PAKTURK 10 - ISMO...PAKTURK 10 th National Interschool Maths Olympiad Class 5 Solutions We believe...

PAKTURK 10th National Interschool Maths Olympiad Class 5 Solutions

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Q1: 11 3

?7 7

A) 1 B) 2 C) 3 D) 4

Solution:

11 3 11 3 142

7 7 7 7

Answer: B

Q2: How many zeros are needed to write the numerical for one million?

A) 3 B) 4 C) 5 D) 6

Solution: 1,000,000 is the numerical for one million. So we need six zeros.

Answer: D

Q3: Which of the following is the simplest fraction form of 75 percent?

A) 2

5 B)

1

4 C)

3

5 D)

3

4

Solution:

7575%

100

After simplification we get 75

100

3

4

Answer: D

Q4: 10 10 10 10 ?

A) 11 B) 111 C) 101 D) 20

Solution:

10 10 10 10

100 1

101

Answer: C

Q5: 1 1 1

?6 3 18

A) 1

9 B)

1

3 C)

1

2 D) 2

Solution:

1 1 1 1 1 2

6 3 18 18 18

18

1

9

Answer: A

Q6: What is the H.C.F of 480 and 516?

A) 4 B) 12 C) 16 D) 24

Solution:

5

480 2 3 5 and 2

516 2 3 43

The H.C.F 2

2 3 12

Answer: B



Q7: How many Rs. 23 balls can you buy for Rs.713?

A) 25 B) 27 C) 29 D) 31

Solution:

The total number of balls you can buy is Rs.713

Rs.23=31

Answer: D

Q8: 48 12 3 ?

A) 108 B) 96 C) 12 D) 15

Solution:

48 12 3

48 36

12

Answer: C

Q9: 0.2 0.4 0.8 ?

A) 0.064 B) 0.64 C) 64 D) 640

Solution:

0.2 0.4 0.8

2 4 8

10 10 10

64

1000

0.064

Answer: A

Q10: What is 20% of 1

350 ?7

A) 70 B) 7 C) 1 D) 10

Solution:

1 20 120% 350 350

7 100 7

1 350 150 10

5 7 5

Answer: D

Q11: What is the quotient when 2014 2014 is

divided by 2014 ?

A) 2014 B) 1 C) 0 D) 2

Solution:

2014 2014

2014

2014

Answer: A

Q12: Which one of the following fractions is the largest one?

A) 7

8 B)

13

16 C)

31

40 D)

63

80

Solution:

7 130.875 0.8125

8 16

31 630.775 0.7875

40 80

It is clear that the largest one is 7

0.8758

Answer: A



Q13: What is the average of first 5 multiples of 5?

A) 7.5 B) 37.5 C) 15 D) 35

Solution:

5 10 15 20 25 7515

5 5

Answer: C

Q14: Which of the following numbers can be the factors of a prime number? A) 1 and 13 B) 1,2 and 7 C) 1 and 15 D) 1 and 21

Solution: A prime number has only two factors and the first one is 1 and the other one is itself. In option A: 1 and 13 are the only factors of 13. As you see one is itself and the other one is 1.

Answer: A

Q15: What percent of 0.2 is equal to 0.4? A) 400 % B) 200 % C) 100 % D) 150 %

Solution:

100 4 100 2 100.4 100

20.2 10 5 2

10

2

5

100 5 2 100 200

Answer: B

Q16: What number will come instead of in

2014 - 12 = 14?

A) 131 B) 139 C) 141 D) 143

Solution:

2014 - 12 = 14

2002 14

2002

14

Answer: D

Q17: The square of 4 has the same value as the square root of a number. Which of the following is the number? A) 256 B) 32 C) 16 D) 64

Solution:

24 ?

16 ?

The question mark represent the square of 16 which is equal to 256.

Answer: A

Q18: 3 2014 2013 2012 ........

Find the missing number.

A) 2007 B) 2006 C) 2017 D) 2008

Solution:

3 2014 2013 2012 ........

6042 2013 2012

2017

Answer: C



Q19: The price of a table is Rs. 1600 and the price of a chair is Rs. 1200. How much money will be left if you buy 2 tables and 4 chairs with Rs. 9600? A) Rs. 1200 B) Rs. 1800

C) Rs. 1600 D) Rs. 1400

Solution: If you buy two tables, it will cost Rs. 32000 and if you buy 4 chairs that will cost Rs. 4800 Total cost will be Rs. 3200 + Rs. 4800= Rs. 8000 The money that will be left is: Rs. 96000-Rs. 8000=Rs. 1600

Answer: C

Q20: What is the highest common factor of 24 and a number that is a multiple of 24?

