10th National ISMO Class 8 Question Paper With Solutions

PAKTURK 10th

National Interschool Math Olympiad Class 8

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Q1: Which of the following numbers is the smallest

one?

A) 36

21 B)

29

14 C)

21

9 D)

19

4

Solution:

361.71

21

212.33

9

292.07

14

194.75

4

At it is shown above, the smallest one is 36

1.7121

Answer: A

Q2: 2 9

?3 8

a b

b a

A) 18

12 B)

3

4

a

b C)

3

4 D)

4

3

b

a

Solution:

2 a

3 b

9 b

8 a

2

3

9

8

1 3 3

4 1 4

Answer: C

Q3: 1

20 ?4

A) 3 B) 4.5 C) 5 D) 6

Solution:

2

1 20 4 1 8120

4 4 4

9 94.5

2 2

Answer: B

Q4: If 5 1

7 86 3

a , then what is the value of a?

A) 1

2 B)

1

3 C)

1

4 D)

1

6

Solution:

5 17 8

6 3

1 5 25 478 7

3 6 3 6

a

a

takin L.C.M.

50 47

6 6

50 47 3 1

6 6 2

Answer: A

Q5: x is a strictly negative integer. Which is the

biggest?

A) 2x B) 2x C) 6 2x D) 2x

Solution:

If x is a strictly negative integer, then all the option

except A will be negative.

But the option A will be always positive, as the product

of two negative integers is a positive integer.

So the biggest one will be 2x

Answer: A

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Q6: 2

20 3 16 ?

A) 3 B) 4 C) 5 D) 11

Solution:

220 3 16

20 9 16

20 25

20 5

25 5

Answer: C

Q7: If 7 9

a b then, what is the value of 9 7a b ?

A) 2 B) 63 C) -63 D) 0

Solution:

After cross multiplication;

9 77 9

9 7 0

a ba b

a b

Answer: D

Q8: 0.001 0.2 0.09

?0.01 0.05 0.1

A) 3 B) 4 C) 5 D) 11

Solution:

0.001 0.2 0.09

0.01 0.05 0.1

1 2 9

1000 10 1001 5 1

100 100 10

1

10 00

1 00

2

1 1 0

10 0

9

5 10 0

1 0

1

1 94

10 10

1 94 1 4 5

10

Answer: C

Q9: What is the average (arithmetic mean) of the 3

quantities 12 n , 12 and 12 n ?

A) 4 B) 12 C) 18 D) 43

n

Solution:

12 n 12 12 n 3612

3 3

Answer: B

Q10: 1 1 1

6 3 2A and

1 1 1

8 4 2B , then

?A B

A) 2

3 B) 1 C)

11

8 D)

15

8

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Solution:

1 1 1 1 1 1

6 3 2 8 4 2

1 1 1 1 1 1

6 3 2 2 8 4

3 2 3

6 2 8

1 31

2 8

4 8 3 15

8 8

A B

Answer: D

Q11: If 3

64b , then 2

2 64b b is:

A) 88 B) -44 C) 0 D) -88

Solution:

3

64

4

b

b

222 64 4 2 4 64

16 8 64

88

b b

Answer: A

Q12:

30 8 4 15 4 8 2?

30 4 2 21 5 5

A) 1

22 B)

1

5 C) 2 D)

1

2

Solution:

30 8 4 15 4 8 2

30 4 2 21 5 5

30 2 60 4

30 8 21 1

32 64

22 22

32

22

22

32 1

64 64 2

Answer: D

Q13:

2 2

2 2

0.8 0.3?

0.6 0.5

A) 1 B) 2 C) 4 D) 5

Solution:

2 2

2 2

0.8 0.3

0.6 0.5

0.8 0.3 0.8 0.3

0.6 0.5 0.6 0.5

1.1

0.5

1.1

0.1

5

10

10

51

Answer: D

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Q14: How many of the following numbers are even

numbers?

8 6

7 0

12 9 9

57

2 2

. 8 11

. 12 9

. 5 4 6

. 5 3 2

. 2013 2012

I

II

III

IV

V

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

Solution:

Note: Any power of even numbers is even number

while any power of odd numbers id odd number.

8 6

7 0

12 9 9

5 57

5

2 2

. 8 11

. 12 9

. 5 4 6

. 5 3 2

. 2013 2012

I even odd odd

II even odd odd

III odd even even

IV odd odd even

even even even even even

V odd even odd

Two of the above expressions are even numbers.

Answer: B

Q15: 2 2

1 1 18 3 2 8 4A

Which of the following is equal to A ?

