s b l 3 phn; hiu ca chng l 4 phn; gi tr 1 phn nh l:76: 4 = 19S b l: 19 x 3 = 57S ln l 19 x7 = 133 (hoc ly 57 +76 = 133 )

22Mt bc nng dn nui 3 con h v 3 con b. Mt hm bc nng dn phi chuyn c 6 con vy qua 1 b sng. Trn sng ch c 1 ci thuyn, v mi ln ch cho c ti a l bc nng dn cng vi 2 con vt. Bit rng mi b sng nu s con h nhiu hn s con b th h s n tht b. Hi bc nng dn phi chuyn 6 con vt trn qua sng nh th no b khng b h n tht?

23Rt gn phn s:122436123636/31623931939312/31

24 o su ca mt ci hang ngi ta gp si dy lm 3 v th mt u xung hang, khi u dy di chm y hang th u dy trn cch ming hang ng 1m. Ngi ta gp si dy lm i v cng th mt u dy xung hang khi u dy di chm y hang th u trn tha mt on di 5m. Hi hang su bao nhiu?Khi gp si dy lm 3 th di si dy ch cn bng 1/3 si dy ban u.Khi gp si dy lm 2 th di si dy ch cn bng 1/2 si dy ban u.1/2 si dy di hn 1/3 si dy l: 1 + 5 = 6 (m)Phn s ch 6 mt l: 1/2 - 1/3 = 1/6 (si dy)Si dy di l: 6: 1/6 = 36 (m) su ca hang l: 36 : 3 + 1 = 13 (m)

25C 2 si dy, si di bng 2 ln si ngn. Ct i mi si 1 on bng 6cm. Th si di c di bng 3 ln si ngn. Hi di mi si ban u?Khi ct mi on i 6cm th on di bng 3 ln on ngn. nh vy on ngn 1 phn, on di 3 phn. thm vo mi on 1 phn ta c on ngn = 2 phn. on di 4 phn. M theo bi th on di = 2 ln on ngn. nn on thm vo l 6cm => on thm vo = 6cm = on ngn => on di

26Hai s thp phn c tng l 15,83. Nu di du phy cu s b sang bn phi mt ch s ri tr i s ln th c 0,12. Tm 2 s .Khi s b c i du phy sang mt ch s th tc l n c gp ln 10 ln. Ta v s gm 10 ln s b v s ln.Lc ny thy rng nu s ln thm vo 0,12 n v th s c 10 ln s b.Vy ta s c o th hai gm s b v s ln mi (bao gm s ln thm 0,12 hoc 10 ln s b).Tng mi lc ny l 15,83 + 0,12 = 15,95.S b l: 15,95 : (10+1) + 1,45S ln l: 15,83 -1,45 = 14,38

27Vi 4 ch s a, b, 1,2 bn Thy vit c 18 s c 3 ch s. Khi tnh tng ca cc s vit th c 6440. Tm ch s a, b.V vi 4 ch s m ch c th vit nhiu nht 18 s c 3 ch s khc nhau th 1 trong 4 ch s cho l ch s 0.Nu a = o th ta c th lp c 18 s c 3 ch s khc nhauTa nhn thy cc ch s 1,2,b xut hin hng trm mi ch s 6 ln cn cc ch s 1,2,b xut hin hng chc, hng n v mi ch s 4 ln.Ta c: (1+2+b) x 644 = 64401+2+b = 6440: 6441+2+b = 10b = 10-1-2b = 7Ngc li nu b = 0 th tng t nh trn a = 7Vy: nu a= 0 th b = 7 hoc nu a= 7 th b = 0.

28S= 1/(1x2) + 1/(2x3) +........+ 1/(99x100)= 1/1 - 1/ 2+ 1/2 - 1/3+ 1/ 3- .............+ 1/99- 1/100= 1-1/100=99/100

29Nm nay tui con t hn tui cha 35 tui v bng 2/9 tui cha. Hi nm nay con bao nhiu tui?Tui con l X,cha l X+35 : X/X+35 = 2/9p s : Con 10 tui,cha 45 tuiC2:Theo bai ra ta co s :con 2 phnb 9 phnhiu s phn bng nhau la 9-2= 7 phn cua 35 tui. Vy 1 phn bng 35 : 7 = 5Tui con l 5 2 = 10

30Hy in cc s thch hp vo ch trng di y , sao cho tng ca 3 s 3 ch trng lin nhau u bng 638... /...../...../ 122/...../....../....../ 193 /..../..../Ta k hiu dy s : A+B+C+122+D++E+193+F+GB+C=526 nn A = 122B+C+122=638,C+D+122=638 nn B=DC+122+D=638,122+D+=638 nn C=Phi tho mn : A+B+C=D++E suy ra A=E=122Thay vo ta dc kt qu : 122,193,323,122,193,323,122,193,323,122.

31Tm n : (n+7) chia ht cho (n-2)n +7 = ( n-2) +9.Mun n+7 chia ht n-2 th 9 phi chia ht cho n-2. V nu 1 s hng v tng chia ht cho 1 s th s hng cn li cng phi chia ht cho s . D dng tm c n= 3, 5, 11.

32Mt cun sch c trung bnh mi trang l 2 ch s. hi cun sch c bao nhiu trang?C 9 trang c 1 ch s( t trang 1 n trang 9). C 90 trang c 2 ch s ( t trang 10 n trang 99) . V vy trung bnh mi trang c 2 ch s th cn c 9 trang c 3 ch s ( t trang 100 n trang 108). Vy quyn sch c 108 trang.

33Tm gi tr ca cc ch s trong php tnh: a,b x c,d = y,yya,b x c,d =y,yy -> ab x cd = yyy = y x111 = y x 3 x 37. Vy yyy l s c 3 ch s chia ht cho 37 v 3. Nu ab = 37 th cd l s c 2 ch s chia ht cho 3. Tuy nhin s ln nht c 3 ch s l 999, chia cho 37 = 27 nn cd < hoc = 27 nn cd = 12,15,18,21,24,27. Nu ab= 74 th cd= y/2 x 3. M 999 chia cho 74 c 13 d 37 nn cd l s c 2 ch s, chia ht cho 3 v c gi tr < hoc bng 13 v y l s chn; ch c cd = 12, y=8 l tha mn. Ngc li, cd cng nhn gi tr = 37 hoc 74, lc ab tnh tng t. Lp bng tnh gi tr ca cc ch s a,b,c,d,y.

34Tm s c 3 ch s,bit rng nu xa i ch s hng n v ca s ta c 1 s mi nh hn s ban u l 252.S v 10 phn, khi xo i ch s hng n v th s ny cn 1 phn, hiu s phn bng nhau l 9. ta ly 252 : 9 = 28 (trng hp chia ht cho 9, cn nu k chia ht ta phi bt s i)vy s l 280 v 279C2: S cho ABC > 252.Nn A phi >=2S cho : 100A+10B+C = 252 + 10A+B90A + 9B + C = 252 -> A phi < 3.T suy ra A phi l 2Thay vo : 9B + C = 72 M C l s c 1 ch s C = 41/2 = 20,5S th 2 => 37.75-20,5 = 17.25

53Xe th nht ch c 25 tn hng. Xe th hai ch c 35 tn hng. Xe th ba ch hn trung bnh cng ca 3 xe l 10 tn. Hi xe th ba ch bao nhiu tn hng?"Xe 3 hn trung binh cng cua 3 xe la 10 tn c hiu la : Ly 10 tn cua xe 3 chia u cho 2 xe con lai thi khi o ca 3 xe ch c s hang bng nhau.+) Trung binh 3 xe ch c s tn hang la :(25 + 35 + 10) : 2 = 35 (tn)+) Xe 3 ch c s hang :35 + 10 = 45 (tn)

54Tnh : S = (1-1/28) x (1-1/36) x (1-1/45) x ..... x (1-1/4950)27/28 = 3x9 / (4x7) = 3/4 x 9/727/28 x 35/36 = (3x9) / (4x7) x (5x7) / (4x9) = 3/4 x 5/427/28 x 35/36 x 44/45 = 3x5/(4x4) x 4x11/5x9 = 3/4 x 11/9......xxxxxx .... x (49x101)/(50x99) = 3/4 x 101/99

551 . Phi nhn 6 vi s no c s lin trc c 2 ch s ging nhau v c hng chc bng 5 ?2. Tm vi xanh di gp 3 ln tm vi . Ca hng bn c 7m vi v 37 m vi xanh , nh vy s m vi cn li 2 tm cng bng nhau . ? Lc cha bn mi tm di bao nhiu m ?1. S lin trc s c 2 ch s ging nhau v hng chc l 5 l 54, vy phi nhn 6 vi 9.

2. Bn mnh 7m, mnh xanh 37 m, tc l bn mnh xanh nhiu hn mnh 30m.Khi , s m vi ca 2 loi bng nhau, vy s m vi xanh hn s m vi l 30m. Bi ton tr v dng hiu t. S m vi l 15m, vi xanh l 45m.

563 bn Bc, Trung, Nam cng chi 1 tr chi. Bc m cc s tng dn cch u 10 bt u t 7. Trung m cc s gim dn cch u 5 bt u t 3007. Nam m cc s tng dn cch u 9 bt u t 207. 3 bn cng m mt lc cho n khi c 3 ni ra 1 s th dng li. Bit rng s cc bn ni ra u bng nhau, tm s C th nhn thy 3 bn cng m cho n khi dng li cng lc, nh vy s ln m ca 3 bn l nh nhau. Khi dng li 3 bn cng dng 1 s. Nh vy nu gi s ln m l x th ta c: 7+ 10x = 207+9x . Gii php ton ny ta tm c s ln m ca 3 bn l 200. Vy s cn tm l: 7+10200=2007.

57C 720 quyn v chia cho 3 lp. Bit 3 ln s v lp 4A bng 2ln s v lp 4B, 5 ln s v 4B bng 3 ln s v 4C.Tm s v 3 lp.Cch 1: dng s on thngV s minh ha bi ton:Ln v 1, lp 4a c 3 phn ng bng lp 4b c 2 phn.Ln v 2, lp 4b c 5 phn ng bng lp 4c(Ch phn on thng minh ha cho lp 4b phi bng nhau c hai ln v nh)Theo nh bi, ba ln s v ca ba lp bng 10 ln s v ca lp 4b.Vy lp 4b c:720 x3:10 = 216 quynTng t, bn tnh tip s v ca hai lp cn li.Cch 2: dng t s:Gi Gi s v lp ln lt l a, b, c. Ta c:3a = 2b nn: a : 2 = b: 35b = 3c nn b : 3 = c : 5Tng t, ta tnh c s v mi lp.

58Php chia c s b chia l 89,thng l 9 v c s d ln nht.hi s chia l bao nhiu?89:9=9 d 8. S chia l 9, s d ln nht l 8

59Tm s thp phn b nht khc nhau c tch bng 20.1,45

60Tm hai s t nhin, bit s ln chia cho s b c thng l 4 d 19 v hiu hai s bng 133S chia 1 phn, cn s b chia sau khi bt i 19 s gm 4 phn nh vy.Hiu s phn bng 3 v 3 phn bng:133-19= 114Mi phn bng 114 : 3= 38Tc l s chia l 38Tnh s b chia bng cch ly: 38+133=171

61Tui con trai bng tui m, tui con gi bng 1/5 tui m.Bit rng tui con trai hn tui con gi 2 tui.Hi tui m l bao nhiu ?Phn s tng ng vi 2 tui l : - 1/5 = 1/20 (tui m)S tui m l :2 : 1/20 = 40 ( tui)p s : 40 tui.

62Trong vn co g va th. Tng cng 15 u va 38 chn. Hi mi loi bao nhiu con?Tng cng c 15 u => c 15 con c g v th. Cc ch th ng thng bng hai chn sau, hai chn trc co ln trc ngc. Nh vy lc ny m 15 con vt ng bng 2x15 = 30 (chn). S chn th co ln l 38 - 30 = 8 (chn). Vy s th l 8 : 2 = 4 (con). S g l 15 - 4 = 11 (con).

63tm s thp phn a,b bit ab=(a+b) . 1,5ta co: ab - 1,5a -1,5b =0 => ( a-1,5)(b-1,5)=2,25 => (2a - 3/2) (2b- 3/2)=2,25 => (2a-3)(2b-3)=9. Vy c cc cp s c th: (-1)x(-9), (-9)x(-1) ; 1x9; 9x1 ; 3x3 ; (-3)x(-3) ==> Cc cp nghin c th: ( 1; -3) ; (-3, 1) ; ( 2, 6) ; (6; 2 ) ; (3,3) v (0,0). Cc s thp phn c th cu thnh: I. -3,1 va 0,0 ( c m n xi) va II. 2,6 ; 6,2 ; 3,3 .

64Trm b c, trm con tru.Tru ng n nm, tru nm n ba.Ba con tru gi chung nhau mt b.Tm s tru ng, nm, gi v s c tng ng?Gi D l tru ng, N l tru nm, G l tru gi. Ta c: 5D + 3N + G/3 = 100Gi s sc n ca mi loi tru tng ln gp 3 ln: ng 15, nm 9, gi 1, s c 100x3=30015D + 9N + 1G = 300Gi s mi con n t i 1 b c. Lc ny tru gi khng n, s c cn li: 300 -100=20014D + 8N = 200 (1)Chia (1) cho 2: 7D + 4N = 100 (4N lun chn nn D phi chn; D v N u>=1 nn D 100)Nu:D=12 th 84 + 4N = 100 => N=4 (12x15 + 4x9 + G = 300) => G = 84D=10 th 70 + 4N = 100 => N=7,5 (loi)D=8 th 56 + 4N = 100 => N=11 (8x15 + 11x9 + G =300) => G = 81D=6 th 42 + 4N = 100 => N=14,5 (loi)D=4 th 28 + 4N = 100 => N=18 (4x15 + 18x9 + G = 300) => G = 78D=2 th 14 + 4N = 100 => N=21,6 (loi)p s: 1). D=12 ; N=4 ; G=842). D=8 ; N=11 ; G=813). D=4 ; N=18 ; G=78

Th li: 12+4+84=100 v 12.5+4.3+84/3=1008+11+81=100 v 8.5+11.3+81/3=1004+18+78=100 v 4.5+18.3+78/3=100

65Nam v Ha c cng s nhn v.Sau khi Nam cho Ha 1/5 s nhn v ca mnh th khi s nhn v ca Nam t hn ca Ha 12 chic. Hi ban u mi bn c bao nhiu nhn v?Hiu s phn bng nhau l:6 - 4 = 2 (phn)Gi tr mt phn l:12 : 2 = 6 (nhn v)S nhn v ca mi bn lc u l:6 x 5 = 30 (nhn v)p s : 30 nhn v.

66Tinh 1x2+2x3+3x4+...+99x100A = 1x2 + 2x3 + 3x4 + 4x5 + ...+ 99x100A x 3 = 1x2x3 + 2x3x3 + 3x4x3 + 4x5x3 + ... + 99x100x3A x 3 = 1x2x3 + 2x3x(4-1) + 3x4x(5-2) + 4x5x(6-3) + ... + 99x100x(101-98)A x 3 = 1x2x3 + 2x3x4 - 1x2x3 + 3x4x5 - 2x3x4 + 4x5x6 - 3x4x5 + ... + 99x100x101 - 98x99x100.A x 3 = 99x100x101A = 99x100x101 : 3A = 333300

67Lp 5A c 37 hc sinh c gio xp vo cc bn hc, mi bn 2 hc sinh. hi cn t nht bao nhiu bn hc c gio xp ch cho hc sinh trong lp.Thc hin php chia: 37 : 2 = 18 (d 1)Vy, c 18 bn hc, mi bn c 2 hc sinh v cn d 1 hc sinh nn cn thm t nht 1 bn hc na.S bn hc cn t nht l:18 + 1 = 19 (bn hc)p s: 19 bn hc.

68Tng din tch hai tha rung trng ng v khoai l 876m vung. Nu chuyn 1/4 din tch tha rung trng ng sang trng khoai thi din tch trng ng v trng khoai bng nhau. Tnh din tch mi tha rung?Sau khi chuyn th tng din tch hai mnh l ko i nn sau khi chuyn mi mnh rung c din tch l 876 : 2 = 438 m2 chuyn 1/4 din tch tha rung trng ng i nn phn cn li l 3/4 din tch tha rung trng ng = 438 m2

Cch 2:khi chuyn 1/4 din tich t trng ng sang trng khoa thi din tch hai manh t bng nhaugi tr ca 1phn l: (876 :2):3=146 (m2)din tch t trng ng la: 146 x4=584 (m2). Din tch t trng khoai l 876-584=292(m2)

69 vui(toan c nc ngoi): Mt hai chn ngi trn mt ba chn. Mt bn chn i vao, n cp mt mt chn, hai chn cm ba chn nem theo bn chn ginh li mt chn. hi bn bao nhiu tui?u bp (2 chn) ngi trn mt chic gh ba chn, chu ch (4 chn) i vao n chm mt ci ui g (1 chn) u bp cm gh nm ch i lai ui g...

