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PAKTURK 10th National Interschool Maths Olympiad Q1: A) 11 3 ? 7 7 1 B) Class 5 Solutions Q4: A) 2 C) 3 D) 10 10 10 10 ? 11 B) 111 C) 101 D) 20 4 Solution: Solution: 10 10 10 10 11 3 11 3 14 2 7 7 7 7 100 1 Answer: B 101 Answer: C Q2: How many zeros are needed to write the numerical for one million? Q5: A) 3 B) 4 C) 5 D) 6 A) Solution: 1,000,000 is the numerical for one million. So we need six zeros. 1 1 1 ? 6 3 18 1 9 B) 1 3 C) 1 2 D) 2 Solution: Answer: D 1 1 1 1 1 2 1 6 3 18 18 18 18 9 Answer: A Q3: Which of the following is the simplest fraction form of 75 percent? Q6: A) 2 5 B) 1 4 C) 3 5 D) What is the H.C.F of 480 and 516? 3 4 A) 4 B) 12 C) 16 D) 24 Solution: Solution: 75% 75 100 After simplification we get 480 25 3 5 and 516 22 3 43 The H.C.F 75 3 100 4 22 3 12 Answer: B Answer: D We believe what is taught with love lasts forever Page 1 of 12 PAKTURK 10th National Interschool Maths Olympiad Q7: Class 5 Solutions How many Rs. 23 balls can you buy for Rs.713? Q10: A) 25 B) 27 C) 29 What is 20% of 31 D) A) Solution: 70 B) 7 350 1 ? 7 C) 1 D) 10 Solution: The total number of balls you can buy is Rs.713 Rs.23 =31 Answer: D 1 20 1 20% 350 350 7 100 7 1 350 1 50 10 5 7 5 Answer: D Q8: A) 48 12 3 ? 108 B) 96 C) 12 D) 15 Solution: Q11: What is the quotient when divided by 2014 ? A) 2014 B) 1 C) 2014 2014 is 0 D) 2 48 12 3 48 36 Solution: 12 Answer: C 2014 2014 2014 2014 Answer: A Q9: A) 0.2 0.4 0.8 ? 0.064 B) 0.64 C) 64 D) 640 Q12: Which one of the following fractions is the largest one? A) Solution: 7 8 B) 13 16 C) 31 40 D) 63 80 0.2 0.4 0.8 2 4 8 10 10 10 64 1000 0.064 Solution: Answer: A 7 0.875 8 31 0.775 40 13 0.8125 16 63 0.7875 80 It is clear that the largest one is 7 0.875 8 Answer: A We believe what is taught with love lasts forever Page 2 of 12 PAKTURK 10th National Interschool Maths Olympiad Class 5 Solutions Q16: Q13: What is the average of first 5 multiples of 5? B) 37.5 C) 15 D) 35 131 B) 139 in C) 141 D) 143 Solution: Solution: 2014 - 12 = 14 5 10 15 20 25 75 15 5 5 2002 14 Answer: C 2014 - 12 = 14 ? A) A) 7.5 What number will come instead of 2002 14 Answer: D Q14: Which of the following numbers can be the factors of a prime number? A) 1 and 13 C) 1 and 15 Q17: The square of 4 has the same value as the square root of a number. B) 1,2 and 7 D) 1 and 21 Which of the following is the number? Solution: A prime number has only two factors and the first one is 1 and the other one is itself. A) 256 In option A: 1 and 13 are the only factors of 13. As you see one is itself and the other one is 1. Solution: Answer: A B) 32 C) 16 D) 64 42 ? 16 ? The question mark represent the square of 16 which is equal to 256. Q15: What percent of 0.2 is equal to 0.4? A) 400 % B) 200 % C) 100 % Answer: A D) 150 % Q18: Solution: 3 2014 2013 2012 ........ Find the missing number. 100 4 100 2 10 0.4 100 0.2 10 2 5 2 10 2 100 5 2 100 200 5 A) 2007 B) 2006 C) 2017 D) 2008 Solution: Answer: B 3 2014 2013 2012 ........ 6042 2013 2012 2017 Answer: C We believe what is taught with love lasts forever Page 3 of 12 PAKTURK 10th National Interschool Maths Olympiad Q19: The price of a table is Rs. 1600 and the price of a chair is Rs. 1200. Class 5 Solutions Q22: Adeel ate 5 slices of cake and Atif ate 7 slices. If there were initially 15 slices of equal size, what fraction of the cake was eaten? How much money will be left if you buy 2 tables and 4 chairs with Rs. 9600? A) Rs. 1200 C) Rs. 1600 A) B) Rs. 1800 D) Rs. 1400 5 4 B) 3 4 C) 3 5 4 5 D) Solution: Solution: If you buy two tables, it will cost Rs. 32000 and if you buy 4 chairs that will cost Rs. 4800 The total slices of cake were eaten is by Atif and Adeel is 7+5=12. The fraction will be Total cost will be Rs. 3200 + Rs. 4800= Rs. 8000 12 4 15 5 Answer: D The money that will be left is: Rs. 96000-Rs. 8000=Rs. 1600 Answer: C Q23: A) Which of the following is equal to 4.25? 