A) 48 B) 36 C) 24 D) 12

Solution: The multiples of 24 are 24, 48, 72, .... As you see above the highest common factor of 24 and any of its multiple is equal to 24.

Answer: C

Q21: The price of a book is Rs. 2400. What percent of the price of the book can Usman pay with Rs. 1800?

A) 75% B) 60% C) 80% D) 72%

Solution:

.1800 1800 375%

.2400 2400 4

Rs

Rs

Answer: A

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?

A) 5

4 B)

3

4 C)

3

5 D)

4

5

Solution:

The total slices of cake were eaten is by Atif and Adeel is 7+5=12.

The fraction will be 12 4

15 5

Answer: D

Q23: Which of the following is equal to 4.25?

A) 5

2 B)

7

4 C)

19

3 D)

17

4

Solution:

425425 17254.25

100100 425

Answer: D

Q24: Which of the following number should be multiplied by 3.125 to get a natural number? A) 4 B) 5 C) 6 D) 8

Solution:

3125 1253125 125 2525 53.125

1000 401000 40 825 5

So if we multiply the final fraction by 8, it will be a natural number.

Answer: D



Q25: ISMO is a four digit number and I , S , M and

O are 4 digits.

2014 2013 2012 ISMO

What is the value of I+S+M+O ?

A) 18 B) 14 C) 8 D) 24

Solution:

2014 2013 2012 ISMO

ISMO=6039

I=6, S=0, M=3, O=9

I+S+M+O 6 0 3 9 18

Answer: A

Q26: Round off 283 to the nearest ten. A) 276 B) 278 C) 280 D) 290

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. After rounding off, the number will be 280

Answer: C

Q27: What is the least common multiple (L.C.M) of first 5 prime numbers? A) 44 B) 2 C) 2310 D) 4110

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

Q28: What is the least common multiple (L.C.M) of

denominators of1

3,

1

5,

1

4, and

1

7?

A) 280 B) 420 C) 105 D) 390

Solution: As any two of the denominators has no common factor, then the L.C.M will be the product of all.

3 5 4 7 420

Answer: B

Q29: Naseera and Minal have 64 toffees in total, but Minal has 12 more toffees than Naseera. How many toffees does Naseera have?

Solution: If we keep 12 toffees for Minal and share the remaining toffes among Minal and Naseera, they will have equal number of toffees. 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.

64 12 52

5226

2

Now both have 26 toffees.

Naseera has 26 toffees and Minal has 38 toffees.

Answer: B

A) 40 B) 26 C) 44 D) 28



Q30: A father bought 22 toys and paid Rs. 1100. What is the price of one toy? A) Rs. 50 B) Rs. 60 C) Rs. 75 D) Rs. 80

Solution:

The price of one toy is 1100

5022

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

Solution:

6060

84 12

84

12

5

7

5

7 is the lowest form and it has 7 in its denominator.

Answer: D

Q32: What is 20% of 40% of 48000? A) 3972 B) 3840 C) 3800 D) 3755

Solution:

20% 40% 48000

20

1 00

4 0

1 00

48 000

80 48 3840

Answer: B

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? A) 88 B) 90 C) 80 D) 84

Solution: He should get 88 in order to increase her average to 80.

72 88 16080

2 2

She scored 8 less than 80, now she need to get 8 more than 80.

Answer: A

Q34: The sum of any two adjacent numbers is equal to the number on them. For example: a+b=c

What is the value of "a" if the sum of numbers in 3rd line is equal to 17? A) 4 B) 5 C) 6 D) 7



Solution: Sum of the number is 3rd line is 17. So

4 17 13a b a b

13

13

a b c

c

4 25

13 4 25

25 17

8

c b

b

b

b

Now we can find the value of a

13

8 13

5

a b

a

a

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 B) Rs. 700 C) Rs. 800 D) Rs. 900

Solution: If he sells 5 items for Rs. 1200, he will get Rs. 6000

He should sell all the 5 items for Rs.9000

=Rs.18005

to get Rs. 90000 So he needs to increase the price of an item from Rs. 1200 to Rs. 1800 to get Rs. 9000 Incensement is Rs. 1800 - Rs. 1200 = Rs. 600

Answer: A

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. What is that number? A) 64 B) 66 C) 78 D) 86

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 64 66 78 86 96

785

Let's check: 64 66 86 96

784

Answer: C

Q37: ABCD is a parallelogram and the length of AE is half of the length of CD.