70Lp 3: Thn ng ang chi ngoai sn , thi m gi kim tra xem con u 5 ga, 6 vit, va 4 con ln? cho n gian cu ta quyt inh m s chn. ln th nht m c tng cng 32 chn. D cho chc chn cu ta m lai - vn 32. thn ng noi ngay voi me s gia cm va ! me than ng kim tra li va cng nhn thn ng noi ung - tai sao vy?V vt ng co mt chn nn 6 con vt m c 6 chn , 10 chn g v 16 chn ln na. V vy m c 32 chn.

711. M hai a cam bng nhau trn bn. Lan ly 3 qu t a bn phi b sang a bn tri. Hi bay gi a bn no nhiu hn a bn no?2. Thu hn Lan 7 nhn v. Lan li cho Thu 5 nhn v. Hi by gi ai nhiu hn ai v nhiu hn bao nhiu nhn v?1. Ban u 2ia bng nhau co x qua ,gj ly 3qua ia phai bo sang ia trai luc nay ia trai co x+3 qua con ia phai co x-3 qua.Vy traj nhju hn phaj 6qua. 2.Tng t bai1 Thu hn Lan 17 nhan v

72Mt tha rung hnh ch nht c na chu vi l 58,5m.Chiu rng bng 5/8 chiu di.V ma va qua thu hoch tnh ra nng sut t c 7 tn/ha.Hi v ma tha rung thu hoch c tt c bao nhiu t thc?V s chiu rng 5 phn; chiu di 8 phn.Tng s phn l 13Vy chiu rng l (58,5 : 13)5=22,5 mChiu di: 58,5 22,5= 36m Din tch ca tha rung : 3622,5=810 m2 T din tch c tnh kt qu ri i v cng n v , kt qu l 5,67 t

73Tnh din tch hnh tam gic bit di y l 4/7 cm v chiu cao bng 2/5 di y.16/245

74Tng ca hai s thp phn l 68,53. Nu chuyn du phy ca s thp phn th nht sang bn phi mt ch s th ta s c s thp phn th hai.Tm hai s thp phn .Khi dch du phy sang phi, ta s c s mi gp ln 10 ln. V s :S th nht: 1 phnS th hai: 10 phnTng s phn l 1+10=11S th nht l 68,53 : 11,1 = 6,23S th hai l 62,3

75Ngi th nht i t A n B lc 8h45 v i vi vn tc 4 km/h. Ngi th hai i t B v A lc 10h15 v i vi vn tc 5 km/h. Hai ngi gp nhau ti C, hi h gp nhau lc my gi. Bit qung ng AB di 24 km.

Lc 10h15 ngi th nht i c(10h15 8h45) x 4 = 6 (km)Lc 10h15 hai ngi cn cch nhau24 6 = 18 (km)Tng vn tc 4 +5 = 9 (km/h)Thi gian i 2 ngi gp nhau l18 : 9 = 2 (gi)Thi im 2 ngi gp nhau l:10h15 + 2 = 12h15

76Mt ngi i t A v B vi v = 12km/gi. khi i t B v A, lc u ngi i vi v = 12km/ gi, sau khi i c 5km th ngi y tng vn tc ln 15km/ gi. v vy thi gian v t hn thi gian i l 24 pht. tnh chiu di qung ng AB.Ta coi C l im trn ng v m ngi bt u tng vn tc ln 15 km/h. Nh vy C cch B 5km.Trn qung ng AC, t s vn tc gia i v v l 12/15 = 4/5, nn t s thi gian i l 5/4.Gi thi gian lc i trn qung ng AC l 5 phn th thi gian lc v trn qung ng AC l 4 phn.Hiu s phn bng nhau l: 5-4 = 1 (phn)1 phn ny chnh l 24 pht.i 24 pht = 2/5 giThi gian i trn qung ng AC lc i l:2/5 x 5 = 2 (gi)Qung ng AC l: 12 x 2 = 24 (km)Qung ng AB l: 24 + 5 = 29(km)

77Bn Lan cn h s my? Nh Lan trong mt ngi nh 8 tng, mi tng c 8 cn h. Mt hm, cc bn trong lp hi Lan:"Nh bn cn h s my?"."Cc bn hy th hi mt s cu, mnh s tr li tt c cu hi ca cc bn, nhng ch ni "ng" hoc "khng" thi. Qua cc cu hi cc bn th on xem mnh cn h s bao nhiu"- Lan tr li.Bn Huy ni:"Mnh s hi, c phi bn cn h s 1, s 2,..., s 63 khng. Nh vy vi nhiu nht 63 cu hi mnh s bit c bn cn h no."Bn Nam ni:"Cn mnh ch cn n 14 cu, 7 cu bit bn tng my v 7 cu c th bit chnh xc bn cn h s my ".Cn em, em phi hi nhiu nht my ln bit c bn Lan cn h s bao nhiu?Ta coi nh cc cn h c nh s t 1 n 64 (v ngi nh c 8 tng, mi tng c 8 cn h). Ta c th hi nh sau:- C phi s nh bn ln hn 32?Sau khi Lan tr li, d "ng" hay "khng" ta cng bit chnh xc cn h ca Lan trong s 32 cn hno. Gi s cu tr li l "khng" ta cng bit chnh xc cn h ca Lan trong s 32 cn h no. Gi s cu tr li l "khng", ta hi tip:- C phi s nh bn ln hn 16?Sau cu hi ny ta bit c 16 cn h trong c cn h Lan ang .Tip tc hi nh vy i vi s ng gia trong cc s cn li. Sau mi cu tr li khong cch gia cc s gim i mt na. C nh vy, ch cn 6 cu hi, ta s bit c cn h Lan .

78Trn mt t c mt ng si c 101 vin. Hai em hc sinh Hong v Huy chi tr chi nh sau: Mi em n lt i phi bc ra t ng si trn ti thiu l 1 vin v ti a l 4 vin. Ngi thua l ngi phi bc vin si cui cng. Gi s Hong l ngi c bc trc, Huy bc sau. Cc em th ngh xem ai l ngi thng cuc, Hong hay Huy? V ngi thng cuc phi suy ngh g v thc hin cc bc i ca mnh ra sao?Huy s l ngi thng cuc. Tht vy s si ban u l 101 l mt s c dng 5k+1, ngha l s nu chia 5 s cn d 1. Hong phi bc trc, do s si ca Hong phi ly l t 1 n 4 do sau lt i u tin, s si cn li s ln hn 96. Huy s bctip theo sao cho s si cn li phi l 96, ngha l s dng 5k+1. Tng t nh vy, Huy lun lun ch ng c sau ln bc ca mnh s si cn li l 5k+1. Ln cui cng s si cn li ch l 1 v Hong bt buc phi bc vin cui cng v thua.

79M i ch v mua cho Nga 27 qu to ging ht nhau v kch thc v khi lng. Tuy nhin ngi bn hng ni rng trong s cc qu to trn c ng mt qu c khi lng nh hn. Em hy dng mt chic cn bn hai bn tm ra qu to nh . Yu cu s ln cn l nh nht.Chia s to thnh 3 nhm, mi nhm 9 qu, ly 2 nhm t ln cn. Nu cn lch v bn no th qu to nh hn nm trong nhm b chnh ln kia. Nu cn bng th tri to cn tm nm trong nhm cn li. Tip tc chia nhm cn li thnh 3 v tin hnh cn tng t. Ta s tm c tri to nh nht vi ch 3 ln cn.

80C 1 con c sn b ri xung h cao 10cm , ban ngy n b ln c 4cm nhng ban m n b tt xung 3cm .Hi bao gi th n b c ln ming h ?Mi ngay m con c sn bo ln c:4-3=1cmSau 6 ngay m con c sn bo ln c:1 x 6 = 6 cmsang ngay th 7 con c sn bo ln n ming h (6+4=10)Nh vy qua 7 ngay -6 m con c sn ln n ming h

81tng 4 s bng 96 bit rng :nu ly s th nht cng thm 3.s th hai bt i 3,s th ba nhn vi 3 v s th t chia cho 3 th chng c cng kt qu?tm 4 s cho..S th 4 : gp 3 ln on thng . S th 3 bng 1/3 on thng . S th 2 bng on thng cng thm 3. S th 1 bng on thng bt i 3. Nh vy coi s th 3 l 1 phn. S th 4 s l 9 phn, s th hai l 3 phn cng thm 3 n v. S th 1 l 3 phn tr i 3 n v. Tng s phn ca 4 s l : 1 + 9 + 3 + 3 = 16 phn. S th 3 l : 96 : 16 = 6. S th 4 l 96 =54. S th 2 l 63 + 3 = 21. S th nht l 63 - 3 = 15.

82Tnh tng: S = 1-1/2 + 1/3-1/4 + 1/5-1/6 + ..... 1/499-1/500S = 1-1/2 + 1/3-1/4 + 1/5-1/6 + ..... 1/499-1/500 = (1 + 1/3 + 1/5 + ..+ 1/499) - (1/2 + 1/4 + 1/6 + ...+ 1/500) - (1/2 + 1/4 + 1/6 + ...+ 1/500) + (1/2 + 1/4+ 1/6 + ...+ 1/500) S = (1 + 1/2 + 1/3 + 1/4 + ....+ 1/500) - 2.(1/2 + 1/4 + 1/6 + ...+ 1/500) = (1 + 1/2 + 1/3 + 1/4 + ....+ 1/500)- (1 + 1/2 + 1/3 + ...+1/250) = 1/251 + 1/252 + ...+ 1/500. Vy S = 1/251 + 1/252 + ...+ 1/500

83Mt hnh thang c din tch l 60m2, hiu ca 2 y bng 4m. Hy tnh di mi y. Bit rng nu y ln tng thm 2m th din tch hnh thang s tng thm 6m26 m vung l din tch tam gic c y 2 m. Chiu cao ca hnh thang cng l chiu cao ca tam gic v bng: 6 x 2 : 2 = 6(m). Tng hai y ca hnh thang l 60 x 2 : 6 = 20(m). y b ca hnh thang l ( 20 - 4 ) : 2 = 8(m). y ln ca hnh thang l 20 - 8 = 12(m).

84Mt th rung hnh thang c trung bnh cng ca 2 y l 30,15m. Nu tng y ln thm 5,6m th din tch tha rung s tng thm 33,6m2. tnh din tch tha rung.Chiu cao hinh thang cung chnh l chiu cao ca phn tha rung hinh tam gic co y 5,6 m: 33,6 x 2 : 5,6 = 12(m). Din tch tha rung hnh thang l 30,15 x 12 = 361,8 m2

85C 10 hp thuc ging nhau. Trong c 1 hp thuc b ht hn s dng. Bn hy cn 1 ln duy nht tm ra hp thuc ht hn s dng. Bit rng 1 vin thuc bnh thng nng 10g, cn vin thuc ht hn ch nng 9g.L 1 b 1 vin, l 2 b 2.... Nh vy L 10 b vo 10 vin. Vy c tt c 55 vin thuc c cn. Tng ng nu ton thuc bnh thng th l 550g. Vy khi cn nu thiu bao nhiu g th s bit l L no.Cch 2: Cn 1 pht 10 hp thuc. sau b tng hp tng hp xung. nu hp no b xung m thy khi lng trn cn thay i bt thng k theo quy lut th l ht hn.

86Mt lp c 32 hc sinh c xp vo mt phng hc c 2 dy bn. Mi bn c 2 ch ngi. Hi mi dy c my bn?32 hc sinh c xp vo 2 dy bn nn mi dy c 16 hc sinh ngi. V mi bn ch ngi c 2 hc sinh nn 16 hc sinh ca mi dy s ngi vo 8 bn. vy mi dy c 8 bn

87Cch y 3 nm tui con bng tui b, 3 nm na tui b gp 3 ln tui con. Tnh tui hin nay ca mi ngi.Cch 1: Goi tui con cach y 3 nm la a (a#0)goi tui b cach y 3nm la b (b#0)T 3nm trc n 3nm sau cach nhau 6nm.Ta co:a x 4 = b (1)Mt khac :( a + 6) x 3 = b + 6a x 3 + 18 = b + 6 (2)Thay (1) vao (2), ta c:a x 3 + 18 = a x 4 + 6a = 12Vy tui con hin nay la 12+3 = 15Tu b hin nay la : 12x4+3 = 51Cch 2: 3 nm na tui b gp 3 ln tui con th tc l tui con bng 1/3 tui b.nh vy tui con 3 nm na nhiu hn tui con cch y 3 nm l : 3 + 3 = 6 tui.M ta thy hiu s tui ca hai b con l khng thay i. Nn v s ta c: Tui con cch y 3 nm = 1/3 hiu s tui hai b con.Tui con 3 nm na = 1/2 hiu s tui hai b con. Nh vy tui con sau 3 nm na nhiu hn tui con cch y 3 nm l : 1/2 - 1/3 = 1/6 hiu s tui hai b con. Hiu s tui hai b con l ; 6 : 1/6 = 36 tui. Tui con 3 nm trc l :1/3 . 36 = 12 tui. Tui con hin ti l : 12 + 3 = 15 tui. Tui b hin ti l : 15 + 36 = 51 tui

88Hin nay tng s tui ca 3 m con l 56 tui. Bit 16 nm na s tui ca m bng tng s tui 2 con. Tnh tui m hin nay16 nm na tng s tui ca 3 m con l 56+163= 104. S tui ca m 16 nm sau l 104:2= 52 tuiS tui hin nay l 52-16=36 tui

89Hai i xe chuyn 689 tn hng. Hi mi i chuyn bao nhiu tn hng? Bit rng 2/5 s hng i 1 bng 4/7 s hng i 2. V 2/5 s hng i 1 = 4/ 7 s hng i 2 nn 4/10 s hng i 1 = 4/ 7 s hng i 2.Coi s hng i 1 l 10 phn, i 2 l 7 phn.2/5 i 1 bang 4/7 doi 2 => 4/10 i 1 = 4/7 doi 2 => Tng s phn bng nhau l 17 => Mi phn bng: 680:17=40 => i 1 chuyn: 4010=400i 2 chuyn: 407=280

90Tm s t nhin nh nht bit rng khi chia s ny cho 29 th d 5 v khi chia cho 31 th d 28Gi s phi tm l A (A#0)=> (A - 5) chia ht cho 29(A- 5) chia 31 d 23 ( v 28-5=23)Khi bt thng ca php chia (A-5) chia 31 i 1 n v th (A-5) s gim i 31n vTa c: 31 chia 29( d 2).S ln bt thng i l : (29 - 23) : 2 = 3 (ln)V s cn tm nh nht nn s ln bt thng s l 3 ln.Vy s cn tm l : 31 x 3 + 23 + 5 = 121

91T mt si dy thep, Huy ct thanh hai phn bng nhau. Phn th nht Huy un c mt hinh vung. Phn th hai Huy un c mt hinh tam giac co ba canh bng nhau. Huy thy canh hinh tam giac u dai hn canh hinh vung 5cm. Hoi si dy thep co dai bao nhiu met?Khi si dy thp ct lm 2 phn bng nhau ta gi chung l on dy thp.Cnh hnh vung l 1/4 on dy thp, cnh hnh tam gic l 1/3 on dy thp.Cnh hnh tam gic hn cnh hnh vung s phn on dy thp l:1/3 1/4 = 1/12 (on dy thp) di on dy thp l:5 : 1/12 = 60 (cm)Chiu di si dy thp l60 x 2 = 120 (cm)

92Cho mt hnh vung v mt hnh ch nht. Cnh hnh vung hn chiu rng 7 m nhng km chiu di 4 m. Tnh din tch mi hnh bit din tch hnh vung hn din tch hnh ch nht l 100 m2.Ghp H(1) vo v tr H(1) nh hnh v. Ta thy din tch H2 + H3 = 100m.M cnh hnh vung hn chiu rng HCN l 7m nn din tch ca H2 l : 7 x 7 = 49m.Din tch ca H3 l : 100 - 49 = 51m.Chiu rng ca H3 l : 7-4 = 3 mChiu di ca H3 l: 51 : 3=17mCnh hnh vung l : 17 + 7 = 24mDin tch hnh vung l : 24 x 24 = 576mChiu rng : 24 - 7 =17 mChiu di : 24 + 4 = 28mDin tch hnh ch nht: 17 x 28 = 476mCCH 2: Gi chiu rng hnh ch nht l a (a#0)Cnh hnh vung l : a+7Chiu di hnh ch nht l : a + 11Ta c:a x ( a+11) + 100 = ( a+ 7) x ( a+7)a x a + a x 11 + 100 = ( a + 7) x a + ( a+7) x 7a x a + a x 11 + 100 = a x a + 7 x a + a x 7 + 4951 = a x 3a = 17Vy chiu rng ca hnh ch nht l 17Chiu di ca hnh ch nht l 17+11=28Din tch hnh ch nht: 17 x 28 = 476m

93Mt tha rung hnh thang c y ln 150m , y b bng 3/5 y ln v chiu cao bng trung bnh cng 2 y. Trung bnh c 100m2 th thu c 62,5kg thc . Hi c tha rung thu c bao nhu t thcy b l 150:53=90Chiu cao l (150+90):2=120Din tch tha rung l (150+90)120:2=1440014400 m2 gp 100 m2 s ln l: 14400:100=144 lnTha rung thu c s t thc l:62,5144=9000kg=90 t

94Trong c ti cha 30% nc, c kh cha 5% nc. Hi c 200kg c tui mang phi kh cn li bao nhiu kg ?Lng nc trong c ti : 200:100x30=60kgLng c nguyn cht( ko cha nc): 200 - 60 =140kgV lng c nguyn cht ko thay i nn c nguyn cht ng vi s % trong c kh l : 100%-5%=95%S kg c kh l: 140:95x100=147 v 7/9kg

95Hai hnh trn c tng chu vi l 47,728m.Bn knh hnh trn b bng 1/3 ln bn knh hnh trn ln. Tnh bn knh mi hnh trn?Sau khi v s on thng ta trnh by nh sau: Chu vi hinh trn b la: 47,728 : (3+1) = 11,932 (m) ; Bn knh hnh trn b l: 11,932 : ( 2 x 3,14 ) = 1,9 (m)Bn knh hnh trn ln l : 1,9 x 3 = 5,7 (m).