5 2 B) 7 4 C) 19 3 D) 17 4 Q20: What is the highest common factor of 24 and a number that is a multiple of 24? Solution: A) 48 B) 36 C) 24 D) 12 Solution: 425 425 25 17 4.25 100 100 4 25 The multiples of 24 are 24, 48, 72, .... Answer: D As you see above the highest common factor of 24 and any of its multiple is equal to 24. Answer: C Q24: Which of the following number should be multiplied by 3.125 to get a natural number? A) 4 Q21: B) 5 C) 6 D) 8 The price of a book is Rs. 2400. Solution: What percent of the price of the book can Usman pay with Rs. 1800? A) 75% B) 60% C) 80% D) 72% Solution: 3125 125 3125 125 25 5 25 3.125 40 1000 1000 40 8 25 5 So if we multiply the final fraction by 8, it will be a natural number. Rs.1800 1800 3 75% Rs. 2400 2400 4 Answer: D Answer: A We believe what is taught with love lasts forever Page 4 of 12 PAKTURK 10th National Interschool Maths Olympiad Q25: ISMO is a four digit number and O are 4 digits. I , S , M and A) 18 Q28: What is the least common multiple (L.C.M) of denominators of 2014 2013 2012 ISMO What is the value of Class 5 Solutions A) 280 1 1 1 1 , , , and ? 3 5 4 7 B) 420 C) 105 D) 390 I+S+M+O ? B) 14 C) 8 D) 24 Solution: Solution: As any two of the denominators has no common factor, then the L.C.M will be the product of all. 2014 2013 2012 ISMO 3 5 4 7 420 ISMO=6039 Answer: B I=6, S=0, M=3, O=9 I+S+M+O 6 0 3 9 18 Answer: A Q29: Naseera and Minal have 64 toffees in total, but Minal has 12 more toffees than Naseera. How many toffees does Naseera have? Q26: Round off 283 to the nearest ten. A) 276 B) 278 C) 280 D) 290 Solution: If we keep 12 toffees for Minal and share the remaining toffes among Minal and Naseera, they will have equal number of toffees. Solution: We will round off the last digit only. As the last digit is 3, it will be round off to 0 but as 3 is less than 5, 8 will remain same. The toffes which we kept for Minal makes the number of toffes of Minal's 12 more than the number of toffees of Naseera's. After rounding off, the number will be 280 Answer: C 64 12 52 52 26 2 Now both have 26 toffees. Q27: What is the least common multiple (L.C.M) of first 5 prime numbers? A) 44 B) 2 C) 2310 Naseera has 26 toffees and Minal has 38 toffees. Answer: B D) 4110 A) 40 B) 26 C) 44 D) 28 Solution: The first prime numbers are 2,3,5,7,11. As they do not have any common, we can multiply all to find the L.C.M. That will be 2 3 5 7 11 2310 Answer: C We believe what is taught with love lasts forever Page 5 of 12 PAKTURK 10th National Interschool Maths Olympiad Q30: A father bought 22 toys and paid Rs. 1100. Class 5 Solutions Q33: A student in class eight scored 72 marks in maths test. How much should she score in order to increase her average to 80? What is the price of one toy? A) 88 A) Rs. 50 B) Rs. 60 C) Rs. 75 B) 90 C) 80 D) 84 D) Rs. 80 Solution: Solution: He should get 88 in order to increase her average to 80. The price of one toy is 1100 50 22 Answer: A 72 88 160 80 2 2 She scored 8 less than 80, now she need to get 8 more than 80. Answer: A Q31: Which one of the following fractions has 7 in denominator when it is reduced to its lowest form? A) 35 28 B) 28 35 C) 3 14 D) 60 84 Q34: The sum of any two adjacent numbers is equal to the number on them. Solution: For example: a+b=c 60 60 12 5 84 84 7 12 5 is the lowest form and it has 7 in its denominator. 