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Turli matematik masalalar

1. Uchoqda sayohat qilganda, yo'lovchilarga o'zlari bilan olishga muayyan og'irlikdagi yuk ruhsat etilgan. Har kilogram ortiqcha yukka yo'lovchi 10 dollar ustama to'lashi kerak. Agar 40 kilogram yuk olib ketayotgan yo'lovchi 50 dollar to'lagan bo'lsa, 80 kilogram olib ketayotgan yo'lovchi qancha pul to'lashi kerak?

2. Ikki yog'ochli kubchaning yoqlarida shunday raqamlar yozilgan-ki, bu ikki kubcha yordamida oyning istalgan kunini tasvirlash mumkin. Bunga erishish uchun qanday raqamlar yozish kerakligini aniq ko'rsating.

3. a = 1, b = 2, c = 3, ... , z = 26 bo'lsin. Quyidagi ifodaning qiymati nechaga teng: (x - a)(x - b)(x - c)...(x - z)?

4. 13 soni tub son va uning aksi 31 ham. Aksi tub son bo'lgan nehcta ikki xonali tub son topa olasiz?

5. Matematika fanidan testda taxmin qilishdan qaytarish uchun Malikning o'qituvchisi har bir no'to'g'ri javob uchun yetti bal olib tashlashini e'lon qildi. Biroq, har bir to'g'ri javob bahoga faqatgina besh bal qo'shadi. Malik hamma misollarga javob berdi va "teng qildi". Boshqacha aytganda, u roppa rosa nol oldi. Malik testdagi 24ta misoldan qanchasiga to'g'ri javob bergan?

6. Linda, Aziza va Iroda qarta o'ynashga qaror qilishdi. Ular hisobni bodom yordamida qilishdi. Ular o'zaro quyidagi shartga kelishishdi: kim o'yinni yutqazsa, boshqalarga ularda qancha bodom bo'lsa shuncha bodom berishi kerak. Birinchi o'yinni Linda yutqazdi va Aziza va Irodaga har birida qancha bo'lsa shuncha bodom to'ladi. Ikkinchi o'yinni Aziza yutqazdi va Linda va Irodaga ularda qancha bodom bo'lsa shuncha bodom berdi. Uchinchi o'yinni Iroda yutqazdi va Linda va Azizaga har birida nechta bodom bo'lsa shuncha bodom berdi. Shu payt, har bir o'yinchida 8tadan bodom qoldi. Har bir o'yinchi qancha bodom bilan o'yinni boshlagan?

7. Sinfda 30ta talaba bor. O'n bittasining ko'zi ko'k. O'n beshtasining sochi qo'ng'ir. Uchta talabaning ko'zi ham ko'k, sochi ham qo'ng'ir. Nechta talabaning na ko'zi ko'k, na sochi qo'ng'ir? 

8. Sug'urta tizimi o'z mijozlariga ular uzoq vaqt kasallik davrida har oy quyidagi reja bo'yicha birinchi 240,000 ming so'm yillik maosh bo'yicha mablag' to'laydi:
               1-oy:                                hech nima
               2-4-oylar:                        oylikning 50%
               5- va keyingi oylar:        oylikning 25%
agar u kasal bo'lsa va xo'jayinidan haq olmasa. Bu reja quyidagi mijozlarga necha pul to'laydi agar:
Tursun ikki oy kasal bo'lgan, yillik maoshi 120,000 so'm va xo'jayinidan kasallik davri uchun haq olmagan bo'lsa?
Murod olti oy kasal bo'lgan, biroq birinchi ikki oy uchun xo'jayinidan haq olgan va yillik maoshi 180,000 so'm bo'lsa?
Iroda yillik maoshi 300,000 so'm, uch oy kasallik davri uchun xo'jayinidan haqini olgan va to'qqiz oy kasal bo'lgan bo'lsa?
      
9. Anjumanda Qozoqiston, O'zbekiston, Tojikiston va Qirg'izistondan jami 15ta guruh qatnashyapti. Har bir davlat turli sondagi guruhlar jo'natgan va har biridan kamida bitta guruh vakil bo'lgan Tojikiston va O'zbekiston jami 6ta guruh jo'natgan. Bitta davlat roppa rosa 4ta guruh jo'natgan. O'zbekiston va Qirg'iziston jami 7ta guruh jo'natgan. Har bir davlat tomonidan nechta guruh jo'natilganini toping? 