A) 42

4 0 2 B) 32 5 2

C) 04 1 D) 12 3

Solution:

Lets find A.

2 21 1 18 3 2 8 4

1 1 6 2 4

2 3 4 5 4 1

1

A

A

A

A

Lets check the options and find out which of them is 1.

A) 424 0 2 16 0 16 0

B) 32 5 2 8 7 1

C) 0

4 1 1 1 2

D) 12 3 15

Answer: B

Q16: If 6 3 60x y and 3 6

4 16

x

y , what is the value

of x y ?

A) 17 B) 15 C) 10 D) 7

Solution:

3

4

x 6

y

16

2 1

4 2

2

x

y

x y

having substitution in 6 3 60x y

6 3 2 60

6 6 60

12 60

5

x x

x x

x

x

2

2 5 10

y x

y

5 10 15x y

Answer: B

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Q17: What is the total number of proper and

improper subsets of set , , , , ,A k l m n r o ?

A) 63 B) 1 C) 64 D) 65

Solution:

Total number of proper and improper subsets is equal

to the number of subsets.

There are 5 elements in the set A

6

2 2 64n

There will be 32 subsets of set A

Answer: C

Q18: a , b and c natural numbers.

5 7

6 4

a b

a c

Which of the following order is correct?

A) a b c B) a c b

C) b a c D) c a b

Solution:

Lets equal to coefficients of a

30 42

30 20

a b

a c

So 30 42 20a b c

The one whose coefficient is the smalest is the greatest

one.

So c a b

Answer: D

Q19: How many subsets of , , ,A I S M O have

only two elements?

A) 4 B) 5 C) 6 D) 7

Solution:

, , , , , , , , , , ,P A I S I M I O S M S O M O

There are 6 subsets of P A which has only two

elements.

Answer: C

Q20: 0.04 0.06 0.09 0.66 0.09 ?

A) 0.36 B) 0.064 C) 0.48 D) 4.8

Solution:

0.04 0.06 0.09 0.66 0.09

0.04 0.06 0.3 0.66 0.3

0.04 0.36 0.36

0.04 0.6 0.6

0.64 0.6

0.8 0.6 0.48

Answer: C

Q21: Simplify 1.44 0.04

0.09 0.04

.

A) 1 B) 2 C) 0.1 D) 0.2

Solution:

1.44 0.04 1.2 0.2 1 12

10.3 0.2 0.50.09 0.04

2

Answer: B

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Q22: The sum of 20% and 25% of a number is 540.

What is the number?

A) 900 B) 1100 C) 1200 D) 1800

Solution:

The sum of 20% and 25% is as the sum of 45%.

The number is 540

100 120045

Answer: C

Q23: To find 10 percent of a number is same as the

divide the same number by:

A) 100 B) 0.1 C) 10 D) 5

Solution:

To find 10 percent of a number is same as the divide

the same number by 10

Because 1

10%10

Answer: C

Q24: Which of the following is false?

A) 1 4 16 7 B) 256 2

C) 144

49

D) 0.4 0.9 0.06

Solution:

A) 1 4 16 1 2 4 7 True

B) 256 16 4 2 True

C)

2

2

144 12 124

9 3 3 True

D) 4 9 2 3 6

0.4 0.91010 10 100

False

Answer: D

Q25: The set , , ,1, , 2A a b c a given.

Which of the following is false?

A) 6n A B) a A

C) a A D) a A

Solution:

a is not a subset of set A. The subsets are usually

represented by a

Answer: D

Q26: What is the value of a if the values of x in the

equation 2 3 4 2 1 18x x satisfies the

equation 2 3 1

3 5 3

x a x a

A) 3

8 B)

3

8 C)

1

8 D)

1

8

Solution:

2 3 4 2 1 18

2 6 8 4 18

10 18 6 4

10 20

2

x x

x x

x

x

x

If 2x , then

2 3 1

3 5 3

4 6 1

3 5 3

20 5 18 3 1

15 3

x a x a

a a

a a

2 8

15

a

1

3

2 8 5

8 3

3

8

a

a

a

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Answer: A

Q27: In a city, 75 % of people use tablet and 55 % of

people use mobile.

At least what percent of people use both tablet and

mobile?

A) 30 % B) 25 % C) 20 % D) 15 %

Solution:

75% 55% 130%

The number of the people of the city cannot be more

than 100%.

That means 30% of the people in the city use both

tablet and mobile.

Answer: A

Q28: If 30% of m is equal to 75% of n , what is 50%

of m if 84n ?