96Bi 1: Bng A ca 1 gii bng c 5 i thi u theo th thc vng trn 1 lt ( cch tnh im: thng: 3; ha : 1 v thua : 0 ). Kt thc vng u tng s im bng A l 26 . Tnh s trn thng, trn ha trong bng A?Bi 2: Bn A c 21 vin bi, bn B c 22 vin bi, bn C c 29 vin bi, bn D c s vin bi bng 2/11 tng s bi ca c 4 bn. Hi bn D c bao nhieu vin bi?Bi 1: S trn u l:5x4:2=10(trn)S im ca trn thng-thua: 3 S im ca trn ha: 2 Mi trn thng hn mi trn ha l: 3-2=1Gi s 10 trn u u l trn thng th s im l:3x10=30Nh vy nhiu hn s im thc t l: 30-26=4Do s trn ha l:4:1=4 (trn)S trn thng l:10-4=6(trn)Bi 2: V s bn D = 2/11 ca 4 bn th bn D 2 phn 4 bn 11 phn nn 3 bn = 11- 2 =9 phn ==> Bn D = 2/9 ca 3 bn. D = (21+22+29) :9 x 2 = 16vin

97mt i nng dn ngy u gt c 20% din tch cnh ng, ngy th hai gt c 30% din tch cn li ,ngy th ba gt c 75% din tch cn li sau hai ngy. Hi cnh ng cn li bao nhju % din tch cha gt?Sau ngy u cn 80% rung.Ngy th hai gt c:8030:100=24% rungSau ngy th hai cn 56% rung.Ngy th ba gt c:5675:100=42% rung.Vy cn 56% - 42% = 14% rung cha gt

982 lp cung trng cyLp 3a trng nhiu hn lp 3b 24 cybit 3b trng c s cy bg 1/3 lp3atim s cy mi lp !V s on thng : Lp 3A c 3phn ,lp 3B 1phn .Nhn s ta c :Hiu s phn bng nhau l :3-1 = 2S cy lp 3B trng c l24:2=12 (cy)S cy lp 3A trng c l12+24=36 (cy )

99Trung bnh cng ca 3 s t nhin l lin tip bng 41. Tm 3 s Cch 1: Tng ca 3 s : 41 x 3 = 123 . Hai s l lin tip hn km nhau 2 n v nn s l th hai hn s l th nht 2 n v, s l th ba hn s l th nht 4 n v. S l th nht l:( 123 - ( 2+4 ) ) : 3 = 39 S l th hai l 39+2 = 41S l th ba l 41+2 = 43. Cch 2: Trung bnh cng ba s cch u nhau s chnh bng s gia nn s l gia bng 41.S l u tin 41-2 = 39 S l th ba l 41+2 = 43

10041......|......45 | 2 | 0........| 52 | 50 |50in s thich hp vao ch trng.S bn tri tr s bn phi cng hng c kt qu l s gia bn trn.97-45=5252-50=250-50=0Hng trn 45-2=43; 2-0=2

STTCu hiLi gii, p n

101Bn trong mt hnh vung ngi ta v mt hnh trn c din tch 28,26 cm2.Tnh din tch hnh vung ?Din tch hnh trn = r . r. 3,14 = 28,26 Suy ra r . r = (28.26 : 3.14) = 9r = 3Nh vy ng knh = 6 cm. suy ra c cnh hnh vung = 6cm.. Din tch hnh vung l 66=36cm2

102Trung bnh cng ca hai s l s b nht c 3 ch s, bit mt s trong hai s l s ln nht c 2 ch s, tm s cn li.S b nht c 3 ch s l 100 Tng ca hai s phi tm l : 100x2=200S ln nht c hai ch s l 99S cn li l : 200-99=101

103Mt ngi i t A n B. Sau khi i c 2100m ngi tnh rng "ta i ht 36 pht. Nu c gi tc ny th n B s mun 40 pht so vi d nh. M ta cn n B sm hn d nh 5 pht. Vy ta phi i vi vn tc 5km/gi". Tnh qung ng t A n B, bit rng ngi tnh ng.Vn tc ngi trong chng ng u l: 2.1x 60:36= 3.5 km/ hTheo u bi thy: chng 2, nu i vi tc 3.5 km/ h th thi gian ( t1) s nhiu hn 45 ' so vi thi gian i vi vt 5km/h (t2). Bit vn tc t l nghch vi thi gian nn t1/t2 = 5/3.5 = 10/7 . Suy ra t1= (45' :3) x 10 =150' =2 .5 h.Chng 2 c chiu di l: 2.5 x 3.5 =8 .75 kmQung ng AB l: 2.1 +8.75= 10.85 km.

104Mt hinh ch nht co chiu rng bng na chiu dai nu tng chiu rng 8cm thi c 1 hinh vung. Tinh chu vi hinh ch nht.Chiu rng /------------/....8cm.../Chiu di /-----------/------------/Chiu rng tng 8 cm th chiu di bng chiu rng nn chiu rng bng 8cm, Chiu di : 8x2=16 cmChu vi : (8+16)x2=48cm

105Ba nm trc cha hn con ln 28 tui, hn con nh 34 tui. Nm nm sau, tui 3 cha con cng li bng 76. Tm tui mi ngi hin nay.Tm tng s tui 3cha con hin ti: 76- (5x3)= 61tHin ti th cha vn hn con ln 28t, hn con nh 34t.S tui ca cha hin ti: (61+ 28 + 34) : 3= 41t. Con ln: 41- 28= 13t. Con nh: 41- 34= 7t.

106bi ton lp 4: Mt mnh vn hnh ch nht c s o cc cnh u l s t nhin v chiu di gp 3 ln chiu rng. Din tch mnh vn trong khong t 30m2 n 50m2. Tnh chu vi mnh vn?Ta thy chiu di gp 3 ln chiu rng nn ta chia hnh ch nht thnh 3 hnh vung bng nhau c cnh l chiu rng ca hnh ch nht nn din tch hnh ch nht gp 3 ln din tch hnh vung c cnh l chiu rng hnh ch nht => din tch hnh ch nht l s chia ht cho 3. din tch mnh vn ch nht trong khong t 30 n 50 m2. Ta c nhng s chia ht cho 3 l nhng s c tng cc ch s chia ht cho 3, vy t 30 -50 c cc s chia ht cho 3 l 30, 33, 36, 39,42,45,48. Din tch hnh vung tng ng l 10, 11, 12,13,14,15, 16.M ta thy din tch hnh vung l tch ca 2 cnh( tch ca 2 s ging nhau) nn 10 =25 (loi), 11=111(loi), 12= 112=26=34 (loi), 13= 113(loi), 14=27(loi), 15=35(loi), 16= 44( nhn). Vy cnh ca hnh vung hay chiu rng ca hnh ch nht l 4, chiu di hnh ch nht l 43 =12m. Chu vi mnh vn l:(4+12) 2=32m

107Co 2 cy da mt cy cao 20 thc. Cy kia cao 30 thc. Mi cy mt b ao cach nhau 50thc . 2 con chim u trn ngon 2 cy cau cung lao xung bt 1con ca di ao cung vi 1 vn tc va cung m vao con ca. Hoi khoang cach t ngon cau ti con ca la bao nhiu thc.?

108Bt Bi u by gi?u tin t nh Bt Bi nhm hng nam lao vt i nhng c 1km bng thay i hng, i v pha ng. nhng i c 1km th Bt bi li thay i nh chuyn hng i v pha bc v ng 1km th thy nh mnh trc mt! bt bi c hoa mt tht khng?ang im cc Bc ca tri t

109Tm s thp phn a,b, bit rng a khc b v a,b = (a+b) x 0,5Phn tch cu to s ta c:a,b=(a+b)x0,5a+ 0,1b=0,5a + 0,5b0,5a= 0,4b5a=4bv a, b l cc s c mt ch s nn => a=4 v b=5s thp phn phi tm l 4,5

110Tnh tng cc ch s ca php tnh S = 333...333x 333...334 (s 333...333 c 2013 s 3, s 333...334 c 2012 s 3)v trong s th nht c 2013 ln ch s 3 v trong s th 2 c 2011 ln ch s 3. nn ch s 3 c s ln l: 2013 + 2011 = 4024. S = 4024 x 3 + 4 = 12076

111Hinh ch nht co chu vi 72cm .nu giam chiu rng i 6cm va gi nguyn chi dai thi din tich giam 120cm2. Tinh chiu dai va chiu rng hinh ch nht o.Chiu di hnh ch nht l : 120: 6 = 20 cmNa chu vi hnh ch nht l : 72:2=36 cmChiu rng hnh ch nht l: 36-20=16 cm

112Tm x, bit: ( 1 + x ) + ( 2 + x ) + ( 3 + x) + .. + ( 200 + x ) = 21100(1+x) +(2+x)+...+(200+x)=21100 1+x +2+x +3+x +...+200+x =211001+2+3+...+200 +200x = 21100Ta c 1+2+3+.. ..+200 =(1+200)+(2+109)+(3+108)+...=100201 = 20100 (v c ([1+200]-1) :2 =100 cp )=>200x = 21100-20100 =1000 x=1000:200 =5

113ton lp 4: Bit din tch hnh bnh hnh ABCD l 24cm2, chiu cao AH l 3cm v bng mt na chiu cao CE. Tnh chu vi hnh bnh hnh?

di CE= 3x2= 6 cmta c SABCD = CE.AD=AH.DCm din tch ABCD=24 cm2, CE= 6 cm=> di cnh AD= 24: 6= 4 cm di cnh DC= 24: 3=8 cmchu vi hnh ABCD = (4+8)x2=24 cm

114Tnh gi tr biu thc : 198 : 2 x 4444 x 2 x 132 : 25 / 33 x 8888 : 5 x 66 : 125 x 530

115Mc lng ca cng nhn tng 20%, gi hng gim 20%. Hi vi mc lng ny th hng mi s mua c nhiu hn hng c bao nhiu %?Ga s lng c l 100% th lng mi l: 120%$Ga s gi hng c l 100% th gi hng mi l 80%. gi hng cT s phn trm gia lng hng mi v hng c l: 120/80 = 150%Vy hng mi s mua nhiu hn hng c l: 150 - 100 = 50%

116Tnh B = 25 + 25 +..+ 25 + 75 + 75 +..+ 75(S 25 c tt c 25 s v s 75 c tt c 25 s)(25 + 75) x 25 = 100 x 25 = 2500

117 200g dung dch mui 3% vo 300g dung dch mui 4%. Hi s c dung dch mui bao nhiu phn trm?Tng khi lng dung dch l:200 + 300 = 500 gam.Lng mui c trong 200 gam dung dch mui 3% l:200 x 3 : 100 = 6 gam.Lng mui c trong 300 gam dung dch mui 4% l:300 x 4 : 100 = 12 gam.Tng lng mui trong c hai dung dch l: 6 + 12 = 18 gam.Dung dch mui thu c c s phn trm mui l:18 : 500 = 0,0360,03 = 3,6 %.p s: 3,6%

118Mt ca hng c 5 r cam v chanh mi r 1 loi ,s qu trong mi r ln lt l 104,115,132,136,148. Sau khi bn c 1 r cam, ngi ch ca hng thy rng s chanh cn li gp 4 ln cam. Tnh s qu mi loi.Sau khi bn i mt r th trong cc r cn li c s qu chanh nhiu gp 4 ln s qu cam.Vy tng s qu cn li phi chia ht cho 5 (4+1=5).Tng s qu 5 r: 104+115+132+148+136=635 (qu)635 l s chia ht cho 5 nhng trong 5 r y ch c 115 chia ht cho 5 nn r c bn i l r ng 115 qu. (Tng s qu cn li mi chia ht cho 5).Tng ca 4 r cn li: 635-115 = 520 (qu)Trong cc r cn li c s qu cam:520:5=104 ( qu cam)s qu cam l : 104+115=219 quS qu chanh : 520-104=416 (qu chanh)p s: 416 qu chanh ; 219 qu cam.

119Mt tri nui g c s g trng bng 25% s g mi.Nu tri mua thm 72 con g trng th s g trng s bng 40% g mi. Hi lc u tri g nui bao nhiu con g ?% s g trng tng thm l 40%-25%=15% s g mi15% ng vi 72 con gvy s mi l : 72:15x100=480 cons g trng l : 480:100x25=120 contng s g ban u ca trang tri l : 480+120=600 ( con g )

120So snh: 1998/1999+1999/2000 va 1998+1999/1999+2000t A=1998/1999+1999/2000B=1998+1999/1999+2000=1998/1999+2000 + 1999/1999+2000Vi 1998/1998>1998/1999+20001999/2000>1999/1999+2000Nn A>B

121Me mua v 500g . Me mun ly ra 300g nu che. Hoi me phai cn th nao nu chi co mt cn hai ia va mt qua cn 100g ma chi 1 ln cn? qu cn mt bn. sau chia s vo hai bn n khi cn thng bng. Bn khng c qu cn chnh l 300g

122Cho hnh thang ABCB. AC ct BD O. Din tch A0B = 4cm2. Din tch DOC = 9cm2. Tnh SABCD?

123Mt hnh vung c din tch l 5 cm2 hoc bt c hnh vung no c din tch khng phi l tch hai s t nhin.Bi ny mnh thy c g hi kh hiu. Nhng m a bi vo y th khng phi l bi ton thng thng.Theo mnh th c th lm nh sau:- ly 1 hnh vung c cnh 1 cm- ly 4 tam gic vung c cnh gc vung ln lt l 1 cn, 2 cm.- xp chng li vi nhau.