10. 52talik standard majmuadan siz bir qancha qarta oldingiz. Tanlangan qartalar orasida kamida bitta xonim, ikkita qarg'a, uchta zo'r (tuz) va to'rtta qisht bor. Eng kami bilan qancha qarta tanlagan bo'lishingiz mumkin?

11. 19ta talaba bo'lgan guruhning har bir a'zosi xaltasida 3, 4 yoki 5ta kitob bor. Kitoblarning umumiy soni 71ta. 4ta kitobi bo'lgan talabalar soni 10ga karrali. Nechta talabada 3ta, nechtasida 4ta va nechtasida 5ta kitob bor?

12. A qishloqning 6800 kishi aholisi bor va u har yili 120 kichiga kamayib boryapti. B qishloqning 4200 kichi aholisi bo'lib, u har yili 80 kichiga ortib boryapti. Necha yildan keyin bu ikki qishloqning aholisi tenglashadi?

13. 8ta sonning o'rta qiymati 6ga, 6ta boshqa sonlarning o'rta qiymati 8ga teng. Barcha 14 sonning o'rta qiymati nimaga teng?

14. 1 dan 200gacha sanaganda, yo'lda qancha 7dan o'tasiz? 

15. Qirralari 10cm, 4cm va 4cm bo'lgan to'g'ri burchakli parallelepiped bo'yaldi va qirrasi 1cm bo'lgan kichkina kublarga bo'lindi. Kublarning necha foizi kamida bir yoqdan bo'yalgan?

16. Saylda 20ta katta kishi yoki 32ta bolalarga yetadigan yemish bor. Agar saylda 15ta katta kishi bo'lsa, yana nechta bolani to'ydirsa bo'ladi?

17. AQShda Dildora va Dilfuza yegulik sotib olishmoqchi bo'lishibdi. Ular pullarini qo'shishganlarida 25, 10 va 5 tsentlik tangalardan iborat $4 chiqibdi. Agar ularda 35 dona tanga va 25 tsentlik tangalar soni 5 tsentlik tangalar sonidan ikki baravar kam bo'lsa, ularda qancha 25 tsentlik tanga bor? 

18. 64-maktabning 120ta yuqori sinf o'quvchilari shahmat, shashka yoki har ikkala to'garak a'zosi. Agar shashka to'garagida 90ta va shahmat to'garagida 70ta o'quvchi bo'lsa, har ikkala to'garakda nechtadan o'quvchi bor?

19. Shunday son toping-ki, agar uni kvadratga oshirsa, 27 qo'shsa, 3ga ko'paytirsa, kvadrat ildiz chiqarsa va 18 ayirsa, hech narsa qolmaydi.

20. Men 100 va 200 sonlari orasidagi sonman. Men o'ngga va chapga bir hil o'qilaman. Mening raqamlarim yig'indisi 8. Men kimman?

21. Maktabda 600 nafar, har bir sinfda esa 30 nafar o'quvchi bor. Har kuni har bir o'quvchining  5ta va har bir o'qituvchining 4ta darsi bor. Har bir darsda to'liq sinf o'quvchilari va bitta o'qituvchi bor. Maktabda nechta o'qituvchi bor?

22. Mening tog'am har bir shag'am qoldig'ini asrab qo'yishini va yettita shag'am qoldig'idan yangi shag'am yasashini aytdi. Agar tog'am 92ta shag'am sotib olgan bo'lsa, nechta shag'am yoqishi mumkin?

23. Ma'lum bir quvur cho'milish hovuzini 2 soatda to'ldirishi mumkin; boshqa quvur esa  uni besh soatda to'ldirishi mumkin; uchinchi quvur esa hovuzni olti soatda bo'shatishi mumkin. Agar hovuz bo'sh bo'lib, uchala quvur bir vaqtda yoqilgan bo'lsa, hovuzni to'ldirish uchun qancha vaqt kerak bo'ladi?

24. Qodir Sevaraga "Agar menga sakkiz dollar bersang, bizda teng miqdordagi pul bo'ladi" dedi. Sevara "Balki, biroq agar menga sakkiz dollar bersang, sendan ikki baravar ko'p pul bo'ladi" deb javob berdi. Har bir qizda qancha pul bo'lgan?

