IMO - Mock Test

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IMO - Mock Test - 9

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Weekly Quiz Competition

Question 1

1.2 / -0

A coach asked 3 players of a basketball team to attempt 25 free throws each during practice. The given table shows the number of free throws each player made in 25 attempts. Based on the information in the table, which is the most reasonable prediction of the number of free throws Armaan will make out of his next 75 attempts?

Free throws
Players	Number of free throws made
Piyush	12
Siddharth	18
Armaan	5

12

60

15

5 Solution

Number of free throws made by Armaan in 25 attempts = 5
∴ Number of free throws made by Armaan in 75 attempts = 5 × = 15

Question 2

1.2 / -0

The given table shows the start and the end time of a movie at a theatre. According to the information in the table, which of the following statements is true?

Movie Time
Start	End
12:30 P.M.	2:45 P.M.
3:00 P.M.	5:15 P.M.
6:45 P.M.	9:00 P.M.
9:20 P.M.	11:35 P.M.

The end time is exactly 2 hours 45 minutes after the start time.

The end time is exactly 2 hours 15 minutes after the start time.

The end time is exactly 3 hours 30 minutes after the start time.

The end time is exactly 3 hours 45 minutes after the start time.

Solution

Time at which the movie starts = 12:30 P.M.
Time at which the movie ends = 2:45 P.M.
So, duration of the movie = 2 hours 15 minutes

Time at which the movie starts = 3:00 P.M.
Time at which the movie ends = 5:15 P.M.
So, duration of the movie = 2 hours 15 minutes

Time at which the movie starts = 6:45 P.M.
Time at which the movie ends = 9:00 P.M.
So, duration of the movie = 2 hours 15 minutes

Time at which the movie starts = 9:20 P.M.
Time at which movie ends = 11:35 P.M.
So, duration of the movie = 2 hours 15 minutes
Therefore, option (2) is true.

Question 3
1.2 / -0

Five girls are standing in a row facing east. Savita is to the right of Urvashi, Tina and Urmila. Urvashi, Tina and Urmila are to the right of Kanika. Urmila is between Urvashi and Tina. If Tina is fourth from the left end of the row, then how far is Urvashi from the right end?

A
First

B
Second

C
Fifth

D
Fourth

Solution

By using the given information, we get following arrangement:

Urvashi is fourth from the right end.
Question 4
1.2 / -0

Figures (i), (ii), (iii) and (iv) constitute the problem set. There is a definite relationship between figures (i) and (ii). Establish a similar relationship between figures (iii) and (iv) by selecting a suitable figure from the options that would replace (?) in figure (iv).

A

B

C

D

Solution

The pattern followed between (i) and (ii) is, and a new element is added at the left bottom.
Hence, option (4) is the correct answer.
Question 5
1.2 / -0

In a joint family, there are father, mother, 4 married sons and three unmarried daughters. Of the sons, two have 2 daughters each, and two have a son and a daughter each. How many female members are there in the family?

A
15

B
12

C
14

D
11

Solution

According to the question, we get following arrangement:

F - Father
M - Mother
S - Son
W - Wife
D - Daughter
Number of female members = 1M + 4W + 3D + 6D = 14
Hence, there are 14 female members in the family.
Question 6
1.2 / -0

Which of the following options can replace the last grid ?

A

B

C

D

Solution

Number of shaded dots are increased by 1 in each step.
In first step, there are 4 shaded dots. In the next step 5, dots are shaded. By following this pattern, answer figure must have 9 shaded dots.
Hence, option (4) is the correct answer.
Question 7
1.2 / -0

Which of the following cubes CANNOT be formed using the net?

A

B

C

D

Solution

2 and 5 have different orientations according to the net. Hence, cube in option (3) cannot be formed using the given net.
Question 8
1.2 / -0

If the first three letters of the word 'ANTHROPOLOGISTS' are written in reverse order, followed by the next four letters written in reverse order, followed by next eight letters written in reverse order, which letter will come exactly in the middle?