7 Answer: D Q32: What is the value of "a" if the sum of numbers in 3rd line is equal to 17? What is 20% of 40% of 48000? A) 3972 B) 3840 C) 3800 D) 3755 A) 4 B) 5 C) 6 D) 7 Solution: 20% 40% 48000 20 40 48 000 1 00 1 00 80 48 3840 Answer: B We believe what is taught with love lasts forever Page 6 of 12 PAKTURK 10th National Interschool Maths Olympiad Class 5 Solutions Q36: A boy selected five numbers as 78, 66, 64, 96,86 and noticed that one of the number is the average of other four numbers. Solution: Sum of the number is 3rd line is 17. So a b 4 17 a b 13 What is that number? a b c 13 A) 64 B) 66 C) 78 D) 86 c 13 Solution: Arrange numbers in ascending order as 64,66,78,86,96 If one of the number is the average of remaining numbers, the average won't change when the average number is also included in the numbers. So, that number will be c b 4 25 Let's check: 13 b 4 25 64 66 78 86 96 78 5 64 66 86 96 78 4 b 25 17 Answer: C b8 Now we can find the value of a a b 13 Q37: ABCD is a parallelogram and the length of AE is half of the length of CD. a 8 13 a5 Answer: B Q35: The price of an item is Rs. 1200. The shopkeeper wants to sell 5 items for Rs. 9000. How much should the shopkeeper increase the price of the item? A) Rs. 600 C) Rs. 800 B) Rs. 700 D) Rs. 900 What is area of parallelogram if the length of AB is 12 cm? 2 2 A) 96 cm 2 C) 64 cm B) 72 cm 2 D) 84 cm Solution: Solution: If he sells 5 items for Rs. 1200, he will get Rs. 6000 The area of parallelogram is height times base. The line segment AE is the height which is half length of CD. The lengths of opposite sides in a parallelogram He should sell all the 5 items for Rs.9000 =Rs.1800 5 are equal. ( CD AB ) to get Rs. 90000 1 1 AE CD 12cm=6cm 2 2 So he needs to increase the price of an item from Rs. 1200 to Rs. 1800 to get Rs. 9000 Area of the parallelogram: AE CD 6 cm 12 cm 72 cm2 Answer: B Incensement is Rs. 1800 - Rs. 1200 = Rs. 600 Answer: A We believe what is taught with love lasts forever Q38: Which four operation sign should be used in order to get 10? Page 7 of 12 PAKTURK 10th National Interschool Maths Olympiad Class 5 Solutions Solution: 7 square on the left, 7 on the rigt, 7 on the bottom and 7x7=49 in middle. Total number of squares will be 70. A) C) , , , , , , B) D) , , , , , , Solution: 7 5 12 See the figure above. 12 4 3 Answer: B 3 8 11 11 1 10 So the sign should be used are 12600 is found wrong by a student as 2 3 5 7 . Q40: , , , The prime factorization of 3 Answer: D 2 What is the missing number in above prime factorization? A) 2 B) 3 C) 5 D) 7 Solution: Let's find the correct prime factorization of 12600. Q39: How many squares will be used in 7th figure? 1st Figure 2nd Figure 12600 23 32 52 7 As you see above in the correct factorization, one 5 is missing in the wrong factorization. 3rd Figure Answer: C Q41: A) 40 B) 70 C) 80 How many squares are there in the figure? D) 100 A) 15 We believe what is taught with love lasts forever B) 17 C) 19 D) 22 Page 8 of 12 PAKTURK 10th National Interschool Maths Olympiad Class 5 Solutions A number multiplied by itself, added 1, the result multiplied by 10, added 3, and the result multiplied by 4. What is the number if the final answer is 2012? Q43: Solution: A) 9 B) 8 C) 7 D) 6 Solution: Let's find the number by starting with 2012 and apply reverse operations. Answer: D 2012 503 4 503 3 500 500 50 10 50 1 49 Mohseen has 1600 marbles. Half of them are blue, one quarter are red, and one eighth are green. Q42: 49 7 7 So the number is 7 What percent of the marbles are of some other colour? A) %10 B) %12 C) %12.5 Answer: C D) %15 Solution: Q44: The average of twelve numbers is 45. The average of ten numbers when two numbers removed is 48. 