25. (1 + 1/2)(1 + 1/3)(1 + 1/4) ... (1 + 1/2005) = ?

26. Qaysi son kattaroq va nima uchun: 191919/999999, yoki 191919191919/999999999999?

27. Omborda ikkita bir xil idish bor: biri moy bilan to'la, ikkinchisi yarmigacha. Ularning og'irliklari 86kg va 53kg. Bo'sh idishning o'g'irligini toping?

28. Quyidagi sonlardan to'rtta to'plam shunday tuzing-ki, har bir to'plamdagi sonlar yig'indisi 300 bo'lsin.
27        41         67         12         To'plam A:     ,     ,      va         
89        24        168        76         To'plam B:     ,     ,      va          
6          31         123    186          To'plam C:     ,     ,      va          
154     91          75        30          To'plam D:     ,     ,      va          

29. 16 sonini bir qancha ketma-ket butun sonlar yig'indisi shaklida ifodalay olasizmi?

30. Ikki butun sonning yig'indisi 968. Ulardan biri nol bilan tugaydi, biroq bu nolni o'chirsangiz, ikkinchi son hosil bo'ladi. Bu qanday sonlar?

31. Har qanday vaqt SS:DD:SS ko'rinishida ifodalanadi. Ya'ni, 3 soat, 54 daqiqa va 20 soniya bo'ladi: 03:54:20. Yana, yilning ixtiyoriy kuni KK/OO ko'rinishida ifodalanadi.  Ya'ni, 5 iyul bo'ladi: 05/07. 0 dan 9gacha barcha raqamlardan foydalanib SS:DD:SS KK/OO shaklda yozish mumkin bo'lgan yilning eng kech vaqtini ayting.

32. Bir qatorda beshta to'p bor: sariq, jigarrang, ko'k, qizil va yashil. Agar ko'k to'p markazda bo'lmasa, qizil to'p ko'k to'pdan ko'k to'p yashil to'pdan qancha uzoq bo'lsa shuncha uzoqda bo'lsa, sariq to'pning chap qo'shnisi qizil to'p bo'lsa, bu to'plarning tartibini toping.

davomi bor...
Various math problems

1. When traveling by aircraft, passengers have a maximum allowable weight for their luggage. They are then charged 10 dollars for every kilogram overweight. If a passenger carrying 40 kg of luggage is charged 50 dollars, how much would a passenger carrying 80 kg be charged?



2. Two wooden cubes have digits painted on each face in such a way that it is possible to display any date of the month. Show clearly how you would label each face to achieve this.


3. Let a = 1, b = 2, c = 3, ... , z = 26. What is the exact value of (x - a)(x - b)(x - c)...(x - z)?

4. The number 13 is prime and so too is its reverse, 31. How many two digit primes can you find for which their reverse is also prime?

5. To discourage guessing on a math test, Malik's teacher announced that she would take off seven points for every wrong answer. However, each correct answer only added five to the score. Malik attempted all the problems and "broke even". In other words, he got exactly zero points. Of the 24 problems on the test, how many did Malik get correct?

6. Linda, Aziza, and Iroda decide to play cards. They keep score using almonds. They agree that when a player loses a hand, she will give each of the others an amount equal to the amount each player already has. Linda loses the first hand and pays Aziza and Iroda the amount of peanuts each has; Aziza loses the second hand and pays Linda and Iroda the amount of peanuts each has; Iroda loses the third hand and pays Linda and Aziza the amount of peanuts each has. At this point, each player has 8 almonds. How many almonds did each player start with?



7. There are 30 students in a class. Eleven have blue eyes. Fifteen have brown hair. Three students have both blue eyes and brown hair. How many students have neither blue eyes nor brown hair?

8. An insurance scheme pays benefits to its members who are sick for extended periods of time at the following rates
       1st month:                                       nil
       2nd-4th months:                             50% of normal salary
       5th and succeeding months:        25% of normal salary
on the first 240,000 som per annum of salary for each month in which the member is sick and is not paid by the employer. How much does the scheme pay to:
Tursun, who is off work for two months, whose salary is 120,000 som per annum, and who gets no sick pay from his employer?
Murod, who is ill for six months, but who is paid normally for the first two months by his employer and whose salary is 180,000 som per annum.
Iroda, whose salary is 300,000 som per annum, who gets 3 months sick pay from her employer, and who has to take nine months off?
      