A
T

B
H

C
S

D
O

Solution

First three letters in reverse order: TNA
Next four letters written in reverse order: PORH
Next eight letters written in reverse order: STSIGOLO
The new word formed is,

So, S is the middle letter.
Question 9
1.2 / -0

Two positions of a dice marked (A, B, C, D, E, F) are shown below. Which letter will be on the face opposite to the face with A?

A
E

B
D

C
B

D
C

Solution

Adjacent faces of A are B, C, E, F. So, face opposite to A is D.
Question 10
1.2 / -0

Which of the following Venn diagrams correctly depicts the relationship among ''Yak, Zebra, Bear''?

A

B

C

D

Solution

Since Yak, Bear and Zebra are not related to each other, so we get the following Venn diagram:
Question 11
1.2 / -0

P, Q, R and S are playing cards. P, R and Q, S are partners. If Q is in the North of S and P is in the West of R, then the position of R with respect of S is _________.

A
North-East

B
North-West

C
South

D
North

Solution

According to the given information, we have:

So, position of R with respect to S is North-East.
Question 12
1.2 / -0

Arrange the following words in the sequence in which they occur in the dictionary.

1. Select
2. Seldom
3. Send
4. Selfish
5. Seller

A
1, 2, 4, 5, 3

B
2, 1, 5, 4, 3

C
2, 1, 4, 5, 3

D
2, 5, 4, 1, 3

Solution

The correct order is:
Question 13
1.2 / -0

Count the number of quadrilaterals of same size used to draw the given figure.

A
9

B
8

C
10

D
18

Solution

Required quadrilaterals of same size and are, A, B, C, D, EL, FK, GJ, HI, LKIJ.

So, required number of quadrilaterals = 9
Question 14
1.2 / -0

Find the next term in the series given below.

3F, 6G, 11I, 18L, ?

A
21O

B
25N

C
27P

D
27Q

Solution

The pattern is:

Also,
So, the next term is 27P.
Question 15
1.2 / -0

In the word MATHEMATICAL, if the first and third letters, the fourth and the sixth letters, the seventh and the ninth letters and the tenth and the twelfth letters were interchanged, then which of the following would be the seventh letter from the left end?

A
M

B
A

C
H

D
I

Solution

The new word formed is,
T A M M E H I T A L A C
So, seventh letter from the left end is I.
Question 16
1.2 / -0

Which single transformation is shown below?

A
Reflection

B
Rotation

C
Translation

D
None of these

Solution

Translation is a term used in geometry to describe a function that moves an object a certain distance. The object is not altered in any other way. It is not rotated, reflected or re-sized. In a translation, every point of the object must be moved in the same direction and for the same distance.
Hence, option (3) is the correct answer.
Question 17
1.2 / -0

Look at the square and the cube shown in figure.

Which of the following statements about both of these figures appears to be true?

A
The square has 4 times as many vertices as the cube.

B
The square is congruent to each face of the cube.

C
The square has 3 fewer sides than the cube has edges.

D
The square has the same number of right angles as the cube.

Solution

A cube has 12 edges. Because all faces are squares and congruent to each other, all 12 edges are of the same length. A point formed where three edges meet is called a vertex. A cube has 8 vertices.
Hence, option (2) is the correct answer.
Question 18
1.2 / -0

The list given below shows the number of students out of 30 who choose different food items in a cafeteria.

(i) 11 students choose pizza.
(ii) 4 students choose hamburgers.
(iii) 3 students choose tacos.
(iv) __?__ students choose salad.

How many students choose salad?