What is area of parallelogram if the length of AB is 12 cm? A) 96 cm

2 B) 72 cm

2

C) 64 cm2 D) 84 cm

2

Solution: 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

are equal. ( CD AB )

1 112cm=6cm

2 2AE CD

Area of the parallelogram: 26 12 72AE CD cm cm cm

Answer: B

Q38: Which four operation sign should be used in order to get 10?



A) , , , B) , , ,

C) , , , D) , , ,

Solution:

7 5 12

12 4 3

3 8 11

11 1 10

So the sign should be used are , , ,

Answer: D

Q39: How many squares will be used in 7th figure?

1st Figure 2nd Figure 3rd Figure

A) 40 B) 70 C) 80 D) 100

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.

See the figure above.

Answer: B

Q40: The prime factorization of 12600 is found

wrong by a student as 3 2

2 3 5 7 .

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.

3 2 212600 2 3 5 7

As you see above in the correct factorization, one 5 is missing in the wrong factorization.

Answer: C

Q41: How many squares are there in the figure?

A) 15 B) 17 C) 19 D) 22



Solution:

Answer: D

Q42: Mohseen has 1600 marbles. Half of them are blue, one quarter are red, and one eighth are green. What percent of the marbles are of some other colour? A) %10 B) %12 C) %12.5 D) %15

Solution:

Blue: 1600

8002

Red: 1600

4004

Green: 1600

2008

The number of marbles in other colour:

1600 800 400 200 200

Percentage will be

20012.516 12.5%

1600 10016

Answer: C

Q43: 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? A) 9 B) 8 C) 7 D) 6

Solution: Let's find the number by starting with 2012 and apply reverse operations.

2012503

4

503 3 500

50050

10

50 1 49

49 7 7

So the number is 7

Answer: C

Q44: The average of twelve numbers is 45. The average of ten numbers when two numbers removed is 48. What is the average of those two numbers which are removed? A) 30 B) 32 C) 44 D) 48

Solution:

The sum of twelve numbers is 12 45 540

The sum of ten numbers is 10 48 480

That means the sum of those two numbers which are

removed is 540 480 60

Average of the two number is 60

302

Answer: A



Q45: In the following diagram AF=BF, BG=GC, AK=KE and BL=LG. What is the total area of shaded regions?

A) 100 cm

2 B) 112 cm

2

C) 108 cm2 D) 148 cm

2

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 2

4 8 32cm cm cm

The area of the second rectangle is 2

4 8 32cm cm cm

The area of first triangle is 28 8

322

cm cmcm

The area of second triangle is 24 8

162

cm cmcm

The total area of the shaded region is 2 2 2 2 2

32 32 32 16 112cm cm cm cm cm

Answer: B

Q46: ABCD is a rectangle and EFGH is a square.

What is the perimeter of shaded region? A) 58 cm B) 60 cm C) 62 cm D) 64 cm

Solution:

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



Q47: The rent of a building increases in a sequence as follow.

Year Rent

2012 Rs. 12000

2013 Rs. 15000

2014 Rs. 19000

2015 Rs. 24000

What will be the rent in 2023? A) Rs. 90000 B) Rs. 100000 C) Rs. 105000 D) Rs. 120000

Solution:

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. So the rent will be Rs. 100000 in 2023

Answer: B

Q48: What is the sum of digits of 111111 111111according the rule below?

1 1 1

11 11 121

111 111 12321

1111 1111 1234321

A) 12 B) 18 C) 24 D) 36

Solution:

According the rule above 111111 111111 will be

equal to 12345654321

Sum of the digits will be

1 2 3 4 5 6 5 4 3 2 1 36

Answer: D

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?

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 23.4

7.83

There are total five parts, so the capacity of the tank is

8 7.8 62.4

Answer: B

Q50: In how many ways the ant can rich the wheat by moving up and right only?

A) 11 B) 12 C) 13 D) 14



Solution: There are total 14 different ways. See the figure below.

Answer: D

PAKTURK 10 - ISMO...PAKTURK 10 th National Interschool Maths Olympiad Class 5 Solutions We believe...

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