9. A total of 15 delegates from Kazakhstan, Uzbekistan, Tajikistan, and Kyrgyzstan are attending a meeting. Each country sent a different number of delegates, and each was represented by at least one delegate. Tajikistan and Uzbekistan sent a total of 6 delegates. One country sent exactly four delegates. Uzbekistan and Kyrgyzstan sent a total of 7 delegates. How many delegates were sent by each country?

10. You take out some cards from a standard pack of 52. Of those selected, there is at least one queen, two cards in the spades suit, three aces and four cards in the diamonds suit. What is the fewest number of cards you could have removed?

11. Each of a group of 19 students have 3, 4 or 5 books in his/her bag. The total number of books is 71. The number of students who had 4 books each is a multiple of 10. How many students have 3 books each, how many 4 and how many 5? Answer:

12. Village A has a population of 6,800, which is decreasing at a rate of 120 per year. Village B has a population of 4,200, which is increasing at a rate of 80 per year. In how many years will the population of the two villages be equal? Answer:

13. The average of 8 numbers is 6, the average of 6 other numbers is 8. what is the average of all 14 numbers?

14. If you count from 1 to 200, how many 7's will you pass on the way?

15. A right-angle parallelepiped with edges 10, 4 and 4 was painted and divided into cubes with an edge of 1. What percent of the cubes are painted at least from one side?

16. There is enough food at a picnic to feed 20 adults or 32 children. If there are 15 adults at the picnic, how many children can still be fed?

17. Sue and Nancy wish to buy a snack. They combine their money and find they have $4.00, consisting of quarters, dimes, and nickels. If they have 35 coins and the number of quarters is half the number of nickels, how many quarters do they have?

18. All of the 120 seniors in Coolidge High School are members of the chess club, the pep club or both. If 90 seniors are in the pep club and 70 seniors are in the chess club, how many seniors are in both clubs?

19. Find the number that, if you square it, add 27, multiply it by 3, take the square root and subtract 18 you end up with nothing.

20. I am a number between 100 and 200. I read the same forward and backward. The sum of my digits is 8. Who am I?

21. There are 600 students in a school, 30 students in every class. Every student has 5, and every teacher has 4 lessons every day. In every lesson there is a full class and one teacher together. How many teachers are there in the school?

22. My uncle said that he saves every candle-leftover, and he can make a new candle from the wax leftovers of seven candles. How many candles can he burn if he bought 92 candles?

23. A certain pipe can fill a swimming pool in 2 hours; another pipe can fill it in five hours; a third pipe can empty the pool in six hours. With all three pipes turned on at exactly the same time, and starting with an empty pool, how long will it take to fill the pool?


24. John says to Brenda, "If you give me eight dollars, we will have an equal amount of money." Brenda responds, "That may be true, but if you give me eight dollars, I will have twice as much money as you." How much money did John and Brenda each have?

25. (1 + 1/2)(1 + 1/3)(1 + 1/4) ... (1 + 1/2005) = ?

26. Which number is greater and why: 191919/999999, or 191919191919/999999999999?

27. In a warehouse there are two identical barrels: one of them is full of oil, the other one is exactly half way. Their masses are 86 kg and 53 kg. What is the mass of an empty barrel?

28. Find four sets of numbers from the grid below that each total 300.
27        41        67        12          Set A is       ,       ,       and          
89        24        168        76        Set B is       ,       ,       and          
6          31        123        186      Set C is       ,       ,       and       
154        91        75        30        Set D is       ,       ,       and          

29. Can you get 16 as the sum of a few consecutive integers?

30. The sum of two whole numbers is 968. One of them ends with a zero, but if you delete this zero, you get the other number. What are these numbers?

31. Any time, can be displayed as HH:MM:SS. So, three fifty four and twenty seconds is 03:54:20. Also, any day of the year can be displayed as DD/MM. So, the 5th of July is 05/07. What is the latest point in the year when you can use all digits from 0 to 9 to display the date in the format HH:MM:SS  DD/MM?


32. There are five balls in a row: a yellow, a brown, a blue, a red and a green. Find their order if you know that the blue ball is not in the middle; the red is the same distance from the blue, as the blue is from the green; the left-side neighbor of the yellow is the red ball.

to be continued...
 
 
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