A
18, because 11 + 4 + 3 = 18

B
26, because 30 - (11 - 4 - 3) = 26

C
12, because 30 - 11 - 4 - 3 = 12

D
20, because 30 - (11 - 4) - 3 = 20

Solution

Number of students who choose salad = 30 - (11 + 4 + 3) = 30 - 18 = 12
Question 19
1.2 / -0

Simplify 14 ÷ (21 ÷ 3) + 7 - 1

A
6

B
7

C
8

D
9

Solution

Using BODMAS, we have
14 ÷ (21 ÷ 3) + 7 - 1
= 14 ÷ 7 + 7 - 1
= 2 + 7 – 1
= 8
Question 20
1.2 / -0

How many right angles are there in a half turn, i.e. 180°?

A
1

B
2

C
3

D
4

Solution

There are 4 right angles in a full turn and 2 right angles in a half a turn.
Question 21
1.2 / -0

Which of the following has fractions in ascending order?

A

B

C

D

Solution

L.C.M. of 3, 5, 9 and 11 = 3 × 3 × 5 × 11 = 495

Now, ,

,

.
Question 22
1.2 / -0

Find the value of X in the given expression.

832.58 - 242.31 = 779.84 - X

A
179.57

B
199.57

C
295.05

D
189.57

Solution

We have,
832.58 - 242.31 = 779.84 - X
X = 779.84 - 832.58 + 242.31
X = 189.57
Question 23
1.2 / -0

Which of the following numbers is completely divisible by 3?

A
297149

B
1790184

C
6392105

D
901352

Solution

A number is divisible by 3 if the sum of the digits is divisible by 3.
(1) 2 + 9 + 7 + 1 + 4 + 9 = 32 is not divisible by 3
(2) 1 + 7 + 9 + 0 + 1 + 8 + 4 = 30 is divisible by 3
(3) 6 + 3 + 9 + 2 + 1 + 0 + 5 = 26 is not divisible by 3
(4) 9 + 0 + 1 + 3 + 5 + 2 = 20 is not divisible by 3
Question 24
1.2 / -0

The given figure is made up of 10 squares of the same size. The perimeter of the figure is 80 cm. Find the area of the figure.

A
250 cm²

B
150 cm²

C
280 cm²

D
190 cm²

Solution

Let the length of side of each small square be x cm.
Then, perimeter of the figure = 16x
80 = 16x x = 80 ÷ 16 = 5
So, length of side of each small square = 5 cm
∴ Area of 1 small square = 5 × 5 = 25 cm²
So, area of figure = Area of 10 small squares = 10 × 25 = 250 cm²
Question 25
1.2 / -0

Which of the following figures have at least one line of symmetry?

A
l and Il

B
I and III

C
II and Ill

D
I, II and III

Solution

Following are the lines of symmetry (in red) of the given figures:

Figure I has a horizontal line of symmetry. Figure II has no line of symmetry. Figure III has both a horizontal and a vertical line of symmetry.
Question 26
1.2 / -0

What must be added to the product of and 3 to make ?

A

B

C

D

Solution

Let the number added be x.
According to question,

So, should be added.
Question 27
1.2 / -0

Which of the following numbers is divisible by 11?

A
1011011

B
1111111

C
22222222

D
3333333

Solution

A number is divisible by 11, if the difference of the sum of numbers at odd places and that of at even places is either 0 or divisible by 11.

Option:1 1011011
Sum of numbers at odd places = 1 + 1 + 0 + 1 = 3
Sum of numbers at even places = 0 + 1 + 1 = 2
Difference = 1 (Not divisible by 11)

Option:2 1111111
Sum of numbers at odd places = 1 + 1 + 1 + 1 = 4
Sum of numbers at even places = 1 + 1 + 1 = 3
Difference = 1 (Not divisible by 11)

Option:3 22222222
Sum of numbers at odd places = 2 + 2 + 2 + 2 = 8
Sum of numbers at even places = 2 + 2 + 2 + 2 = 8
Difference = 0 (Divisible by 11)

Option:4 3333333
Sum of numbers at odd places = 3 + 3 + 3 + 3 = 12
Sum of numbers at even places = 3 + 3 + 3 = 9
Difference = 3 (Not divisible by 11)

From options, only 22222222 is divisible by 11.
Question 28
1.2 / -0

35% of a number is 189. What is 25% of the number?