124Mt hnh ch nht c chu vi 80cm. Nu tng chiu di 5cm th din tch ca hnh ch nht tng 75cm2. Tnh din tch hnh ch nht ban u.Chiu di tng thm 5cm th phn din tch tng ln s l mt hnh c c mt cnh l 5cm v mt cnh l chiu rung ca hnh ch nht. Chiu rng ca hnh ch nht l: 75:5 = 15cmNa chu vi hnh ch nht l: 80:2 = 40cmChiu di hnh ch nht l: 40-15= 25cm. Din tch hnh ch nht ban u l: 15 25 = 375 cm2

125Em c mt cc sa em ung ht 1/3 cc sau em y kcao v ung ht 1/6 cc, sau em li y kcao v ung ht 1/2 cc,ln ny em li y kcao v ung ht khng cn mt git, hi em ung bao nhiu sa v kcao?Ban u em c 1 cc sa, em ung ht m khng thm sa. Vy ng nhin em ung ht 1 cc sa. Cn cacao th em ung l:1/6+2/6+3/6=1 (cc)p s: 1 cc sa v 1 cc cacao

126Nu nh. a-1=b+2=c-3=d+4=e-5 theo ban ch cai nao ln nht a ,b ,c ,d hay e ? Giai thich?Theo bi: a-1 = b+2 = c-3 = d+4 = e-5 ta c:a-1=b+2 => a-b=2+1=3>0 => a>b (1)a-1=c-3 => a-c=1-3=-2 => c>a(2)b-d=4-2=2>0 => b>d (3)c-3=e-5 => e-c=5-3=2>0 => e>c (4)T (1), (2), (3) v (4) => e>c>a>b>dVy e ln nht

127Mt ng ch tri cht li $80,000 chia u cho cc con. Mt gi trc khi cht, ng bo sa di chc v loi ra mt s con c hng phn chia. Cc con cn li chia thm c $24,000 mi ngi. Hi vy: ng ch tri c my ngi con?Khi tt c cc con c chia tin th mi phn tin l 80,000$ : s conSau khi c mt s con khng c chia tin th mi phn tin l 80,000/(s con- s con ko c chia), tng thm c 24,000$. Suy ra:80000 : (s con- s con ko c chia ) 80000 : s con = 24000Khai trin v rt gn : 10 x s con =3 x s con (s con- s con ko c chia)S con ko c chia = 3x s con x s con/ ( 3 x s con +10)v s ngi con ko c chia l s t nhin nn thc hin thay cc gi tr s ngi con c chia l 1,2,3 vo (1) ta tm c s ngi con ca ch tri l 5 ngi v c 3 ngi con ko c chia

128ng b Gia, ng b Bch v ng b Phn trong hi Cao Nin cng i d mt bui vn ngh gy qu. Cc v cng ngi mt hng gh di c nh s 1, 2, 3, 4, 5 v 6. c bit l qu v ny ngi xen k nhau (Mt b ngi cnh mt ng), nhng ch c mt b ngi cnh ng chng ca mnh. B Gia ngi gh s 2 v b Phn khng ngi gh s 6. Hi vy: b no ngi k ng chng ca mnh?ng Phn ngi gn b Phn( 1. ng Bch 2. b Gia 3. ng Phn 4. b Phn 5. ng Gia 6.b Bch)

129Mt bc nng dn c 17 con tru trc khi qua i bc li di chc cho 3 ngi con nh sau: Ngi con th nht c 1/2 s tru, ngi con th 2 c 1/3 s tru, ngi con th 3 c 1/9 s tru, ba anh em khng bit chia nh th no v phi nh n bc hng xm, theo cc chu th bc hng xm chia tru cho ba anh em nh th no?"Mn" thm 1 con tru. Nh th, bc s c 18 con.Ngi con th nht c 9 con, ngi con th hai c 6 con, ngi con th ba c 2 con.

130Cho tam giac ABC. Trn BC ly im M sao cho BM = 2MC, trn AC ly im N sao cho NC = 3NA.a) So sanh din tich tam giac ABN va din tich tam giac MNC.b) Keo dai AB va MN ct nhau tai E. Tinh din tich tam giac ABC bit din tich tam giac AEN = 6 cm2.a. SBNA = 1/4 SABC (1)SBNC = 3/4 SABC (2)SNMC = 1/3 SBNC (3)(2) + (3) => SNMC = 1/3 x 3/4 SABC = 1/4 SABC (4)(1) + (4) => SBNA = NMCb. SEMB = 2 SEMC => SENB = 2 SENC=> (SABN + SAEN) = 2SENCM SENC = 3SAEN=> SABN + SAEN = 2 x 3 = 6SAEN=> SABN = 5 SAEN (5)(1) + (5) => SABC = 4 x 5 = 20 SAENSABC = 120cm2

131Tm 1 s 2 ch s bit s gp 5 ln tng ca cc s ca n.V s c 2 ch s gp 5 ln tng 2 ch s ca s , nh vy s c hai ch s phi l s chia ht cho 5 v th ch s tn cng phi l 0 hoc 5.Nu tn cng l 0 th tng hai ch s bng ch s hng chc nh vy ch c s 50 cn cc s c tn cng l 5 th gm c cc s 15, 25,, 85, 95.Sau dng phng php th chn s tm c kt qu l 45

132Mt mnh vn hnh ch nht c chu vi l 150m, nu gim chiu di 5m, tng chiu rng 5m th din tch khng i. Tnh din tch mnh vn.Nu gim chiu di 5m, tng chiu rng 5m th din tch khng i, c ngha l di ca chiu rng v chiu di s i cho nhau nn chiu di s hn chiu rng l 5m.Na chu vi hnh ch nht l 150: 2 = 75m. Chiu rng l: (75 - 5): 2 = 35mChiu di l: 35+5 =40mDin tch l: 3540 =140m2

133Tm x :bit 1 / 1 x 2 + 1 / 2 x 3 + 1 / 3 x 4 ++ 1 / ( x 1) . x = 15 / 161 / 1 x 2 = 1-1/2 v 1/2x3 = (1/2)-(1/3) tng t n 1/(x-1).x=(1/x-1)-(1/x). Cui cng ta c php tnh 1+(1/x-1)-(1/x)=15/16.

134Hai hnh vung c hiu chu vi l 20 cm, c hiu din tch l 125 cm2. Tnh din tch mi hnh. Hiu chu vi l 20 -> hiu 2 cnh hnh vung l 5 cm.Gi cnh hnh vung ln l a. V hnh s thy hiu S ca hai hnh vung l:5 x a+ 5 x ( a-5)= 125 -> a =15. Vy din tch 2 hnh vung ln lt l 225 v 100.

135Khi vit thm ch s 8 vo bn phi mt s t nhin ta c s mi hn s c 332 n v. Tm s t nhin ban u?Khi vit thm 1 ch s vo bn phi 1 s t nhin th s tng 10 ln thm gi tr tng ng ch s thm vo.Vy, khi thm ch s 8 vo bn phi s t nhin th n tng ln 10 ln v 8 n v.Bn v s on thng minh ha: s c l 1 phn th s mi l 10 phn bng nhau nh th, thm 1 on c gi tr l 8.S mi hn s c 332 n v, vy s ban u l:(332 - 8) = 9 = 36.

136 nh s trang ca mt quyn sch ngi ta phi dung ht tt c 234 ch s. Hi quyn sch c bao nhiu trang ?T trang 1 n trang 9 dng 9 ch s T trang 10 n trang 99 dng 180 ch s. Cn li 45 ch s dng ng s trang c 3 ch s; c 45 : 3 = 15 trang c 3 ch s. S trang sch: 9 + 90 + 15 = 114 trang .

137Thnh ph A cch thnh ph B 274km. Cng lc, mt xe gn my i t A B v 1 xe du lch i t B v A. Sau 2 gi, h gp nhau im C cch A 84km. Tnh vn tc ca mi xe.Cch 1:Vn tc xe gn my l: 84:2=42 km/hon ng t B n C l 274-84=190 (km)Vn tc xe du lch l 190 : 2= 95 (km/h)Cch 2: Vn tc xe my l: 84: 2= 42 (km/h)Qung ng xe gn my v xe du lch cng i trong mt gi (cn gi l tng hai vn tc) l:274: 2= 137 (km)Vn tc xe du lch l:137 42= 95 (km/h)

138Bi 1: Nm nay con 4 tui v km cha 30 tui. Hi bao nhiu nm na th 2 ln tui con bng 7 ln tui cha?Bi 2: Trc y 8 nm.tui ca lan bng na tui ca lan sau 8 nm.tnh tui ca lan hin nay ?Bi 3: Con hi b "nm nay b bo nhiu tui ?"b tr li "ly mt na tui ca b cng vi 7 th c tui ca b cch 12 nm" hy tnh tui ca b hin nay ?Bi 1: V hiu s tui ca 2 ngi khng i theo thi gian nn c s :Con: 2 phnCha: 7 phnHiu s tui: 5 phnVy tui con khi l (30:5)2=12Sau 12 4=8 (nm) th 7 ln tui con bng 2 ln tui cha.Bi 2. Tui Lan sau 8 nm hn tui Lan trc 8 nm l 8+8=16 (tui). v s :Ta c hiu s phn l 2 1=1. Tui ln trc y 8 nm l 16: 1= 16Tui Lan hin ti l 16 + 8= 24 tui Bi 3: V s on thng tui b l 1 phnThm vo phn 7. Tui b cch y 12 nm l 2 phn bt i 12 tui.M tui b thm 7 bng tui b cch y 12 nm.Theo s ta c tui b hn tui b l:12 + 7= 19. Nh vy tui b l 19 2=38

139Khi cng hai s thp phn, mt hc sinh vit nhm du phy ca mt s hng sang bn phi mt hng nn c tng l 132,1. Hy tm hai s , bit tng ng l 57,94 ?Gi s hc sinh vit nhm du phy ca s thp phn th haiV hc sinh vit nhm du phy sang phi 1 hng tc l cng s thp phn th nht vi 10 ln s thp phn th hai, hiu gia tn ng v tn sai bng 9 ln so thp phn th haiHiu gia tng sai v tng ng l : 132,1-57,94=74,16S thp phn th hai l : 74,16:9=8,24S thp phn nht l : 57,94-8,24=49,7

140Tnh nhanh: 8.21+ 9.26+ 10.31+......+ 27.11+ 28.16t A = 8,21 + 9,26 + 10,31 +.........+ 27,11 + 28,16 s hng ca A l : (28,16-8,21):1,05+1 =20 s hng => A = ( 8,21+28,16)20:2= 36.3710=367,3

141Thay ch s thch hp vo du * trong php tnh sau :18 x 19 x 20 x 21 = 14*640(Trong * l ch s)S 3

142Cho 1 bi c gm 64 vung. ng cho ca mi vung bng 2cm. Ngi ta nm vo bn c 150 vin bi th c 21 vin bi bn ra ngoi. Hi c hay khng ba vin bi trn bn c m khong cch gia hai vin bi ty khng ln hn 2cm? Bottom of Form

S vin bi cn li trn bn c l 150 - 21 = 129V 139 = 642 + 1 nn theo nguyn l Dirichle s tn ti t nht 3 vin bi nm trong cng 1 , v 3 vin ny khong cch gia 2 vin ty s nh hn ng cho vung = 2cm

143Ton lp 3 : 1/3 tm vi bng 1/4 tm vi xanh. Bit hai tm vi di 84m. Tm di 2 tm vi?Tm vi chia lm 3 phn, tm vi xanh chia lm 4 phn. V 1/3 tm vi bng tm vi xanh nn c 2 tm vi c chia u thnh 7 phn bng nhau. di ca mt ohn l 84 :7 =12m di tm vi l 123=48m

144C 9 vin bi ging ht nhau nhng c mt vin c khi lng khc loi. Hi cn cn it nht bao nhiu ln tm ra vin khc loi . ( s dng cn thng bng )Chia 3 phn bng nhau, cn 2 phn(ln 1),- TH1:nu thng bng tc vin khc loi phn 3 vin cn li cn li, ly 2 trong 3 vin cn(Ln 2), nu thang bng th vin cn li l khc loi. Nu khng thang bng, ly 1 tronghai vin cn vi 1 vin khc(ln 3) th s tm ra vin khc loi- TH 2:Nu khng thng bng, em chia 6 vin lm 3 phn, cn 2 phn mi bn 2 vin(ln 2),+ nu thng bng tc hai vin cn li c 1 vin khc loi.Ly 1 trong hai vin cn vi mt vin bt k(ln 3) th s ra vin khc loi+ Nu khng thng bng tc trong 4 vin c 1 vin khc loi, em 2 vin cng bn cn(ln 3), nu = nhau th vin khc loi bn kia. em 1 trong hai vn cn vi 1 vin bt k (ln 4)s ra vin khc loiNh vy chc chn tm ra vin khc loi th phi cn t nht 4 ln>

1451 x 2 x 3 x.......x 98 x99 x100 co tan cung bao nhieu chu so 0?Ta c: 5,15,35, 45,55, 65,85,95, 25 = 5 x 5, 75 = 5 x 5 x 3,Ta li c: 10 = 2 x 5, 20 = 4 x 5,30 = 5 x 6,40 = 5 x 8, 50= 5 x 5 x 2, 60 = 5 x 12, 70 = 5 x 14, 80 = 5 x 16, 90 = 5 x 18,100 = 5 x 5 x 4Mi ch s tn cng l 5 nhn vi mt ch s chn to ra mt ch s 0.C 24 ch s tn cng l 5 nn tch trn c 24 ch s 0.

1461 HCN co chu vi 72 cm. Nu giam chiu rng i 6cm va gi nguyn chiu dai thi din tich giam i 120 cm2. Tinh chiu dai va chiu rng cua HCN.Gim chiu rng i 6cm tc l phn din tch gim i bng 6 ln chiu dichiu di ca hnh ch nht l: 120:6=20 (cm)na chu vi ca hnh ch nht l : 72:2=36 cmchiu rng ca hh ch nht l : 36-20=16 cmp s : chiu di : 20cm;chiu rng : 16(cm)

147 bi ton lp 2 nh sau: "C hai con ng i t nh Minh n nh Bnh, c 3 con ng i t nh Bnh n trng. Hi t nh Minh n trng c bao nhiu cch m phi i qua nh Bnh?"c 2 cch chn con ng i t nh Minh sang nh Bnh. C 3 cch chn con ng t nh Bnh n trng. Vy c : 2x3=6 cch chn ng t nh Bnh n trng.

148Cho mnh vn hnh ch nht c din tch l 196 mt vung. Mnh vn c chiu di gp 4 ln chiu rng. hy tnh chu vi mnh vn V mnh vn hnh ch nht ra.Chia chiu rng lm 1 phn th chiu di lm 4 phn nh th.Vy mnh vn c chia lm 4 mnh nh hnh vung (cnh mnh vn hnh vung ng abwngf chiu rng mnh vn ban u) c tng din tch l 196 mt vung.Din tch mt mnh nh l: 196 : 4 = 49 mt vung.Vy cnh mnh vn hnh vung nh l: 7 mt, v 7 x 7 = 49.=> Chiu rng mnh vn hnh ch nht l 7 mt, chiu di l: 28 mt.Chu vi bng 70 mt

149C mt ng b trc khi cht li mt n nga v di chc chia nga cho cc con nh sau:Ngi con c c 1 con nga v 1/11 s nga cn li.Ngi con th 2 c 2 con nga v 1/11 s nga cn l.Ngi con th 3 c 3 con nga v 1/11 s nga cn l.Ngi con th 4 c 4 con nga v 1/11 s nga cn l..................................................................................C chia nh vy n ngi con t th va ht s con nga.Hi ng b c bao nhiu ngi con v bao nhiu con nga?p s: 10 ngi con v 100 con nga

150Tm s nh nht khi chia s cho 3 th cn d 2, chia cho 5 cn d 3 v chia cho 7 cn d 223

151Cho tng A = 1/2 +1/3 + 1/4 +....+ 1/16 +1/17.CMR A ko phi l s t nhin?Ta c:1/2 + 1/3 + 1/6 = 1 (1)1/8 x 4 < 1/4 + 1/5 + 1/7 + 1/8 < 1/4 x 4hay 1/2 < 1/4 + 1/5 + 1/7 + 1/8 < 1 (2)1/18 x 9 < 1/9 + 1/10 + 1/11+....+1/17 < 1/9 x 9hay 1/2 < 1/9 + 1/10 + 1/11+....+ 1/17 < 1 (3)T ( 1), (2) v (3), ta c:1 + 1/2 + 1/2 < A < 1+ 1+ 1hay 2 < A < 3vy A ko phi s t nhin.

152lp 4- 5: Ban vit ln lt cac s t 1 n 100 ln bng. Sau chn ra mt s s bt ki, xoa cc s i v viet thay ln bng tng cc ch s ca cc s bi xa. c tip tuc lm nh vy- s cui cung cn lai trn bng l bao nhiu? ti sao vy?

153Mt php nhn c tha s th hai l s c 2 ch s ging nhau.nu vit cc tch ring thng ct th tch ng hn tch sai 9018 n v.tm tha s th nht?Tha s th nht : 501 khi tha s th 2 = 22Tha s th nht : 334 khi tha s th 2 = 33Tha s th nht : 167 khi tha s th 2 = 66

154lp 4 : (hi kh)1)hai hinh tam giac ct nhau bao nhiu im?2) V hai hinh tam giac sao cho phn chung nhau ( giao) va hp ( tng) ca no cung l hinh tam gic!

