Grade 4 (Primary 4) : Singapore International Math Olympiad Challenge 2019 [PDF]

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Singapore International Math Olympiad Challenge 2019



GRADE 4 (PRIMARY 4) July 7, 2019 Time: 1 hour 30 minutes NAME: GRADE: COUNTRY:



INSTRUCTIONS 1. Please DO NOT OPEN the contest booklet until the Proctor has given permission. 2. There are 25 questions. Section A: Questions 1 to 15 score 2 points each, no points are deducted for unanswered question and 1 point is deducted for wrong answer. Section B: Questions 16 to 25 score 4 points each, no points are deducted for unanswered or wrong answer. 3. Shade your answers neatly using a pencil in the Answer Entry Sheet. 4. PROCTORING: No one may help any student in any way during the contest. 5. No electronic devices capable of storing and displaying visual information is allowed during the course of the exam. Strictly No Calculators are allowed into the exam. 6. Students must show detailed working and transfer answers to the Answer Entry Sheet. 7. No exam papers and written notes can be taken out by any contestant.



Rough Working



SIMOC 2019, Primary 4 (Grade 4) Contest Section A (Correct answer – 2 points| No answer – 0 points| Incorrect answer – minus 1 point) Question 1 Find the value of 87 × 27 + 72 × 87 + 87. A. B. C. D. E.



2700 7200 8700 9700 None of the Above



Question 2 I am thinking of a number. First, I multiply it by 2, then add 14 to the result. Then divide the sum by 7 and subtract 3 from the result. I will get 9 as my final answer. What number am I thinking of? A. B. C. D. E.



35 14 21 42 None of the Above



Question 3 Study the pattern below. 11 15 52 What is the value of A? A. B. C. D. E.



28 82 68 64 None of the above



12 16 56



13 17 60



14 18 A



SIMOC 2019, Primary 4 (Grade 4) Contest Question 4 Figure 1 is called a “stack map.” The numbers tell how many cubes are stacked in each position. Figure 2 shows these cubes, and Figure 3 shows the view of the stacked cubes as seen from the front.



3 4 2 1



Figure 1



2 2 4 1 3 1 Figure 2



Figure 3



Figure 4



Which of the following is the front view for the stack map in Figure 4?



A



B



C



D



E



Question 5 A “funny number” is a number formed by writing two digits followed by their product. For example, 6  7 = 42 , so 6742 and 7642 are “funny numbers”. The first digit of a “funny number” cannot be a 0. What is the difference between the largest and smallest “funny number?” A. B. C. D. E.



9837 9541 9581 9081 9881



Question 6 In a certain month, the number of Thursdays is more than the number of Wednesdays. Also, the number of Sundays is less than the number of Saturdays. On what day of the week will the 27th of that month fall? A. B. C. D. E.



Monday Tuesday Wednesday Friday Sunday



SIMOC 2019, Primary 4 (Grade 4) Contest Question 7 What is the remainder when the number 1111111111 ⏟ is divided by 7? 10 1𝑠



A. B. C. D. E.



3 4 5 6 None of the Above



Question 8 A boy always tells the truth on Mondays and Tuesdays, always tells lies on Saturday, and tells either truth or lies on the rest of the days of the week. For six days in a row, he was asked what his name was and he gave the following answers: Tom, Brad, Tom, John, Brad, John. What is the boy’s name? A. B. C. D. E.



Tom Brad John Brad or John Impossible to determine



Question 9 Study the pattern below. 3⨂5 = 3 + 4 + 5 + 6 + 7 8 ⨂ 3 = 8 + 9 + 10 11 ⨂ 7 = 11 + 12 + 13 + 14 + 15 + 16 + 17 100 ⨂ 2 = 100 + 101 What is the value of 10 ⨂ 4 ? A. B. C. D. E.



10 14 40 50 None of the above



SIMOC 2019, Primary 4 (Grade 4) Contest Question 10 If a digit 𝑎 is added to the left of the one-digit number 8 and a digit 𝑏 is added to the right of it, a 3-digit number 𝑎8𝑏 is formed. If this number 𝑎8𝑏 is a multiple of 3, what is the largest possible product 𝑎 × 𝑏? A. B. C. D. E.



8 56 84 96 None of the Above



Question 11 Ann, Betty and Clare, each bought beads from a market. Ann bought 400 beads more than Betty. The total number of beads of Ann and Betty bought were 900 more than Clare’s. If the three of them bought 4500 beads in total, how many beads did Clare buy? A. B. C. D. E.



