2009 METROBANK-MTAP-DEPED MATH CHALLENGE NATIONAL FINALS GRADE 6 TEAM ORAL Part 1: 15 seconds (11 items) 1. Manila time is 4 hours ahead of Dubai time. A trip from Manila to Dubai, takes nine hours. What time will you arrive in Dubai if you leave Manila at 8:00 P.M.? Solution 8:00 P.M. + 9 hours is 5:00 A.M. 5:00 A.M. – 4 hours is 1:00 A.M. Answer: 1:00 A.M. 2. How many digits are there in the number N = 210 x 58? Solution 210 x 58 = (2 x 5)8 x 22 = 108 x 4 = 100 000 000 x 4 = 4 000 000 000 Answer: 9 3. The faces of a big cube are painted. Then the cube is cut into 125 unit cubes. How many of the unit cubes have exactly two painted faces each? Solution bottom layer: 4 x 3 unit cubes upper layer: 4 x 3 unit cubes middle layers: 4 x 3 unit cubes total number of unit cubes with exactly two painted faces each = (4 x 3) + (4 x 3) + (4x3) Answer: 36 4. What is the smallest number which when multiplied by 20 will give a perfect cube? Solution 20 = 22 x 5 So the smallest number that should be multiplied by 20 so that the product is a perfect cube is 2 x 52 which is equal to 50. Answer: 50 5. On a quiz show, each question is worth four times as much as the previous question. The fourth question is worth P1,600. How much was the first question worth? Solution 1600 ÷ 4 ÷ 4 Answer: P25
÷ 4 = 25
6. In 3 ___ 6 ___ (-9), what two different basic operations can you place in the ___ that will result to the least answer? Solution The bigger the absolute value of a negative number, the smaller is the negative number. So x (for multiplication) should be placed before -9. ÷ (for division) cannot be placed after 3 because it will be performed first and performing division then multiplication will not result to the least answer. - (for subtraction) cannot be placed after 3 also because 3 – 6 is -3 which when multiplied by -9 gives a positive answer, Therefore, + (for addition) should be placed after 3. So, 3 + 6 x (-9) = -51 Answers: +, x (order must be correct) 1
7. What number will you add to the numerator and denominator of
1 so that the 7
result becomes 4 times? Solution 4 times
1 4 is . 7 7
4 8 is equivalent to , so 7 should be added to both the numerator and 7 14 1 denominator of . 7 1+ 7 8 4 = = . That is, 7 + 7 14 7
But
Answer: 7
8. In an election, one of the two candidates got 45% of the votes and this was 20 votes less than that of the other candidate. How many votes did the winner get? Solution Total number of votes = 20 ÷ (55% - 45%) = 20 Number of votes of the winner = 200 x .55 = 110 Answer: 110
÷ .10 = 200
9. What is the sum of the even numbers from 1 to 100? Solution 102 2 + 4 + 6 + … 96 + 98 + 100 102 Pair the numbers so that each pair will total 102 as shown above. Then multiply 102 by the number of pairs which is 25. So 25 x 102 = 2550 Answer: 2550 10. Use all the 4 one-digit prime numbers to form two fractions with the smallest possible sum. What are the fractions? Solution These prime numbers are 2, 3, 5, and 7. For the sum of the two fractions to be the smallest, their denominators must be 5 and 7. Now, 2 3 29 3 2 31 + = while + = . 5 7 35 5 7 35 2 3 , Answers: 5 7
11. By how many percent is the volume of a rectangular prism increased when the length and the height are each doubled? Solution Original volume = l x w x h New volume = 2 x l x w x 2 x h = 4 x l x w x h Increase = 400% - 100% = 300% Answer: 300% Part 2: 30 seconds (5 items)
2