155T 100 n 200 c:a) bao nhiu s l?b) bao nhiu s chn?c) bao nhiu s?d) nu vit ln lt cc s ln giy th s c bao nhiu s 0?t 100 n 200 c (200-100):1+1 = 101 s-dy trn bt u l s chn v kt thc l s chn nn s s chn hn s s l l 1 s.vy c 50 s chn v 51 s l.- T 101 -> 109 c 9 ch s 0.- T 110 - 190 c 9 ch s 0- s 100 v 200 c 4 ch s 0vy tng cng c 9 x2 + 4 = 22 ch s 0

156tim s t nhin nho nht chia 2 d 1 ,chia 3 d 2 ,chia 4 d 3 va chia 5 d 4.(A+1)chia ht cho 2,3,4,5s nh nht chia ht cho 2,3,4,5 l 60s cn tm l 59

157Mesi ngh ra mt s. S ny ln hn 4 ln ca 60 nhng nh hn 5 ln ca 50. La mt s co hai ch s ging nhau, va tng cc ch s l s c 2 ch s. hi s l s no?244

158C mt can 3lt v mt can 5lt ru.rt h mnh 1lt vi.ong y can 3l, ht 3l can 3l vo can 5l. ln 2 li ong y can 3l v tip vo can 5l, lc ny can 5l c 5l, 1l cn li can 3l. nh vy l ong c 1l ri

159Mt b gi i ch vi mt r trng, khng may r trng b mt con nga dm ln nt by. Ngi ch nga ngh n b thit hi v hi b gi c bao nhiu trng trong r.B gi qun bng s trng trong r. B ch cn nh l khi b ly trng ra tng cp th cn d 1 trng trong r. Ging nh vy, khi b ly trng ra tng 3, 4, 5 v 6 trng mi ln, cng cn d 1 trng trong r. Tuy nhin, nu b ly ra 7 trng mi ln th sau cng khng cn qu trng no trong r.Hi vy, c t nht l bao nhiu trng trong r ca b gi?S trng phi l s chia cho 2, 3, 4, 5, 6 d 1. Nhng li chia ht cho 7. S chia ht cho 2, 3, 4, 5, 6 c tn cng l 0.Gi s trng l a. Ta c a chia ht cho 2, 3, 4, 5a+1 chia ht cho 7S chia ht cho 6 l 30, 60, 300, 600.a chia ht cho 2, 3, 4, 5. Vy a nhn gi tr: 300, 600.a+1 chia ht cho 7.Vy s 301 tha mn. Do c t nht 301 qu trong r ca b gi.

160Bn An lm 45 bi ton, c gio chm im nh sau: mi bi lm ng c 10 im, mi bi lm cha hon thnh c 5 im, mi bi lm sai b tr 5 im. Lm xong 45 bi ton An c tng s im l 230 im. Hi An lm ng bao nhiu bi ton, bit rng c 8 bi An lm cha hon thnh.

161C 60 qu cu b ngoi ging ht nhau, nhng c mt qu b li nng hn mt cht. Vi mt cn thng bng ( hai a v khng c qu cn)- cn t nht bao nhiu ln cn pht hin ra qu cu b li?Ln 1: (20-20-20). Mi bn 20 qu.-Nu cn thng bng=> qu cu li nm trong nhm 20 cn li.- Nu bn no nng hn th nm trong nhm 20 nngLn 2:(7-7-6). Mi bn 7 qu.- Nu cn nng hn th nm trong nhm 7 nng.- Nu cn thng bng th nm trong nhm 6.* Xt trng hp 1( Nu cn nng hn th nm trong nhm 7 nng)-Ln 3: (2-2-3) Cn mi bn 2 qu.-Nu cn nng hn th nm trong nhm 2 nng.- Nu cn thng bng th nm trong nhm 3.**Xt trng hp (Nu cn nng hn th nm trong nhm 2 nng):Ln 4 : (1-1) cn mi bn 1 qu l ok.**Xt trng hp:( Nu cn thng bng th nm trong nhm 3)Ln 4: (1-1-1)cn mi bn 1 qu.- Nu cn thng bng => qu li l qu cn li.- Nu cn nng hn th qu li l qu nng hn.* Xt trng hp 2:(Nu cn thng bng th nm trong nhm 6)Ln 3 : ( 2-2-2) cn mi bn 2 qu.- Nu cn thng bng th nm trong nhm 2 cn li.- Nu cn nng hn th nm trong nhm 2 nng.**Xt trng hp (Nu cn nng hn th nm trong nhm 2 nng):- Ln 4 : ( 1-1) Mi bn mt qu l ok.**Xt trng hp:(Nu cn thng bng th nm trong nhm 2 cn li)Ln 4 : ( 1-1) Mi bn 1 qu l ok

162Lp 5: Khi lp 5 c 375 hc sinh. Trc khi ngh Tt cc thy c cho nhiu bi tp v nh. Nhng trc Tt, 2/3 s hc sinh n v na s hoc sinh nam hon thnh bi tp v nh, v nh vy s hc sinh nam, n cha hon thnh ht bi tp bng nhau. Hi c bao nhiu hc sinh nam v bao nhiu hc sinh n?2/3 n hon thnh bi tp=> 1/3 n cha hon thnh bi tp. Tng t c 1/2 nam cha hon thnh bi tp.Khi 1/3 s n cha hon thnh bi tp bng 1/2 s nam cha hon thnh bi tp. Vy t s gia s n v s nam l 3/2. Coi s n l 3 phn bng nhau th s nam l hai phn nh th. S hc sinh n l: 375: (3+2)x3=225 (em). S hc sinh nam l: 375-225= 150 (em)

163Mt on nam n tm bn sngTo nh bn nhau chuyn v chng1 thip 2 chng tha 7 thip1 chng 2 thip 4 chng khngHi bao nhiu nam, n tm bn sng?12 chng - 10 thip

164Bi 1: 61 + 61 = 122. 72 + 72 = 144. 83 + 83 = 166. 94 + 94 = 188.Bi 2: 2+6+3+(4+5-8)=122+6+3+4+5-8=127+3.2+5-8=10Bi 3:Mi con u xung mt cy th thiu mt cy tc l tha 1 con; nu 2 con u 1 cy th tha 1 cy tc l thiu 2 con. Tng s con u 1 cy 1 con t hn tng s con u 2 con 1 cy l: 2 + 1 = 3 ( con).S con trn 1 cy m 1 con u mt cy t hn s con trn 1 cy m mi cy u 2 con l: 2 - 1 = 1 ( con). S cy l: 3: 1 = 3 ( cy). S con chim l: 3x1 + 1= 4 ( con) hoc 3x 2 - 2 = 4 ( con)Bi 4: bn 1: 13 ht, bn 2: 7 ht, bn 3: 4 ht.

165Mt bi ton lp 4 nh: Mt s chia cho 3 d 2; chia cho 7 d 4. Hi s chia cho 21 d bao nhiu ?A = m x 3 + 2 => A + 10 = m x 3 + 12A = n x 7 + 4 => A + 10 = n x 7 + 14=> A + 10 chia ht cho 3 v 7.A + 10 chia ht cho 3 x 7 = 21Vy A chia 21 d ( 21-10) = 11.

166Vi su que dim hy xp bn tam gic u m mi cnh ca mt tam gic c di l mt que dim.Xp theo kiu hinh chop u, co ay la hinh tam giac u, 3 que dim con lai dng ln nh kiu kim t thap ai cp la c, 3 mt bn la 3 tam giac u,

167Bi ton lp 4 nh: Trc y 8 nm tui m gp 4 ln tui con.Hin nay tui con bng 2/5 tui m. Tnh tui mi ngi hin nay.con 16 - m 40

168Lp 3 -4 : Mt nh nghin cu mi truong mun vuot qua mt sa mac cn 6 ngay ng. Hoi nguoi o cn bao nhiu nguoi khun vc giup vic, bit rng c nha nghin cu v ngi gip vic ch mang c lng thc n v nc ung cho 4 ngy ng ca mt nguoi?2 ngi mang cho 1 ngi n trong 4 ngyvy 1 ngi mang cho 2 ngi n trong 2 ngy. 1 ngi n trong 6 ngy th cn 3 ngi mang.Vy cn thu 3 ngi.

1692con meo: meo vn va meo en cung xut phat 1luc v cung 1ich.meo vn bc ngn hn 20% so vi mi bc cua meo en.nhng meo vn lai bc nhah hn meo en nn s bc cua meo vn nhiu hn 20% s bc cua meo en. hoi meo nao ti ich trc?Coi mi bc cua meo en la 100% thi mi bc cua meo vn la 80%.80% = 4/5Vy coi 1bc cua meo en la 1phn thi 1bc cua meo vn la 4/5 bc meo en.Khi meo en bc 100 bc thi meo vn bc dc : 100:100(100%+20%)=120 bc.Thi gian meo en bc dc 100 phn thi meo vn bc c: 1204/5=96 phn.Vy meo en n trc

170A Thi lp 3 cai gh va 4 cai ban ht ung 8h. Cung A Thai lp 4 cai gh va 3 cai ban thi chi. ht 7h15phut. Hoi A Thai lp 1 cai ban ht bao nhiu thi gian?12 gh v 16 bn lm ht s thi gian l: 8 x4= 12gi. 12 gh v 9 bn lm ht s thi gian l: 7h15x 3= 21h45 . 7 bn lm ht s thi gian l: 32h- 21h45= 10h15. i : 10h15= 6151 bn lm ht: 615 : 7 = 87pht v 6/7pht.

171C bn con tu cch nhau mt khoang ng bng nhau. Mt chic l tu ch khch, mt chic ch hng, v mt chic c bit. Hi chic th 4 th no v u?1. tu ngm ang i di bin 2. tu bay ang bay trn tri. 3. con tu c bit do thuyn trng Jack Sparrow ch huy i tim tu ma do Barbossa li hai tu nay mi ch mi ni.

172Thng ca php chia hai s t nhin l s ln nht c mt ch s. Tng ca s b chia, s chia, s thng v s d l 2251. Tm s b chia ca php chia bit s d l s d nh nht c th.Thng l 9; t s ca 2 s l 1/9. Tng bao gm 10 ln s chia + 9 + s d => 2 ln s d + 9 = 11 => s d = 1; S chia l 224S b chia = 224 x 9 + 1 = 2017

173Tm 2 s c hiu bng 81 bit rng nu vit thm mt ch s 3 vo bn phi s b tr v gi nguyn s tr th ta c hiu mi bng 867.S bi tr u la a, sau la 10a+3.Hai kt qua hiu cho ta bit s bi tr a thm 3 ln hn s bi tr u la 867-81 n vi nn ra phep toan la 10a+3-a=867-81 hay a=87 s tr la 6

174Tm 2 s bit s th 2 c 3 ch s v gp 2 ln s th nht, ng thi nu xa i ch s 4 hng trm ca s th 3 th ta c tng mi bng 335.gi s th 2 l 4bcs th nht l 4bc/2theo u bi ta c: bc+4bc/2=335bc+400/2+bc/2=335bc=90vy s th 2 l 490s th nht l 490/2=245

175C mi bi ton. Hi c nhiu nht bao nhiu cch lp mt ton gm bn bi ton trong mi bi ton cho ?c 210 cch lp.

176Tm tng ca 2 s bit hiu ca 2 s bng 142 v hiu bng na s b.hiu bng na s b nn s b l : 142x2=284s ln l : 284+142=426tng ca hai s l : 284+426=710cch 2 :s b l 142x2=284v s b = ( tng - hiu):2 nntng hai so l : 284x2+142=710

177Lp 2-3:1) tinh tng 1+2+3+4+5+6+7+8+9+102) thay i mt s du + bang du - , kt qu bang 5 ?3) giai thich tai sao khng th thay dau +, - kt qu bang 0?1. S dng tnh cht kt hp:(1+9) + (2+8)+( 3+7) + ( 4+6) + 5 + 10 = 10 + 10 + 10 +5 + 10 = 55.2. Ta thy tng ca dy s l 55. M mun thay du " + " bng du " - " c kt qu l 5 th ta phi chia dy s ra l 2 phn: 1 phn c tng l 30, 1 phn c tng l 25 l c.V d: ( 1 + 9) + ( 2 + 8) +(3+7) -( 4+ 6) - 5 - 10 hay chnh l: 1 + 2 + 3 - 4 - 5 - 6 + 7 + 8 + 9 - 10. Ngoi ra cn rt nhiu cch thay du "+" thnh " - " khc vo trong dy s. Ta ch vic da vo cch chia thnh 2 phn nh trn v da vo cch tnh tng trn phn 1 p dng.3. V tng ca dy s l 55 v l 1 s l. Mt s l th ko th chia ra l 2 v bng nhau c tc l khng l cho php tnh ca dy s c kt qu bng 0 c. V vy, ko th thay du " + " bng du "-" kt qu bng ko c.

178Trong hp c 15 vin bi xanh, 16 vin bi . Hi khng nhn vo hp phi ly ra t nht bao nhiu vin bi chc chn c:a) 2 vin khc mu nhaub) 2 vin cng muc) 5 vin v 3 vin xanha) 17 - b) 3 c) 20

179C 3 tm vi bng nhau. Sau khi bn i 38m tm th 2 v 17m tm th 3 th tng s m vi cn li ca 2 tm ny bng s m vi ca tm th nht nht. Hi lc u mi tm vi bao nhiu m?V s vi cn li ca 2 tm bng 3/4 s vi ca tm 1 nn nu ta coi s vi ca tm 1 l 4 phn th s vi ca tm 2 v 3 l 8 phn. S vi cn li chim 3 phn nn s vi bn chim s phn l: 8 - 3 = 5( phn). 5 phn ng vi s vi l: 38 + 37 = 75(m). Lc u mi tm vi di s mt l: 75 : 5 x 4 = 60(m)

180Mt hnh ch nht c chu vi 1608m chiu rng km chiu di 164m. Tnh din tch hnh ch nht.Na chu vi hnh ch nht l :1608:2=804(cm)Theo u bi ta c s : 164Chiu di hcn: |--------|-----|Chiu rng hcn: |--------|Hai ln s o chiu rng l :(804 -164 ):2 =320 (cm)S o chiu rng hnh ch nht l320:2=160(cm)S o cdi hcn l160+164 =324(cm)Dtch hcn l324160=51840 (cm2)

181Vit s ln nht co 4 ch s ma tng cac ch s bng 9 hiu ch s hang n vi va hag nghin la 5V tng cc c.s =9 v hiu gia ch s hng n v v ch s hng nghn l 5 nn ta th ch s hng nghn chn c s 1 v 2 tho mn, ch s hng nghn 3 loi. M ta phi vit s ln nht c th nn ch s hng nghn phi l 2. Suy ra 2007.

182Khi vit thm ch s 8 vao bn phai 1 s t nhin ta c s mi hn s cu 332 n vi tim s t nhin luc u .Khi vit thm s 8 vo bn phi th c s mi = 10x s c + 8. Vy s c l: (332-8):9= 36.

183tnh nhanh :20-30+40-50+60-70+80=80-70+60-50+40-30+20=10+10+10+20=50

184Lanhn Hu 8bg hoa. Hnghn Lan 4 bg. Hi Hng hnhu bnhiu bng?hu : /-----------/lan: /-----------/-----8 bng--/hng/------------/-----8--------/--4 bng-/t s hnh vHng hn hu s bng hoa l : 8+4=12 bng

1851) Cac bn hoc sinh ng u nhau thnh mt vng trn. Mi ngi c nhn mt s theo th t la 1, 2 , 3, 4 , .... Bit rng bn co th t s 10 i din vi bn co s 43. Hoi trong vong trn c bao nhiu bn?3) hoa Mng-du mi ngy sinh ra gp i.(nhung hoa dc sinh ra li sinh sn tip) Vi th chi 112 ngay l ph y ao. Hi co 8 hoa Mng du thi sau bao nhiu ngy s kn ao?4) trn mt hon o co hai loai vt. Loai 40 chn v loai trn 3 u. tng cng c 26 u v 298 chn. loi 40 chn thi ch c 1 u. Hi loai trn tinh 3 u thi co bao nhiu chn?

1) Ci ng h c 60 pht, 10 pht thng vi 40 pht, ng vi na vng, cc bn na vng hn 3 v tr, vy c vng cc bn hn 6 v tr tc c 66 bn4)Loi 40 chn c ti a 7 c th, tng s u loi 3 u ch trong khong 19 n 26, trong s u phi chia ht cho 3, c 2 trng hp: 21:3=7 v 24:3=8 u tha mn, vi s chn tng ng l 298-5x40=98 v 298-4x40=138; s chn phi chia ht cho s c th th ch c 98:7=14 chn.vy loi 3 u c 14 chn.

186Cho A= 1x2+2x3+3x4+4x5+....+ 29x30Tnh Ax3=?Ax3= 1x2x3 + 2x3x3+.....+29x30x3ly B= 1x2x3+ 2x3x4+......+29x30x31B- Ax3= 0 + 1x2x3+ 2x3x4+ 28x29x30= B- 29x30x31. Suy ra Ax3= 29x30x31

187An ni ;''tui t 3 nm trc y ng bng 1/2 tui t 2 nm na '' tnh tui An hin nay.Tui An trc y 3 nm km tui An sau 2 nm na l:3 + 2 = 5 (tui)Coi tui An trc y 3 nm l 1 phn th tui An sau 2 nm na l 2 phn nh thHiu s phn l:2 1 = 1 (phn)Tui An trc y 3 nm l:5 : 1 = 5 (tui)Tui An hin nay l:5 + 3 = 8 (tui)

188So snh cc s sau: 13/15 ; 1313/1515 ; 131313/1515151313/1515 cng chia c t v mu cho 101 s = 13/15131313/151515 cng chia c t v mu cho 10101 s =13/15. Vy 3 phn s bng nhau.