1150 1550 1800 2700 None of the Above



SIMOC 2019, Primary 4 (Grade 4) Contest Question 12 The temperature relationship between degrees Celsius (C) and degrees Fahrenheit (F) 9



9



is given by 5 × 𝐶 + 32 = 𝐹. For example, 20° Celsius is equal 5 × 20 + 32 = 68° Fahrenheit. At what degree Celsius will the value of the temperature in degrees Fahrenheit be exactly 5 times the value of the temperature in degrees Celsius? A. B. C. D. E.



10 20 30 40 50



Question 13 3 6 of the marbles in Box B are equal in number to of the marbles in Box U. There is a 5 7 total of 85 marbles in the 2 boxes. How many marbles are there in Box U?



A. B. C. D. E.



35 50 60 70 None of the Above



SIMOC 2019, Primary 4 (Grade 4) Contest Question 14 It takes 2 goats and 3 cows 6 days to eat 2 acres of grass. It takes 6 goats and 5 cows 10 days to eat 8 acres of grass. How many days will it take 8 goats and 8 cows to eat 17 acres of grass? A. B. C. D. E.



5 12 15 17 None of the Above



Question 15 At a snack bar, the cost of 7 sandwiches, 5 drinks and 1 dessert is $32, while the cost of 10 sandwiches, 7 drinks, and 1 dessert is $45. Find the cost of 1 sandwich, 1 drink, and 1 dessert. A. B. C. D. E.



$6 $7 $7.50 $19 None of the Above



SIMOC 2019, Primary 4 (Grade 4) Contest Section B (Correct answer – 4 points| Incorrect or No answer – 0 points)



When the answer is a 1-digit number, shade “0” for the tens, hundreds and thousands place.



Example: if the answer is 7, then shade 0007



When the answer is a 2-digit number, shade “0” for the hundreds and thousands place.



Example: if the answer is 23, then shade 0023



When the answer is a 3-digit number, shade “0” for the thousands place.



Example: if the answer is 785, then shade 0785



When the answer is a 4-digit number, shade as it is.



Example: if the answer is 4196, then shade 4196



Question 16 Study the pattern. 1 4



2 3



What is the value of x ?



1 15



3 7



1 x



4 13



SIMOC 2019, Primary 4 (Grade 4) Contest Question 17 ABCD is a square of side length 12 cm. Point L is any point on side AB. Points H and I divide side AD into three equal parts. Points J and K also divide side BC into three equal parts. Finally, points G, F and E divide side DC into four equal parts. Find the total area (in cm2) of the shaded region.



SIMOC 2019, Primary 4 (Grade 4) Contest Question 18 The numbers 11, 12, 13, 14, 15, 16, 17, 18 and 19 are placed in the 9 boxes shown below. The numbers 15, 16, and 19 have been placed accordingly. If the sum of the numbers placed horizontally is equal to the sum of the numbers placed vertically, what is the sum of all possible values of 𝑎?



Question 19 Calculate the following 192 × (



1 1 1 1 ) + + + 4 × 7 7 × 10 10 × 13 13 × 16



SIMOC 2019, Primary 4 (Grade 4) Contest Question 20 Tom made number 869 using 19 matchsticks as shown below. He wants to construct the greatest possible four-digit number by moving exactly three matches. Find this greatest possible value.



(The figures of all the digits from 0 to 9 are shown below.)



Question 21 Several commuters were on a bus when it started its journey from a bus interchange. 1 At the first bus stop, 2 more than of the commuters alighted. At the second bus stop, 3 1 4 more than of the remaining commuters alighted. At the third bus stop, 8 more 3 1 than of the remaining commuters alighted. Then the bus was left with 16 3 commuters. How many commuters boarded the bus at the bus interchange?



SIMOC 2019, Primary 4 (Grade 4) Contest Question 22 ̅̅̅̅̅ is 9 times the 2-digit number 𝑎𝑏 ̅̅̅, find the number 𝑎𝑏 ̅̅̅. If a three-digit number 𝑎1𝑏



Question 23 The number of my house is a 4-digit number. One day, on my way home, I accidentally turned the number of my house upside down. I noticed that the new number formed by turning it upside down is bigger than the original number by 4872. What is the number of my house?



SIMOC 2019, Primary 4 (Grade 4) Contest Question 24 Find the value of 2 + 4 + 8 + ⋯ + 512 + 1024



Question 25 All the sides of the figure below meet at right angles. Use the numbers 1, 2, 3, 4, 5, 6, 7 and 8 to represent the sides a, b, c, d, e, f, g and h in some order. Find the largest possible area of the figure.



Rough Working