1. Introduction…. Our objectives…. Go To Math Challenges Math Challenges for Second Year Students!!!

2. In this part of our blogsite you will find yourselves solving math challenges one after another!!!! Hence you will learn more and more about math and it’s mysteries. HOME

3. To enhance and amplify the abilities of the students about math To have fun answering math challenges To apply their mathematical learning and such HOME

4. GOOD LUCK!!!! HOMENext

5. Challenges #1 Challenges #2 Challenges #3 Challenges #4 Challenges #5 Challenges #6 Challenges #7 Challenges #8 Challenges #9 Challenges #10 Challenges #11 Challenges #12 Challenges #13 Challenges #14 Challenges #15 Challenges #16 Challenges #17 Challenges #18 Challenges #19 Challenges #20 ANSWERSANSWERS HOMEHOME

6. CHALLENGE #1 4 2X+Y = 256, 4 x+2y = 1024. What is the value of y? BACK

7. CHALLENGE #2 A number is called “CUTE” if it has exactly four positive integer divisor. What pecent of the first 25 positive integer are cute? BACK

8. CHALLENGE #3 If 1 * 3 = 5, 6 * 9 = 21 and 8 * 2 = 18. Find the value of 11 * 20. BACK

9. CHALLENGE #4 A man and his grandson have the same birthday. For six consecutive birthdays, the man is an integral number of times as old as his grandson. How old is the man? BACK

10. CHALLENGE #5 Divide the number 185.058 into three parts such that half of the first part, a third of the second part and a quarter of the third part are all equal. How much is each part? BACK

11. CHALLENGE #6 A man paces off thirty steps east, followed by ten steps north, ten steps east, and twenty steps north. How far is he from his starting point? BACK

12. CHALLENGE #7 What is the value of x 3 +1/x 3 if (x+1/x) 2 =3? BACK

13. CHALLENGE #8 If ab=2, bc=4 and ac=8, find abc. BACK

14. CHALLENGE #9 In a number of cows and chickens, the number of legs is 14 more than twice the number of heads. How much can you find about the number of cows and chickens involved? BACK

15. CHALLENGE #10 Express in simplest form the quotient x+x 2 +x 3 +x 4 +x 5 +x 6 +x 7 x 3 +x 4 +x 5 +x 6 +x 7 +x 8 +x 9 BACK

16. CHALLENGE #11 If x 4 +y 4 = 2 and x 8 +y 8 = 3, what is the value of x 16 +y 16 ? BACK

17. CHALLENGE #12 The sum of the squares of two numbers is 225 and the square of their sum is 441. what is reciprocal of their product? BACK

18. CHALLENGE #13 A rectangular pool is 50% longer than it is wide. It is surrounded by a path 1 meter wide. If the area of the path is 44 sq. meters, what is the area of the pool? BACK

19. CHALLENGE #14 How many guests were present at a Chinese dinner if every two guests shared a bowl for rice, every three guests shared a bowl for broth, every four guest shared a bowl for meat and 65 bowls were used altogether BACK

20. CHALLENGE #15 Mang Itoy was single for 2/5 of his life. For 1/3 of the remainder he had wife, and for the remaining 24 years he has a widower. How old was he when he died? BACK

21. CHALLENGE #16 What is the largest number that evenly divides the sum of any five consecutive numbers? BACK

22. CHALLENGE #17 Move one digit to make 101 – 102 = 1 true. BACK

23. CHALLENGE #18 Find the sum of the digits of all numbers in the sequence 1, 2, 3, 4, …………….…….10,000. BACK

24. CHALLENGE #19 Laura can buy a bracelet and a watchband for P500, or a watchband and a locket for P600, or a locket and bracelet for P700. how much does each cost BACK

25. CHALLENGE #20 Two candles of equal length start burning at the same time. One of candles will burn down in 4 hours, the other in 5 hours. How many hours will they have to burn before one candle is three times the length of the other? BACK

26. THE ANSWERS Next

27. 1. Y=2 2. Explore! All primes have to be obviously omitted. The 1 st one he is 6 with 1, 2, 3 and 6 as divisors. The others are 8, 10, 14, 15, 21 and 22. Hence 7/25 = 28% are cute. Ask students to generalize which positive integers are cute. (Those which are products of two primes) 3. 11 * 20 = 42 4. 61 yrs. old 5. The first = 41,124 second = 61,680 the third = 82,248 6. 60 7. (x+1/x)2 = x2 + 2 +1/x2=3 => 8. abc= 8 9. Y=7 and there is no way to find x. If the equation is 2x+4y = 14+2 (x+y). 10. 1/x 2 Next

28. 11. 8 1/2 12. 20x 2 + 17x + 3 = (4x+1)(5x+3); 2173= 20(10) 2 + 17 (10) +3 = 41(53) 20173 = 20 (100) 2 = 17 (100) + 3 = 503 (401) 13. W= 8m L= 12m 14. 60 guest 15. 60 yrs. old 16. 5 17. 101- 10 2 =1 18. 180,001 19. Locket=P 900 Bracelet =P300 Wallet =P200 20. 40/11 hours HOME