189Cho hnh ch nht ABCD,trong K l trung im AB , CK ct DB ti I. Tnh S hnh ch nht ABCD, bit rng Din tch AKID =20 cm2.Ta thy: SAKD=1/4 SABCD= SKBD. SBCD=1/2SABCD.Xt 2 tam gic BKD v BCD c chung y BD, din tch gp 2 th chiu cao xung y BD cng gp i nhau. Vy din tch CID cng gp i din tch DKI( v chung y DI), tc l din tch SDKI=1/3SDCK=1/6SABCDSAKID =(1/6+1/4) SABCD =5/12 SABCD1/12 l 20: 5= 4 cm2SABCD=4x12=48cm2

190C 7 ci bnh nng chia u cho 12 ngi, hi phi ct bnh nh th no mi ci bnh ko b ct thnh qu 5 phn?Ln 1 ly 3 ci bnh ra, mi ci chia lm 4 phn bng nhau, vy c tt c 12 phn, mi ngi 1 phn bnh.Ln 2 ly 4 bnh cn li ra, chia u mi ci thnh 3 phn bng nhau, mi ngi cng c 1 phn bnh.Nh th chia u cho mi ngi 7/12 ci bnh u nhau m khng cn chia mi bnh qu 5 phn.

191Ko thc hin phep tinh , tim ya,(y_476)x2=2196x3b,(y+10248):3=(6800_5480)x6A, (y-476)x2=2196x3(y-476)x2=2196x2+2196(y-476)x2-2196x2=2196(y-476-2196)x2=2196(y-(476+2196)x2=2196(y-2672)x2=2196(y-2672)x2=1098x2(y-2672)x2-1098x2=0(y-2672-1098)x2=0(y-(2672+1098)x2=0(y-3770)x2=0y-3770=0y=3770S: y=3770

192Lp 3-4:Thng, Li, Hin, Lnh c 52 hoa im tt. Ngi no cng gp phn. Hin va Lnh at tng cng 33 hoa im tt. Nhng nhiu nht li l Thng. Hi Li co bao nhiu im tt?Hin + Lnh = 33 hoa im tt nn trung bnh mi bn ko qu 17 hoa (v Thng nhiu hoa nht)Tng 4 bn c 52 hoa nn Thng + Li = 19 hoaLn hn 17, nh hn 19 ch cn li 18. Vy Thng 18 hoa v Li ch c 1 hoa im tt.p s: 1 hoa

193Hai bn Minh H thc hin mt tr chi nh sau: H ln lt ni mt s t nhin khc 0. Minh ni trc 1 s khng ln hn 10. H ni tip mt s ln hn s m Minh va ni nhng ln hn khng qu 10 n v, v c tip tc nh vy ... Ai ni s 100 l ngi thng cuc. Vy Minh phi ni nhng s no chc chn thng cuc1;12;23;34;45;56;67;78;89;100

194Hin nay b 70 tui, chu trai 12 tui, chu gi 8 tui. Hi sau bao nhiu nm na tui b bng 2 ln tng s tui ca hai chu?Gi s trong nh c 1 ngi ng bng tui b. Vy tui ca c ng v b l : 70 + 70 = 140 (tui).Tng tui ca 2 chu l : 12 + 8 = 20 (tui)Mi nm 2 chu tng 2 tui , 2 ng b cng tng 2 tui. Do hiu s gia tng tui ca ng b v tng tui ca hai chu khng i v lun bng: 140 - 20 = 120 (t)Khi b gp 2 ln tng tui ca 2 chu th tng tui hai ng b gp tng tui 2 chu l:2 + 2 = 4 (ln)Tng tui ca 2 chu khi l:120 : (4 -1) = 40 (t) (dng hiu t)C 2 chu tng thm: 40 - 20 = 20 (t)S nm tui b gp 2 ln tng tui 2 chu l: 20 : 2 = 10 nm

195on ng AB di 28 km. An v Bnh xut pht cng mt lc t A. An i vi vn tc 13 km/h. Bnh i vi vn tc 7 km/h. Hi sau bao lu on ng cn li ca Bnh gp 3 ln on ng cn li ca An?oan duong AB dai 28 km.An v Binh xuat phat cng mot luc t A. An di voi van toc 13km/h. Binh di voi van toc 7 km/h. Hoi sau bao lau oan duong con li cua Binh gap 3 lan doan duong con lai cua An?

196S nam sinh ca trng Tiu hc Bnh Minh bng 125% s n sinh ca trng. Nu thm 54 n sinh th s n sinh bng 95% s nam sinh.Hi lc u, s nam sinh ca trng TH Bnh Minh hn s n sinh ca trng l bao nhiu em?Ta c : 125% = 5/495% = 19/20Ban u s n so vi nam bng : 4/554 hc sinh ng vi : 19/20-4/5=3/20( s nam)s nam: 54 : 3/20 = 360s n : 360 x 4/5 = 288

197Mt HCN c 2 ln chiu rng th hn chiu di 5m. Nhng 2 ln chiu di li hn 2 ln chiu rng 10m.Tnh chu vi HCN .Chiu rng ly 1 phnChiu di ly phn v bt i 5m.Chu vi hnh ch nht gm 4 on chiu rng v 2 phn nh ca chiu di cn li ng vi 10mVy chiu rng l: 5+5=10Chiu di l: 10+5=15Chu vi ca hnh ch nht l 50 mc rong ba lay 1 pan; chieu dai lay 2 pan va bt i 5m. ban se nhin thay chu vi HC nhat gom 4 doan chieu rong va 2 phan nho cua chieu dai con lai ng voi 10m. Vay chieu rong se la 5+5= 10; chieu dai la 10+5=15. Chu vi l 25 m

198Lc 7h30 ngi A i t A n B vi v1 = 15km/h. Lc 8h30 Ngi B i t B v A vi v2= 12km/h. Hai Ngi gp nhau ti C v cng quay v B. Tnh AB? Bit khi Ngi A quay v A th qung ng ngi A i c gp 3 ln qung ng ngi B i c.(Ton chuyn ng lp 5)Biet ngA di... => 2.AB=3.2.BC hay AB=3.BC Thi gian ngi A i l 2BC/15. Thi gian ngi B i l BC/12. Ta co tA=tB+1 =>BC=9kmSuy ra AB= 93=37 km

199Hay chng t rng 1/2+1/3+1/4+1/5+1/6+1/7+1/8 khong la so tu nhienCch1:Chon MS chung la 3.5.7.8=> Mu s chnT s cua PS 1/2 : 3.5.7.4 ;PS 1/3: 5.7.8PS 1/4: 3.5.7.2PS 1/5: 3.7.8PS 1/6: 5.7.4=> Cac TS nay u chnPS 1/8 : 3.5.7 => TS nay leVy TS la s le ma MS la s chn.=> tng trn khng la s t nhinCch 2:Coi tng trn la S nhe1/3+1/4+1/5+1/6+1/7+1/8 > 6/8 =3/4Vy S > 1/2 +3/4 = 5/4. (1)Ma 1/4+1/5+1/6+1/7 < 1/4 x 4 = 11/2 + 1/3 +1/8 = 23/24Vy S< 1 + 23/24 < 2 (2)T (1) va (2) => 5/4 < S ta c PT: 1+1+1=1 ( Loi)TH2: (a,b)= (1,2) => ta c PT: 1+1/2+1/4= 1 (Loi)TH3: (a,b) ln hn hoc bng 2. Vy 1/a.a ; 1/a.b ; 1/b.b u nh hn hoc bng 1/2.2 = 1/4. Vy 1/a.a + 1/a.b +1/b.b lun nh hn hoc bng 3x1/4 = 3/4 < 1 vi mi a, b.KL: PT ko c nghim nguyn dng (PCM)

206=4/3 x 9/8 x 16/15 x 25/24x.....x100/99=2x2x3x3x4x4x5x5x.....x10x10/1x3x2x4x3x5x4x6x....x9x11=(2x3x4x5x....x10 ) x (2x3x4x5x...x10) / (1x2x3x4x....x9 ) x (3x4x5x...x11)=10x2/11=20/11

207Ton Lp 5) Ti mt trng hc u nm c s hc sinh nam bng s hc sinh n. Cui hc k 1 trng nhn thm 38 em n v 6 em nam, nn s hc sinh n chim 52% s hc sinh ton trng. Hi u nm trng c bao nhiu hc sinh? 52% = 13/25N lc sau l 13 phnTng s nam v n lc sau l 25 phnNam lc sau 25-13=12 phnM ban u nam = nN thm hn nam thm 38-6=32 hc sinhVy 32 hc sinh ng vi : 13-12=1 phnN lc sau: 32:1x13=416 hc sinhN ban u: 416-38=378 hc sinhTng hc sinh lc u: 378 x 2 = 756 hc sinh

208Lp 4 :Tm tt c cc s c ba ch s m bn thn s v s tip theo n cng c tng cc ch s l s lGi s cn tm l abc.Do s lin sau ca n cng c tng cc ch s l l nn c=9 (nu c#9, th hai s lin tip nhau khng cng tnh cht tng cc ch s u l)Nhn thy b#9, v nu b=9, s lin tip khng tho mn iu kin bi.Nh vy s phng n s bng s cc s c 2 ch s, hng n v khc 9, v tng cc ch s l s chn.S phng n = 5x4+4x5=40

209LP 4: C 25 con gia sc trn ng c. S b sa bng 3 ln s nga, s b con bng 2 ln s ln. bit rng khng phi con nga no cng cng mu lng. hi mi loai bao nhiu con ang trn ng c?3 con ln; 6 con b; 4 con nga v 12 con b sa

21013 s t nhin khc nhau, c tng bng 92. Hi l nhng s no?13 s l: a1=14, M>= 1+2+..+11+13+14=93>92). Nn suy ra ai=i (110, 28 >10, ...., 98 >10. Nn 8x18x28x....x98 > 8x10x10x...x10 (9 ch s 10) = 800....0 (9 ch s 0) > 2732010. Vy ko th thc hin php tr trn.

218Co bao nhiu s chn co hai ch s . Tinh tng cua day s oC tt c cc s chn c 2 ch s l: (98-10) : 2 + 1 = 45 (s)V c 45 s nn c 22 cp c tng bng nhau. Nn 10 + (98 + 12) + (96 + 14) + ... = 10 + 110 x 22 = 2430.

219Tng hai s t nhin l 77. Nu ly s ln chia cho s b ta c thng l 7 v d 5. Tm hai s Tng s phn l 7+1 = 8S b= (77-5) : 8 = 9S ln = 9x7 +5 (s d-hiu) = 68Hoc 77-9=68

220Ngi ta xp nhng hinh lp phng nho canh 1cm thanh hinh lp phg ln canh 1,1dm. Sau o ngi ta sn cac mt cua hinh lp phg ln. Hoi co bao nhiu hinh lp phg nho khng c sn mt nao?1,1 dm = 11 cm.Sau khi xp c hnh lp phng cnh 11cm, nu bc b 1 lp bn ngoi theo din tch ton phn ca hnh hp ln( bao gm cc hnh lp phng nh cnh 1cm th bn trong s l nhng hnh lp phng nh cnh 1cm khng c sn mt no.Khi bc b lp ngoi, cnh hnh lp phng ch cn:11 - 2 = 9(cm)S hnh lp phng nh khng c sn mt no:9 x 9 x 9 = 729 (hnh)

221Bac Ba k:hi con tre 1ngay bac ganh u gach xy 3cai nha ba gian nu ganh thm 1ganh thi xy c 4cai nha va tha 16vin gach.bac gthich rng:hi o nha tre 3gian chi phai t 2vin gach vao 1chn ct,mi nha ba gian co 12ct.tinh s gach bac a ganh?Gi s vin gch xy 1 ngi nh l a (vin ). Khi s gch bc gnh xy 3 ngi nh l: 3 x a ( vin )V gnh thm 1 gnh th xy 4 ngi nh v tha 16 vin nn 1 gnh ca bc c s gch xy 1 ngi nh v tha 16 vin tc l1 gnh ca bc c a + 16 ( vin )V s gnh ca bc va xy 3 ngi nh c 3 x a vin nn ta c 3 x a phi chia ht cho a + 16 . Suy ra 3 x (a + 16 ) - 3 x a = 48 chia ht cho a + 16Mt khc, mi ngi nh cn c 2 x 12 = 24 ( vin ) t vo ct, do vy a > 24 => a + 16 > 40 m 48 chia ht cho a + 16 nn a + 16 = 48 => a = 32S gch bc gnh l: 32 x 3 = 96 ( vin )

222Trong ti c 18 vin bi v 10 vin bi xanh. Hi nu khng nhn vo ti th phi ly ra t nht bao nhiu vin bi?a. c chc chn 1 vin bi xanh? b. c chc chn 1 vin bi ?Phn a l 19 cn b l 11 vin bi

223Mt xe hang luc u d inh ch 621kg gao c chia u thanh 9 bao. Nhng sau o mi bao thm vao 5kg gao va xe chi ch 7 bao. Hoi xe hang o ch c bao nhiu ki-l-gam gao?Theo d inh ban u thi mi bao gao cn nng la 621 : 9 = 69kgsau khi thm 5kg mi bao nng la 69 + 5 = 74kgs gao thc ch la 74 x 7 = 518 kg

224nga hi c 1 s hoa 2025.S t nhin ln hn 40, nh hn 50 m c tn cng 5 l 45Th li 45 x 45 = 2025 ( ng )Vy cnh hnh vung bng 45m

227Trong k kim tra hai mn Ton v Ting Vit va qua ca mt trng tiu hc c 70,5% tng s hc sinh t im kh, gii mn Ton. 64,5% tng s hc sinh t im kh, gii mn Ting Vit. 18% tng s Hc sinh khng t im kh, gii c hai mn Ton v Ting Vit. Tm t s % hc sinh t im kh , gii c hai mn Ton v Ting Vit.S hc sinh gii kh Ton hoc Ting Vit l100% - 18 % = 82%S hc sinh gii kh Ting Vit m khng gii kh Ton l82% - 70,5% = 11,5%S hc sinh gii kh Ton m khng gii kh Ting Vit l82% - 64,5% = 17,5%S hc sinh gii kh c Ton v Ting Vit l82% - 11,5% - 17,5% = 53%

228Lc 6h ti A 1 chic thuyn xui dng theo dng nc n im B. Thuyn dng li ti B 30phut. Ri quay v A v n A lc 9h30phut. Tnh qung ng AB bit vn tc thc ca thuyn l 25km/h. Vn tc dng nc l 5km/h.

229Trong hp c 12 vin bi ,10 vin xanh, 9 vin vng v 3 vin trng. Khng nhn vo hp phi ly ra t nht bao nhiu vin bi chc chn c 5 vin bi cng mu?16

230An c 27 vin bi Bnh c 49 vin bi hi phi bt bao nhiu vin bi s bi ca An =1/3 s bi ca Bnhkhi bt i 1 s bi th s bi ca An bg 1/3 s bi ca Bnh tc l s bi ca An t hn 2 phn s bi ca BnhS bi ca An sau khi bt i l (49-27):2=11S bi m An bt i l 27-11=16S bi ca Bnh sau khi bt l 49-16=33

231Tm mt phn s bit phn s c gi tr l 3/5 v nu bt t s i 9 n v th c phn s mi bng .V s T s chim 3 phn . Mu s chim 5 phn. Khi bt t s i 9 n v th mu s gp i t s tc chia 1 phn thnh 2 na bng nhau v = 9 n v. Vy 1 phn l: 9 x 2 = 18. T s l 18 x 3 = 54. Mu s l 18 x5 = 90.

232Hi c ba hp bi, tng s bi ca hp th nht v hp th hai l 33 vin, tng s bi hp th 2 v 3 l 28 vin, tng s bi hp 3 v 1 l 31 vin. Hi mi hp c bao nhiu vin?Ly (tng ca hp 1 v 2 cng tng ca hp 2 v 3 cng tng ca 1 v 3) s c: 2 ln tng ca 3 hp bng 92Vy tng ca c 3 hp: 92 :2=46 vin biSuy ra s vin bi ca hp 1 l: 46-28=18 vins vin bi ca hp 2 l: 46-31=15 vins vin bi ca hp 3 l: 46-33=13 vin

233Cho hnh tam gic ABC vung ti A, c chu vi l 72cm. di cnh AB = di AC, di AC = 4/5 di cnh BC. Tnh din tch hnh tam gic ABCAB=3/5BC, A V DNG TON TNG T TM HAI CNH GC VUNG RI TNH S

234Mt ngi i ch bn trng.Ln th nht bn mt na s trng v thm 1 qu,ln th 2 bn mt na s trng cn li v thm 2 qu,ln th 3 bn mt na s trng cn li v thm 3 qu th va ht s trng.Hi ngi bn bao nhiu qu trng?Cn li sau ln th 2: 3:1/2=6Cn li sau ln th 1: (6+2):1/2=16Ban u: (16+1):1/2=34

235tm quy lut v vit thm ba s na vo dy s sau: 1, 2, 6, 24,.....1x2.2x3.6x4.24x5.......