A) 110 B) 120 C) 105 D) 115

Solution:

30% 75%

30

100

m n

75

100m

30

n

75m 2 5

n

m n

If 84n ;

2 5 84m 5 42

210

m

m

The question is to find 50% of m

That is 50

210 105100

Answer: C

Q29: What percent of the numbers from 1 to 100 are

divisible by 4?

A) 20% B) 25% C) 24% D) 40%

Solution:

The numbers from 1 to 100 divisible by 4 are

4,8,12,16,20,.........,100

There are total 25 numbers from 1 to 100.

That is 25 out of 100, which is 25%

Answer: B

Q30: 144 9 3

?9 81 27

A) 1

3 B) 3 C)

1

4 D) 4

Solution:

PAKTURK 10th



144

9

9

81

3

27

1 116

9 9

14

3

1

3 4

Answer: D

Q31: The numbers which are equal to sum of square

and square root of itself known as awesome numbers.

Example: 2

4 4 16 2 18

Which of the following numbers is also awesome

number?

A) 84 B) 120 C) 196 D) 424

Solution:

29 9 81 3 84

Answer: A

Q32: Based on the diagram below, which of the

following is false?

A) a b e B) a c d

C) 180a b c D) 180d e

Solution:

A) a b e True (Sum of the measures of any two

interiror angles is equal to the measure of the third

angle)

B) a c d True (Sum of the measures of

any two interiror angles is equal to the measure of the

third angle)

C) 180a b c True (Sum of the measures of

agles of any traingle is equal to 180 )

D) 180d e False ( d e cannot be

daterminined with the given information)

Answer: D

Q33: What is the average of the squares and the

cubes of first 3 prime numbers?

A) 27 B) 33 C) 35 D) 41

Solution:

The first three prime numbers are 2,3 and 5. Their

squares are 4, 9 and 25 respectively while their cubes

are 8, 27 and 125 respectively.

The average of the squares and the cubes will be

calculated as;

4 9 25 8 27 125 19833

6 6

Answer: B

Q34: One pipe can fill a tank three times as fast as

another pipe. If together the two pipes can fill the tank

in 36 minutes, then the slower pipe alone will be able to

fill the tank in:

A) 81 min B) 108 min

C) 144 min D) 192 min

Solution:

PAKTURK 10th



1 1 1

3 36

4 1

3 36

3 144

48

x x

x

x

x

48min

3 144min

x

x

Answer: C

Q35: It takes six people eight hours to stuff 10,000

envelopes.

How many people would be required to do the job in

three hours?

A) 4 B) 12 C) 16 D) 18

Solution:

Six people in one hour can stuff 10,000

12508

envelopes.

One person can stuff 1250

6 envelopes in one hour.

One person can stuff 1250

3 6256

envelopes in

three hours.

The number of people who can stuff 10,000 envelops in

3 hours can be calculated by 10,000

16625

Answer: C

Q36: What is the tenth term of the pattern below?

10 9 8 7, , , , ......

1024 512 256 128

A) 1

2 B)

1

4 C)

3

4 D)

3

8

Solution:

The numerator decreases by 1, so the 10th term will be

1.

The denominator decreases by half. 1024, 512, 256, 128,

64, 32, 16, 8, 4, 2. The 10th term will be 2.

So the 10th term of the number pattern will be 1

2

Answer: A

Q37: Iqra is 10 years old. Her mother Asma is 4 times

as old as Iqra.

How old will Asma be when Iqra is twice as old as she

is now?

A) 80 years B) 70 years

C) 60 years D) 50 years

Solution:

Asma is 4 times Irra. If Iqra is 10 years old, then Asma

will be 40 years old.

When Iqra will be twice of her present age, mother will

be 50 years old. Because both will increase by 10.

Diffrennce af ages does not change.

Answer: D

Q38: In the diagram below, lines K and L are parallel,

and lines Mand N are parallel.

PAKTURK 10th



What is the value of "a" if b=10?

A) 4 B) 8 C) 10 D) 12

Solution:

10 40a and 4 20b are supplemantary angles.

10 40 4 20 180

10

10 180 60 40

10 80

8

a b

b

a

a

a

Answer: B

Q39: The shadow of a tree which is 300 cm long is

240 cm long while the shadow of Yasir is 144 cm long.

How tall is Yasir in centimeters?

A) 180 B) 184 C) 175 D) 190

Solution:

This question can be solved by direct proportion.

Yasir will be 300

144 240

x tall.

240 144 300

180

x

x cm

Answer: A

Q40: There are two sections A and B of a class,

consisting of 36 and 44 students’ respectively. If the average weight of section A is 40kg and that of section

B is 35kg, find the average weight of the whole class.