1. There are many numbers which divide 109 with a remainder of 4. List ALL twodigit numbers that have this property. Solution 109 – 4 = 105 105 = 3 x 5 x 7 Multiply two factors of 105 at a time, i.e. 3 x 5, 3 x 7, and 5 x 7. Answers: 15, 21, 35 2. Nic puts together 42 one-cm cubes to form a rectangular prism. If the perimeter of the base is 18 cm, what is the height of the prism? Solution The area of the base must be a divisor of 42. But 42 = 3 x 7 x 2. For the perimeter to be 18 cm, the base must be 7 cm x 2 cm. Therefore the height of the prism is 3 cm. Answer: 3 cm 3. Colored pens are sold in packs of 3 pens or packs of 5 pens. What is the least number of packs one needs to buy to have exactly 42 colored pens? Solution To obtain the least number of packs, maximize the packs of 5. 42 ÷ 5 = 8 remainder 2 The sum of the smallest multiple of 5 and the remainder 2 that is divisible by 3 is 12. So, 4 packs of 3 pens and 6 packs of 5 pens. And 4 + 6 = 10. Answer: 10 4. On four long quizzes where the scores could be from 0 to 50, Lina had an average score of 45. What was the lowest score that she could have obtained on one test? Solution To get the lowest possible score on one test, Lina’s score in each of the 3 other quizzes should be perfect. This gives 3 x 50 = 150 as her total score in 3 quizzes. Her total score in 4 quizzes is 4 x 45 = 180. So, her score in 1 quiz must be 180 – 150 = 30. Answer: 30 5. During typhoons, the weather is reported every 18 minutes on Channel 3 and every 12 minutes on Channel 6. Both stations broadcast the weather at 1:30 P.M. When is the next time that the stations will broadcast again the weather at the same time? Solution The least common multiple of 18 and 12 is 36. So 1:30 P.M. + 36 minutes is 2:06 P.M. Answer: 2:06 P.M. or 14:06
Part 3: 60 seconds (5 items)
3
1. Using the digits 2, 3, 5, 6, and 7 what two-digit number and three-digit number can be formed whose product is the smallest? Solution For the product to be smallest, the digit 2 must be the tens digit of the two-digit number and the digit 3 must be the hundreds digit of the three-digit number. Then 5 must be the ones digit of the two-digit number and 6 must be the tens digit of the three-digit number. This is so because the multiplier 25 is the smallest possible. Answer: 25 and 367 2. Two joggers run around an oval track in opposite directions. One jogger runs around the track in 56 seconds. The joggers meet every 24 seconds. How many seconds does it take for the second jogger to run around the track? Solution 24 4 = 56 7 24 4 = , n = 42 n 7
1−
Answer: 42 3. Mang Jose makes wooden legs for stools and tables. Each stool uses 3 legs while each table uses 4 legs. Mang Jose has made 68 legs. How many stools and tables can he make if he makes at least 1 of each kind? Give two possible combinations. Solution 68 ÷ 4 = 17 tables Therefore one possible combination is 4 stools and 14 tables. For the other combinations on the number of stools (s) and the number of tables (t), the number of stools should be multiples of 4 in order to use all the legs. Answer: (s, t) = (4, 14), (8, 11), (12, 8), (16, 5), (20, 2) 4. Ms. Cruz computed the average score of his mathematics class with 50 pupils as 83. But she discovered that Lea’s score of 81 was misrecorded as 31 and Ben’s score of 65 was misrecorded as 85. What is the correct average of the class? Solution 81-31 = 50 so Lea’s recorded score is 50 less than her actual score. 85-65 = 20 so Ben’s recorded score is 20 more than his actual score. 50 – 20 = 30 should be added to the total of the scores of the class 30 ÷ 50 = .6 So 83 + .6 = 83.6 Answer: 83.6 or 83.60 5. In the pattern below, number in row 25? 1 3 5 7 9 13 15 21 23
what is the difference between the last number and the first
11 17 25
19 27
29
Solution The differences between the last number and first number in rows 1, 2, 3, 4, and 5, respectively are 0, 2, 4, 6, and 8. The 25th number in this pattern is 48. Answer: 48
4