236C 10 ngi, mi ngi ghi s tui ca 9 ngi cn li. Thng k c l 90, 91, 92, 93, 93, 97, 98, 99, 100, 101. Hi s tui ca ngi cao tui nht l bao nhiu?

9 ln tng s tui ca 10 ngi : 90+91+92+...+101=954Tng s tui ca 10 ngi: 954:9=106Tui ngi ln nht: 106-90=16

237Bn ngi n 5 ngy, ngy n 2 ba th ht 18kg go. Hi 9 ngi n 7ngy,ngy 3 ba th ht bao nhiu kg go?(Mc n cc ba nh nhau)Tam sut kep.4ngi - 5 ngay - 2ba-18kg=>1ngi - 1ngay - 1 ba = 18 : 4 : 5 : 2 =9/20kg=> 9 ngi - 7ngay - 3 ba = 9/20 x 9 x 7 x 3 = 1701/20kg = 85,05 kg

238Tnh nhanh: 3/2+7/6+13/12+21/20+...+133/1323/2+7/6+13/12+21/20+...+133/132=1+ 1/2 + 1+ 1/6 + 1+ 1/12 + 1+ 1/20+......+ 1+ 1/132=(1+ 1 + 1+.....+ 1) + ( 1/2+ 1/6+1/12+ 1/20+....+ 1/132)= 11+ ( 1/12+ 1/23+1/34+1/45+.....+1/1112)=11+ ( 1-1/2+1/2-1/3+1/3-1/4+1/4-1/5+......+1/11-1/12)=11+(1-1/12)= 11+11/12=143/12

239Vi I chy y b nc trong 48 gi.Vi II chy y b th mt thi gian nhanh gp ri vi I.Vi III chy mt thi gian nhanh gp ri vi II.Tnh thi gian b nc y khi 3 vi cng chy vo 1 b y.

Gp ri c hiu l 3/2 gi vi 1 chy c: 1/48 b vi 2 chy 1/48 x 3/2 = 1/32 b vi 3 chy : 1/32 x 3/2 = 3/64 b

240La v Ng cng nhau th hng,cc bao hnf u nng bng nhau.La ku ca l mang nng.Nga bn ni"Bn cn ku ni g?Nu ti bt cho bn mt bao hngth chng ta mi mang nng ngang nhau.Cn nu bn bt cho ti mt bao hng th s bao hng cu ti gp i cu bn".Tnh xem mi con mang my bao hng?Nga chuyn sang la 1 bao th s bao 2 con bng nhau, vy nga hn la 2 bao.Nu chuyn 1 bao t la sang nga th nga hn la : 1+2+1 = 4 baoV s La sau khi chuyn: 1 phnNga sau khi nhn 2 phnKhi chuyn i 1 bao th la cn 4 baoLc u la c 4+1=5 baoLc u nga c 5+2=7 bao

241Mt s em chia cho 54 th d 37, nu em chia cho 27 thi c thng l 19 v cn d. Tm s .27 x 2 = 54 Khi chia s cho 27 th thng gp 2 ln so vi thng chia 54/ 37 chia cho 27 thng tng thm 1 n v v d 10. S = 19 x 27 + 10 hoc ( 19 - 1 ) : 2 x 54 + 37=523

242

243Ngi ta xp nhng hnh lp phng nh cnh 1cm thnh hnh hp ch nht di 15cm, rng 10cm, cao 70cm. Sau ngi ta sn cc mt ngoi ca hnh hoopj ch nht va xp. Hi c bao nhiu hnh lp phng c sn 1 mt?13682+1382+868 = 1768+208+544=2520

244Khng quy ng t hoc mu, hy so snh 2 phn s 13/15 v 133/153.Ta c: 13/15 = 1 - 2/15 = 1- 20/150. 133/153 = 1-20/153.Ta thy 150 < 153 nn 20/150 >20/153 suy ra 1- 20/150 < 1- 20/153 hay 13/15< 133/153

2451) Tim so co hai ch s ab sao cho ab=(a+b)^22) Tim so co BN ch s abcd sao cho abcd=(ab+ cd)^21, ab= (a+b)x (a+b) a*10+b= a*a+ 2*a*b+ b*b a*10 - a*a - 2*a*b+b- b*b =0 a*( 10 -a - 2 *b) + b*( 1- b) =0 a*( 10 -s- 2*b) =0 v b *(1-b)= 0 v 10> a>0,10> b>=0 nn a*( 10- a- 2*b)=0 th 10- a- 2*b =0, b*(1-b) =0th b=0 hoc 1-b=0. vi b =0 th thay vo 10- a- 2*0 =0 a = 10 loi. vi 1-b= 0 b=1 th thay vo 10 - a- 2*1 =0 a= 8 nhn. vy s cn tm 81.2, abcd= 2025 (abcd= ab *100 + cd = ab*ab+ ab*cd +ab*cd +cd*cd)

247Xun, h , thu, ng cng nhau nh c. Mi vn thng c 1 im,mi vn hoa c 0,5 im, mi vn thua c 0 im. H c 1,5 im, thu, ng mi bn c 1 im. Hi xun c bao nhiu im?Ta thy: Mi 1 bn phi u vi 3 bn cn li 1 vn c nn tng s vn c l: 4 x 3= 12 (vn)Tuy nhin, mi bn li c tnh 2 ln ( Xun u vi H hay H u vi Xun ch coi l 1 vn ) nn tng s vn c thc t c c l: 12 : 2 = 6 ( vn )Mi vn d kt qu th no lun c tng im l 1 im. 6 vn s c tng l 6 imV tng s im thu c ca tt c cc vn l 6 im, nn tnh s im ca Xun ta ch cn ly tng s im tr i s im ca cc bn cn li, tc l: 6 - 1,5 - 1 - 1 = 2,5 (im)

248Cho 2 s t nhin x v y. X c th l 7, 8 hoc 15; y c th l 63, 68, 19. Tm gi tr ln nht v nh nht ca x/y.Ta c :15/19> 15/63> 15/687/19> 7/63> 7/688/19>8/63>8/68Mt khc : 15/19>8/19>7/19nn PS ln nht l 15/19ta li c : 15/68> 8/68>7/68Vy PS nh nht l 7/68

249Mt t d kin i t A n B vi vn tc bng 45km/gi n B lc 11 gi. Do tri ma, ng trn m bo an ton giao thng nn mi gi xe ch i c 35km v n B chm mt 30 pht so vi d kin. Tnh thi gian t xut pht t A.Ta c t s vn tc 45km/gi v vn tc 35km/gi l 45/35 = 9/7. V trn cng qung ng vn tc t l nghch vi thi gian nn t s thi gian i vn tc 45km/gi v thi gian i vi vn tc 35km/gi l 7/9. Hiu thi gian l 30 pht. (v s ). Thi gian i vi vn tc 45km/ gi l: 30 : (9 - 7) x 7 = 105 pht. 105 pht = 1 gi 45 pht. Thi gian xut pht l: 11 gi - 1 gi 45 pht = 9 gi 15 pht

250Khi t tinh thc hin phep nhn mt s t nhin vi 145, mt hc sinh a s y t cac tich ring thng ct vi nhau ri cng cac tich ring nh cng cac s t nhin nn tim c tich sai la 5120. Hay tim tich ung.Tch sai: A x 1+ A x 4 + A x 5 = 5120A x 10 = 5120A = 512Tch ng : 512 x 145 = 74240

251Mt ngi lm thu c nm s c tr cng 100 quan tin v mt b qun o. Nhng anh ta ch lm 7 thng thi xin thi vic nn c thanh ton 20 quan tin v b qun o. Hi b qun o ng gi bao nhiu quan tin?12 thng = 100 quan + 1 b qun o7 thng = 20 quan + 1 b qun o=> 5 thng = 80 quan10 thng = 160 quan2 thng = 32 quan12 thng = 192 quan=> 1 b qun o : 192 - 100 = 92 quan

252Tm s t nhin ln nht c cc ch s khc nhau m tng cc ch s ca n bng 21S t nhin ln nht khi c nhiu ch s nht:Ta thy: 0+1+2+3+4+5+6 = 21=> S l 6543210

253ALADIN mua mt b bt Mc, bt Bi, v Thc k. nu gi bt mc ch cn mt phn nm, gi bt bi cn mt na, v gi thc k cn hai phn nm th khi ALADIN phi tr 80 quan tin. Nu Gi bt mc cn mt na, gi bt bi cn mt phn t v gi thc k cn mt phn ba th phi tr 120 quan tin. Hi ALADIN phi tr bao nhiu tin cho c ba th? Bt mc v bt bi ci no t hn?280 quan

2541^2 + 3^2 +5^2+...99^2Gi tng phai tinh la A ta thy A = (1^2+ 2^2+3^2+4^2+....+ 100^2) - 4x( 1^2+ 2^2+3^2+4^2+....+ 50^2 ) = 100x(100+1)x(2x100+1)/6 - 4x50x(50+1)x(2x50+1)/6 = 166650

255Tm phn s bit thm vo t 1 n v th phn s c gi tr l 4/5. Nu bit t s 4 n v th phn s c gi tr l .Ta thy t s thm 1 n v s ln hn t s bt i 4 n v l 5.Sau khi thm bt t s ta c 2 phn s mi c cng mu s v c t s hn km nhau 5 n v.4/5 = 16/203/4 = 15/202 phn s trn c cng mu nhng t s hn km nhau 1 n v.Vy 2 phn s sau khi thm bt t s m tha mn t s hn km nhau 5 n v l4/5=16/20=80/1003/4=15/20=75/100Phn s ban u l 79/100

256Mt lp hc c 33 hc sinh. Tt c u tham gia th thao. Ngy no cng vy c 22 em tham gia bi li v 22 em bng. Trong s ngi hm nay bng, hm qua c 15 em bi li va 15 em bng. Tnh hnh cng ng nh vy vi cc em hm nay tham gia bi li. Hi c bao nhiu bn c 2 hm ch bi li?4 bn c hai hm ch bi li.

257Mt phong hoc dang hinh hp ch nht co chiu dai 10m, chiu rng 5,5m va chiu cao 3,8m. Nu mi ngi lam vic trong phong o u cn 6m khi khng khi thi co th co nhiu nht bao nhiu hoc sinh trong phong o, bit lp hoc chi co 1giao vin va th tich ac trong phong chim 2m3.Th tich phong hoc la:105.53.8=209 (m3)Th tich dung va th tich khng khi giao vin dung la.2+6=8 (m3)S hoc sinh ti a trong phong hoc la.(209-8):6=33 d 3.S hoc sinh trong phong phi la s nguyn nn trong phong co ti a 33 hoc sinh.

258Cho biu thc M=2004: m5 ( m l s t nhin khc 0). Tm m biu thc M c gi tr ln nht.m = 1

259Mt lp c 30 hc sinh. trai nhiu hn gi. Mt hm c lp i xem phim. trong gi ngh cc em gi th mua bnh scla, cc em trai th mua bnh sa. C hai loi bnh gi l s nguyn. Nu cc c gi mua bnh sa, cn cc cu con trai mua bnh socola thi lp tit kim c 2 (n vi) tin. Hi c bao nhiu hoc sinh nam v hoc sinh n?16 nam, 14 n

260C 7 ci cc nga trn bn, mi ln c chuyn chiu ca ba ci cc( hoc ang up th nga hoc ngc li). Hi sau bao nhiu bc th tt c cc cc u p xung?3 lnLn 1 Up 3 caiLn 2 up 2 cai va nga 1 cai a upLn 3 up 3 cai ang con nga!

261Cho tam gic u ABC, gi D l im gia AB. k DE , EF, va FG vung gc ln lt vi AC, CB, va AB. Tinh din tich tam giac GDE bit din tich ABC bang 1.3/32

262Ti mt cuc thi, hc sinh phi tr li 20 cu hi. mi cu nu ung c cng thm 5 im, nu sai thi bi tr 2 im. Cu no khng tr li thi nhn 0 im. BT CHI thi at kt qu 48 im. Hi c bao nhiu cu tr li ng?Gi s 20 cu u tr li ng th s im l:5x20=100So vi thc t, s im d ra l:100-48=52S d c s im ny do:Nng cu khng tr li t 0 ln 5Nng cu sai t -2 ln 5 (tc l nng ln 7)Ta lp bng tm s cu khng tr li v s cu sai (tng s im ca 2 loi cu ny l 52). (Em khng bit k bng!!!)C 2 TH:1)Ta tm c 6 cu sai v 2 cu khng tr li, suy ra s cu ng l:20-(6+2)=12(cu)Th li:12x5-6x2+2x0=482)Ta c 1 cu sai, 9 cu khng tr li. S cu ng l:20-(9+1)=10(cu)Th li:10x5-1x2+9x0=48

263Tm 3 s bit tng 3s l 162,5 v s th 1 2 = s th 2 3= s th 3 4.S th 1/s th 2=3/2=6/4S th 2/ S th 3=4/3S th 1 la 6 phnS th 2 la 4 phnS th 3 la 3 phnS th 1: 162,5:(6+4+3)6=75S th 2: 75:64=50S th 3 : 50:43=37,5

264a)S(BED) = 1/3 S(ABD) ( ED x 3 = AD, chung chiu cao h t B)S(ABD) = 2/5 S(ABC) ( BD=2/5 BC, chung chiu cao h t A)=> S(BED) = 1/3 x 2/5 = 2/ 15 S(ABC)Vy S(ABC) =30cm2b) Coi S(BED) l 2 phnS(EDC) l 3 phnS( ABE) l 2x2 = 4 phn=> S(BEC) l 2 + 3 = 5 phnT s S(BEC)/S(ABE) = 5/4M hai hnh ny chung y BE => chiu cao h t C = 5/4 chiu cao h t A xung y BES(ECN) =5/4 S(AEN) ( chung y EN, chiu cao h t C = 5/4chiu cao h t A xung y EN)M hai hnh ny chung chiu cao h t E xung AC nn CN= 5/4 AN

265C 4 t c phn cng lm v sinh sn trng. Nu ch c t 1, 2, 3 cng lm th sau 12 pht s lm xong. Nu ch c t 2, 3, 4 cng lm s lm xong trong 15 pht. Nu ch c t 1,4 lm th lm trong 20 pht. Hi trung bnh mi t s lm xong cng vic trong bao lu?1' t 123 lam c 1/12 cng vic. 1' t 234 lam c 1/15 cng vic. 1' t 14 lam c 1/20 cng vic. 1' ca 4 t lam c (1/12+1/15+1/20):2=1/10. Vy thi gian ca 4 t lam ht cng vic la 1:1/10=10'.Trung binh 1 t lam trong khoang thi gian la 104=40'.

266Trung bnh cng ca ba s l 1008 . Tm ba s bit rng s th nht gp ri s th hai v bng 1/3 s th ba .S th nht chim 3 phnS th 2 chim 2 phn ( v s th nht gp ri s th 2 m)S th 3 chim 9 phn ( v s th nht bng 1/3 s th 3 m)Ta c:Tng 3 s l : 10083=3024Tng s phn bng nhau l: 3+2+9=14Gi tr 1 phn l : 3024: 14= 216S th nht l: 2163=648S th2 l : 2162=432S th 3 l : 2169=1944

267Tim s ln nht c cc ch s khc nhau sao cho khng th chn t ba ch s c tng ca chung l 19?

268Hnh tam gic c di y 5/7m v chiu cao bng 3/5 di y. Tnh din tch hnh tam gic .Chiu cao ca tam gic 5/7 x 3/5 = 3/7 m Din tch tam gic l 5/7 x 3/7 x 1/2 = 15/98 m2

269Nm nay tri ma gi thun ha, vn da ca nh An Tim kt nhiu qu ln. Qu ki lc t 100kg, trong lng ng t 1% cn lng nc l 99%.Nhng An tim li bun du v nh mch v - khng mang v nhanh thi phi nng da bc hi, lng ng mi ngy s tng gp i - ngt qu. V An tim thng chng , chiu hm sau lng lng mn c xe ko 60kg ra gip chng mang c qu da v nh. Hi v AN TIM lm sao mang dc v?