A) 35.25 B) 36 C) 37.25 D) 38

Solution:

If the average weight of section A is 40. It means the

total weight is 40 36 1440 .

If the average weight of section B is 35. It means the

total weight is 44 35 1540 .

The total weight of both section A and B is

1440 1540 2980

The average weight of whole class is 2980

37.2580

kg

Answer: C

Q41: The numbers are arranged according to a rule.

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What is A+B+C?

A) 76 B) 84 C) 92 D) 98

Solution:

In the first diagram; all the numbers depend on 8.

32 is four times 8.

18 is two more than two times 8.

36 is four more than four times 8.

Same rule is followed in the second diagram.

Lets apply the same rule in the third diagram to find

A,B and C

four times 7 is equal to B. So B=28

two more than tow times 7 is C. So C=16

Four more four times 7 is A. So A=32

28 16 32 76A B C

Answer: A

Q42: In the diagram below, ABCD is a rectangle.

Line FD is 6 3 units long, line EB is eleven units

long, and the measure of angle ECD is 60 . What is

the length of line EF ?

A) 10 3 B) 10 C) 5 3 D) 5

Solution:

The properties of 30 ,60 ,90

Answer: B

Q43: What is the number indicated by question

mark?

A) 44 B) 55 C) 80 D) 18

Solution:

2

2

2

2

2

49 6 1

64 5 3

9 3 0

49 7 0

81 1 8

The suitable value for placing question mark is 18

Answer: D

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Q44:

4 7 10

3 5 7

1 2 3

3 5 7

A

B

Which of the following is correct?

A) 3A B B) 121

105A B

C) 7

3A D)

1

4B

Solution:

4 7 10

3 5 7

1 2 3

3 5 7

4 7 10 1 2 3

3 5 7 3 5 7

4 1 7 2 10 3

3 3 5 5 7 7

3 5 71 1 1 3

3 5 7

A

B

A B

A B

A B

Answer: A

Q45: Which number will come instead of A?

A) 45 B) 27 C) 15 D) 5

Solution:

We get the same result (108) by multiplying the

numbers which are indicated by red lines.

4 108

27

A

A

The value of A is 27.

Answer: B

Q46: Three lines intersect in one point. Two angles

are given in the figure. How many degrees is the grey

angle?

A) 52 B) 54

C) 56 D) 58

PAKTURK 10th



Solution:

In the figure above, the angles indicated by a are

vertical angles which are congruent.

The angles a , 180 a and 124 a are

supplementary angles

108 124 180a a a

a

108 a 124 180

180 232

52

52

a

a

a

a

Answer: A

Q47: In the triangle ABC, what is the value of x if

AB AC

?

A) 42 B) 46

C) 48 D) 50

Solution:

14 116 180

180 130

50

x

x

x

Answer: D

Q48: How many squares are there in the figure

below?

A) 25 B) 30 C) 41 D) 45

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Solution:

The red squares shows the number of all the squares in

the figure. There are total 41 squares in the figure.

Answer: C

Q49: Find the area of shaded region if the line

segments AC, AB and BC are the diameters of the

circles.

A) 225

12 cm2

B) 2

24cm

C) 224 25 cm D)

225cm

2

Solution:

The area of the right angled triangle is

28cm×6cm=24cm

2

The area of the semicircle with radius 5 cm is:

22

25 π25cm 25 πcm

2 2 2

cm


22

24 π16cm

8πcm2 2

cm


22

23 π9cm 9 πcm2 2 2

cm

The total area of the semicircles is

2 2 29 25π8πcm πcm cm

2 2

Sum of the non-shaded areas of two semicircles with

the radius 4 and 3 is: (The area of the semicircle with

radius 5 - the area of the triangle)

225πcm -24cm

2

The area of shaded region of both semicircle with the

radius 4 and 3 is 2 225π 25π

cm cm -24cm 24cm2 2

Answer: B

PAKTURK 10th



Q50: In the figure shown above, lengths AB, AC, and

CD are all 4 2 units. Angles B and D are both 45°.

What is the perimeter and area of ABCD?

A) Area : 8 2

Perimeter :16 8 2 B)

Area : 8

Perimeter :8 8 2

C) Area : 16

Perimeter :8 8 2 D)

Area : 32

Perimeter :16 8 2

Solution:

The side AB and the side AC are congruent, so

45BCA and 90BAC .

The area of the rectangle is

4 2 4 2 32AC AB

By applying Pythagorean theorem,

2 22

4 2 4 2

8

BC

BC

The perimeter of the rectangle is

2 8 4 2 16 8 2

Answer: D

10th National ISMO Class 8 Question Paper With Solutions

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