1600 800 2 1600 Red: 400 4 1600 Green: 200 8 Blue: What is the average of those two numbers which are removed? A) 30 B) 32 C) 44 D) 48 Solution: The number of marbles in other colour: 1600 800 400 200 200 The sum of twelve numbers is The sum of ten numbers is 12 45 540 10 48 480 200 Percentage will be 16 12.5 12.5% 1600 100 16 Answer: C That means the sum of those two numbers which are removed is 540 480 60 Average of the two number is 60 30 2 Answer: A We believe what is taught with love lasts forever Page 9 of 12 PAKTURK 10th National Interschool Maths Olympiad Class 5 Solutions Q46: Q45: In the following diagram AF=BF, BG=GC, AK=KE and BL=LG. ABCD is a rectangle and EFGH is a square. What is the total area of shaded regions? What is the perimeter of shaded region? A) 58 cm C) 62 cm 2 A) 100 cm 2 C) 108 cm B) 60 cm D) 64 cm 2 B) 112 cm 2 D) 148 cm Solution: Solution: Lets find the all shaded region by finding the area of four parts. We have two rectangles and two triangles. The lengths of sides are mentioned by red text. The area of the first rectangle is 4 cm 8 cm 32 cm The area of the second rectangle is 2 4 cm 8 cm 32 cm2 The area of first triangle is 8 cm 8 cm 32 cm 2 2 4 cm 8 cm The area of second triangle is 16 cm 2 2 The perimeter of the shaded regions is the lengths which are shown by red colour. The sum of the lengths of two red part is 6 cm. ( AB FG ) The perimeter is 10cm+16cm 10cm 6cm 6cm 10cm 6cm=64 cm Answer: D The total area of the shaded region is 32 cm2 32 cm2 32 cm2 16 cm2 112 cm2 Answer: B We believe what is taught with love lasts forever Page 10 of 12 PAKTURK 10th National Interschool Maths Olympiad Class 5 Solutions Q47: The rent of a building increases in a sequence as follow. Year 2012 2013 2014 2015 Q49: The tank of a car has 23.4 litre petrol when the pointer (arrow) is as in the figure. The tank is empty when the pointer shows 0. What is the capacity of the tank? Rent Rs. 12000 Rs. 15000 Rs. 19000 Rs. 24000 What will be the rent in 2023? A) Rs. 90000 C) Rs. 105000 B) Rs. 100000 D) Rs. 120000 Solution: A) 62 B) 62.4 C) 64.8 D) 72.4 Solution: There are total 8 equal parts from 0 to 1 and the pointers at the end of third part. The capacity of three parts is 23.4. It means that the capacity of one part is The incensement in 2013 is Rs. 3000, in 2014 is Rs. 4000, in 2015 is Rs. 5000. The incensement increases by Rs. 1000 every year. 23.4 7.8 3 There are total five parts, so the capacity of the tank is 8 7.8 62.4 Answer: B So the rent will be Rs. 100000 in 2023 Answer: B Q48: What is the sum of digits of according the rule below? 111111 111111 Q50: In how many ways the ant can rich the wheat by moving up and right only? 11 1 11 11 121 111 111 12321 1111 1111 1234321 A) 12 B) 18 C) 24 D) 36 Solution: According the rule above equal to 12345654321 Sum of the digits will be 111111 111111 will be A) 11 1 2 3 4 5 6 5 4 3 2 1 36 B) 12 C) 13 D) 14 Answer: D We believe what is taught with love lasts forever Page 11 of 12 PAKTURK 10th National Interschool Maths Olympiad Class 5 Solutions Solution: There are total 14 different ways. See the figure below. Answer: D We believe what is taught with love lasts forever Page 12 of 12