270Hy vit tt c cc s c 3 ch s t ch s 0,8,9Chn hng trm: c 2 cch chn ( tr 0)/ Hng chc c 3 cch chn, hng n v 3 cch chn: 2 x 3 x 3 = 18 s

271Tm nhng s c 2 ch s m khi cng thm vi 4 th tng cc ch s gim i mt na?19, 28, 37, 46

272Mt hnh lp phng c th tch l 64 dm3. Tnh din tch ton phn ca hnh lp phng .Ta thy:3x3x3=274x4x4=64Do DT ton phn l: 4x4x6=96(dm2)

273Bi 1: V gi tin 1 bn t hn 1 gh l 325000 nn s tin mua 6 bn nhiu hn mua 6 gh l:325000x6=1950000 .Vy mua 6 bn 10 gh th ht 5470000.Gi s i 6 bn thnh 6 gh th s tin gim 1950000. Khi mua 6 gh v 10 gh ht s tin l:5470000-1950000=3520000.Gi tin mt gh l:3520000:16=220000.Mua 10 gh th ht:220000x10=2200000.S tin cn li mua bn, vy mi bn c gi l(:5470000-2200000):6=545000.p s:Ci bn c gi l:545000 ngBi 2: quay hnh vung thnh hnh thoi.Vy dxd: 2 = 40 ( d - ng knh hnh trn - d - ng cho hnh thoi)=> d x d = 80M S(hnh trn) = r x r x 3,14=> r x r = 80 : 2 : 2 = 20S( hnh trn) = 20 x 3,14 = 62,8=> tng : 62,8 - 40 = 22,8

274B v con cng ua v ch. B bc c 6 bc thi con bc c 7 bc. B cho con i trc 30 bc thi bt u ui theo. 3 bc ca b di bng 5 bc ca con. Hi sau bao nhiu bc thi ui kp?Con ang i trc b 30 bc nn cn s ln bc 6 bc l 30 : 3 = 10 lnvy b phi bc 10 x 6 = 60 bc

275Trung bnh cng ca 5 s l lin tip l 61. tm 5 s .Cch 1: v 61 l TBC ca 5 s l lin tip nn n bng s gia. V hai s l k lin nhau hn km nhau 2 n vi nen ly 61-2 se duoc s lin trc 61; cn ly 61 cng 2 th c s lin sau 61. ...... Nm s phi tm l 57; 59; 61; 63; 65Cch 2:Tnh tng ca 5 s phai tm 61 x 5 = 305 sau v s on thng a v dng ton tm s khi bit tng v t s ; S u tin 1 phn, s th hai 1 phn nh vy v thm 2 n v, s th ba gm 1 phn v 4 n v. Tng t nh vy v s . S u tin c tnh nh sau: ( 305 - ( 2+4+6+8 ) ) : 5 = 57 Sau cng thm 2 th c s 59; cng thm tnh cc s cn li.

276nhn dp ngy l, ca hng gim gi 10% 1 chic in thoi, tuy vy ca hng vn li 8% gi vn. Hi nu khng gim gi th ca hng li bao nhiu % gi vn?Cch 1: Coi Gi cha gim : 100%=>Gi khi gim : 90%Coi gi vn : 100%=> Gi khi gim : 108%Gi cha gim/Gi khi gim : 100/90= 30/27Gi khi gim/ gi vn : 108/100=27/25=> Gi cha gim so vi vn : 30 : 25x 100% = 120%vy li 20%Cch 2:Gia s tin vn la 100.000 thi gia ban sau khi giam la 108.000, tg ng vs 90%. Nh vy gia ban ban u se la 108.000 : 90 * 100 = 120.000. => lai so vi gia vn la 20%

277C bao nhiu s chn c ba ch s c lp thnh t cc ch s 2,3,5 va 7v l s chn nn s cn tm s l ab2, a chn 1 trong 4 s nn a c 4 cch chn b cng c 4 cch chn vy lp c 4 4 = 16 s

278Bi 1: Hai ngi cng lm mt cng vic trong 16 gi th xong. Nu ngi th nht lm trong 3 gi v ngi th hai lm trong 6 gi th h lm c 25% cng vic. Hi mi ngi lm mt mnh cng vic trong bao lu s hon thnh?Bi 2: CHo mt tam gic ABC c din tch l 216m2, AB = AC v BC = 36m. Trn cnh AB ly im M sao cho MB = 2/3AB, trn cnh AC ly im N sao cho NC = 2/3AC v trn cnh BC ly im I sao cho BI = 2/3BC. Ni M vi N v N vi I c hnh thang MNIB. Tnh:a) Din tch hnh thang MNIBb) di on MNBi 1: V ngi 1 l trong 3h, ngi 2 lm trong 6h c 25% cng vic. Vy ngi 1 lm trong 12h v ngi 2 lm trong 24h th xong cng vic. Do ngi th 2 lm 1 mnh trong 12h c 1/4 cng vic. Do vy ngi th 2 lm 1 mnh ht 12x4=48h.1h ngi 2 lm 1/48 cng vic 1h 4 ngi 1 lm l 1/16 - 1/48 = 1/24 cv. Vy ngi th 1 lm 1 mnh trong 24hBi 2:a) S(MNBI)=144b) MN=12

279Lc 6h sng mt chic tu thy ch khch xui dng t A n B ri ngh li 2h n khch, sau li ngc dng v v n A lc 3h20phut chiu cng ngy. Hy tnh qung ng t A n B, bit rng thi gian i xui dng nhanh hn thi gian i ngc dng 40 pht v vn tc ca dng nc bng 50m/pht.120km

280C 40 bnh c ng vo hp gm 2 loiMi hp ln c 3 bnhMi nh c 2 bnhS hp ln nhiu gp 2 s hp nhMi loi c bao nhiu hp?2 hp ln va 1 hp nho co s bnh la 32 +2= 8 (chic bnh) s cp la 40:8=5 S hp ln: 5.2=10 S hp nho: 5.1=5

281Khi bn mt sn phm nu gim 10% th li 8%, Hi nu khng gim th li bao nhiu phn trm.Ta c: ( 0,9gi bn- gi gc)/gi gc = 0.08. Bin i c gi bn = 1.2 gi gc.Li sut khi gi bn khng i l: ( gi bn- gi gc)/ gi gc= ( 1.2 gi gc- gi gc)/gi gc = 0,2 = 20%

282Thuyn Trng Jack ni vi con trai: Nu ly ba ln bnh phng tui ca con thm 26 thi bng bnh phng tui ca b.Tui b v con l 100> a > b > 0. Nh vy th: a x a = 26 + 3 x b x b. Do 3xbxb l s chia ht cho 3, m 26 chia 3 d 2 nn a x a cng phi chia 3 d 2, nhng iu ny ko bao gi xy ra v axa ch c th chia ht cho 3 hoc chia 3 d 1.

283Cho 2 s 9 v 11. Hy tm s a sao cho m mi s cho tr i a th c 2 s mi c thng bng 2Cng bt mi s i a n v th hiu 2 s ko i.Hiu ca 2 s sau khi bt l 11-9 = 2T s ca 2 s sau khi bt l 1/2S b sau khi bt bng :2 : ( 2 - 1 ) x 1 = 2S ln sau khi bt l : 2 x 2 = 4.S cn tm l : 9 - 2 = 7 hay 11 - 4 = 7

284Hy cho bit c tt c bao nhiu phn s m tng ca t s v mu s ca mi phn s bng 2013?y l li gii ci bp ca em:Xut pht t: Thm vo t (mu) v bt mu (t) cng 1 s th tng (t +mu) s khng i. Ta c :1/2012; 2/2011; 3/2010;..;2010/3; 2011/2; 2012/1D dng thy c 2012 phn s c t + mu=2013

285Hnh vung c 4 cnh m theo ng th i c mi hnh vung c 3 cnh. 4 hnh l i 12 cnh ht 1h15'=75 pht. Cn AB ng xanh th mi hnh ht 1 canh. vy 4 hnh l 4 cnh. i ng xanh it hn i ng 1/3. Vy thi gian ng xanh i ht l: 75:3=25 pht.

286Tm mt s c 3 ch s, bit rng tch cc ch s l s trn chc c 2 ch s v nu thm vo s 12 n v th ta c s c 3 ch s ging nhauNhn xt s cn tm phi c cc ch s khc 0.111-12= 99 (loi v l s c 2 ch s)222-12=210( cng loi lun v c ch s 0)333-12=321(loi gp v tch cc ch s khng trn chc)444-12=432(loi v l do nh trn)555-12=543 (chn)666-12=654(loi gp v tch cc ch s l s c 3 ch s)Ti ay ta khng xt tip v tch s l s ln hn 2 ch s.Do s cn tm l 543

287Khi cng mt s thp phn co ba ch s phn thp phn vi mt s t nhin,do s sut,mt hoc sinh a bo qun du phay cua s thp phn va t phep tinh nh cng hai s t nhin.vi vy kt qua cua phep tinh tng thm 1232,766 n vi. Tm s thp phn o.t s thp phn cn tm l 1 phn th s qun du phy l 1000phnNh vy s 1232,766 tng ng vi 1000-1=999 phnDo s thp phn cn tm l:1232,766:999=1,234

288Cho tam gic ABC, D l im chnh gia BC, M l im chnh gia AD. BM ct AC ti E. Chng minh EC = 2 AE.Ni M vi C. Ta co din tich MBD bng MDC vi chung chiu cao ha t M va BD =DC. Mt khac ta co din tich MBD=ABM vi AM=MD va chung ng cao ha t B. Vy din tich MBD=ABM=MDC. Din tich BMC=BMD+DCM=2ABM nn chiu cao ha tC gp i chiu cao ha t A, chung ay BM. T o din tich AME=EMC vi chung ay ME va chiu cao ha t C gp i ha t A. Suy ra 2AE= EC vi din tich AME=EMC chung ng cao ha t M

289Mt quyn sch c s trang hn 300 v t hn 5000. Tt c cc trang c nh du v tt nhin l bt u t trang th nht (1.) anh du nhng trang cui cng, ngi ta cn 23 ch s. Hi quyn sch c bao nhiu trang? ( nu quyn sch t hn 300 trang , xc inh mi kh nng c th ?)1004 trang.

290Mt onn hoc sinh xp thnh hang 10m ang i u bc. Bn lp trng i t cui hng ln u hng ri quay li i v cui hng. Bit rang lp truongr i nhanh bng 3 ln on ang i. Hi c on i c nao nhiu m?

291Cho hnh thang ABCD, y AB= 2/3 y CD, AC v DB ct nhau ti E.a) Tnh S AED bit S ABE = 4 cm2.b) So snh AE v EC.a. V ng cao BH xung AC, ng cao DI xung AC : c S(ABC) = 2/3 S(ADC) (chung chiu cao hnh thang, y AB = 2/3 DC) . M hai tam gic ny c chung y AC nn chiu cao BH = 2/3 DI. Xt trong tam gic ABE v ADE c: chung y AE, chiu cao BH = 2/3 DI. -> S (ABE) = 2/3 S (ADE) -> S(ADE) = 4X3/2 = 6 cm2b. Din tich ADC=3/2ABC vi DC=3/2AB,cung chju cao hinh thang. Goi chiu cao ha t D va B n AC la H va L. DH=3/2BL vi chung ay AC va din tich ADC=3/2ABC. Din tich ADC=BDC vi chung ay DC va chiu cao bng nhau. Hai tam giac nay co chung tam giac DEC nn din tich AED=EBC. AE=2/3EC vi din tich AEB=EBC,DH=3/2BL. Din tich BEC=3/2ABE=3X4:2=6 cm vungvi chung chju cao, AE=2/3EC. Vy SADE bng 6cm2. Cu a ta a chng minh AE=2/3EC

292cho hnh vung cnh 1 dm, ni trung im 4 cnh to thnh hnh vung th 2. Li ni trung im bn cnh hnh vung th hai c hnh vung th 3, c nh th n hnh vung th 10. Tnh tng din tch 10 hnh vung

293M chia cho 3 d 1, M chia 5 d 4 hoi M chia 15 d my?S cng thm 11 th chia ht cho c 3 v 5 hay chia ht cho 15. Vy s chia cho 15 th d 4 (15-11=4)

2942 s thp phn c tng bng 106,16. Nu chuyn du phy ca s b sang phi mt hng ta c mt s mi hn s ln 106,8 n v. Tm s ln.

29560-61+50-51+40-41+30-31+20-21+10-11+70{70-61}+{60-51}+{50-41}+{40-31}+{30-21}+{20-11}+10=9+9+9+9+9+9+10=64

296Tm quy lut ca dy s sau v vit tip 2 s na : 2,3,9,31, . . ..Quy lut cua day la mi s hang k t s hang th 3 bng tich hai s hang lin trc no ri cng vi s th t cua s hang o. Nh s 9=2x3+3(s 9 ng vj trj th 3 trog day) 31=3x9+4. Vy 2 s tjp theo la 9x31+5=284 va 31x284+6=8810

297Cho ba s thp phn: 7,12; 8,46 v s th ba ln hn trung bnh cng ca c ba s l 2,26. Tm s th ba?V on thng (biu din tng ca 3 s) chia lm 3 phn bng nhau mi phn l trung bnh cng (TBC), Ta thy 7,12+8,64+2,26=2xTBCSuy ra: TBC=17,84:2=8,92Vy s th 3 l: 8,92+2,26=11,18

298Cho 1 hnh vung, nu tng cnh hnh vung thm 7cm th din tch hnh vung tng thm 371 cm2. Tm din tch hnh vung cho.Gi cnh hnh vung l a, ta c biu thc sau: (a7)+(a7)+(77)=371 2(a7)+49=371 2(a7)=371-49=322 (a7)=322:2=161 suy ra a=161:7=23

299Cho dy s 6, 7, 9. 12, 16. hi s 61 l s hng th bao nhiu ca dy?Theo quy lut tng dn th 61 l s hng ng th 11.V 6,7,9,12,16,21,27,34,42,51,61

300Cho tam giac ABC vung tai A. AB=30cm. N la trung im cua AB. M la trung im cua BC. Ni CN va AM giao nhau O. Hay tim dai ng cao cua tam giac AOC ha t O ?

STTCu hiLi gii

301Tm 3 ch s a, b, c bit 1/ (a+b+c) = 0,abc1/(a+b+c) = 0,abc tc l 1000/(a+b+c) = abc. Tc (a+b+c) l c s ca 1000. abc>100 nn c s (a+b+c) < 1000/100=10.cc c s 3 nn ch c th l 4 hoc 8.th 2 trng hp:a+b+c=4, abc=1000/4=250 khng tha mn.a+b+c= 8, abc=1000/8=125. ng tha mn yu cu u bi.

302Mt san phm trong siu thi ngay u c ban vi gia 20.000. Hm sau do ha gia nn s ngi mua san phm tng thm 12,5% so vi ngay u. Hoi hm sau gia san phm la bao nhiu?

303c bao nhiu s c 3 ch s khng chia ht cho 5?C 900 s c 3 ch s. Ta i tm s s hng chia ht cho 5 trong cc s . Cc s chia ht cho 5 to thnh mt dy s cch u vi khong cch l 5: 100, 110, 115...., 995. Vy c: (995 -100): 5 +1 = 180 s c 3 ch s chia ht cho 5. Vy c s s hng chia ht cho 5 l: 900 - 180 = 720 s

304S=1/4+1/9+1/16+...+1/10000chng to S Chiu cao h t nh A = 1/2 chiu cao h t nh C.S(AOD)= 1/2 S(DOC)( chung y DO, Chiu cao h t nh A = 1/2 chiu cao h t nh C)M S(AON) = S(DON)=> Coi S(AON) = S(DON) l 1 phn=> S(DOC) l (1+1) x 2 = 4 phnT s S(DOC)/S(DNC) = 4:(1+4)= 4/5M S(DNC) = 1020:2=100 cm2=> S(DOC)= 1004/5=80 cm2S(ABCD) = 2020 = 400 cm2S(MBCO) = 400-(100+80)= 220 cm2

308Khng thc hin php tnh lm cach nao tht gon xac inh cc s con thiu trong cc tch sau y:1) 15 x 14 x 13 x 12 x11 =3603xy ?2) 1 x 3 x 5 x 7 x 9 x 11 = 10 x9y ?

a.1514131211=5314134311=920141311chia ht cho 9 v10 nn y=0. M:3603x0 chia ht cho 9 nn 3+6+0+3+x+0 chia ht cho 9. Suy ra x = 6.b.1357911 chia ht cho 5 v 9. M tch khng c s chn nn y=5. M: 10x95 chia ht cho 9 nn 1+0+x+9+5 chia ht cho 9 . Suy ra x=3

309"bai toan chia tao" Nu mi ngi 4 qua thi tha 11 qua .nu mi ngi 6 qua thi thiu 21 qua . Hoi co bao nhiu qua , bao nhiu ngi ? .Gi s ngi c chia to l a, ta c