A
315

B
135

C
540

D
125

Solution

Let the number be x.
Then, 35% of x = 189
= 540
Now, 25% of 540 = = 135
Question 29
1.2 / -0

If P and Q represents the prime digits, then find the value of P and Q respectively.

A
3, 3

B
7, 5

C
1, 5

D
7, 3

Solution

∴ P = 7, Q = 3
Question 30
1.2 / -0

Which of the following figures satisfy the given conditions?

A
A

B
B

C
C

D
D

Solution

(i) Faces : ABC, ACD, ABD and BCD
Edges : AB, AC, AD, BD, DC, BC
Vertices : A, B, C, D

(ii) Faces : ABDF, ABCE, BDC, AFE, FECD
Edges : AE, FE, AF FD, EC, DC, BD, BC, AB
Vertices : A, B, C, D, E, F
Question 31
1.2 / -0

Which of the following numbers is divisible by 3?

A
700458

B
2345162

C
6594832

D
7145221

Solution

A number is divisible by 3, if the sum of digits of the number is divisible by 3.
Now,
(1) 7 + 0 + 0 + 4 + 5 + 8 = 24 is divisible by 3.
(2) 2 + 3 + 4 + 5 + 1 + 6 + 2 = 23 is not divisible by 3.
(3) 6 + 5 + 9 + 4 + 8 + 3 + 2 = 37 is not divisible by 3.
(4) 7 + 1 + 4 + 5 + 2 + 2 + 1 = 22 is not divisible by 3.
So, only 700458 is divisible by 3.
Question 32
1.2 / -0

The number line given below represents ________.

A
2 + 3 = 5

B
5 - 2 = 3

C
5 - 3 = 2

D
5 + 3 = 3 + 5

Solution

If we are counting towards right, then it means we are making the number by adding.
Hence, number line represents 2 + 3 = 5.
Question 33
1.2 / -0

In the Gobi Desert, temperature of -60° F was recorded but in Sahara Desert on the same day it was 186° F. What is the difference between these two temperatures?

A
246°C

B
126°F

C
126°C

D
246°F

Solution

Temperature in Gobi Desert = -60°F
Temperature in Sahara Desert = 186°F
∴ Difference between the two temperatures
= 186° - (-60°) = 186° + 60° = 246° F
Question 34
1.2 / -0

The given star is formed from 12 identical equilateral triangles. The perimeter of star is 72 cm. What is the perimeter of shaded hexagon?

A
42 cm

B
36 cm

C
48 cm

D
30 cm

Solution

Let the side of each equilateral triangle be x cm.
Given, perimeter of star is 72 cm.
Then,
12x = 72 x = 6
So, side of each equilateral triangle = 6 cm
Now, perimeter of shaded hexagon
= 6 × side of equilateral triangle
Perimeter = 6 × 6 = 36 cm
Question 35
1.2 / -0

Karan is k years old. Rahul's age, r, is 6 more than 2 times Karan's age. Which of the following equations best represents Rahul's age?

A
r = (6 + 2)k

B
k = 2r + 6

C
r = 2k + 6

D
k = (6 + 2)r

Solution

Age of Karan = k
2 times Karan's age = 2k
6 more than 2 times Karan's age = 2k + 6
∴ Age of Rahul (r) = 2k + 6
Question 36
1.2 / -0

Which of the following is an ISOSCELES triangle?

A

B

C

D

Solution

An isosceles triangle is a triangle with two equal sides.
In CDE, CE = DE = 6.2 cm
So, CDE is an isosceles triangle.
Question 37
1.2 / -0

Look for the pattern in the three sequence of numbers given below.

2, 4, 6, 8, 10
7, 14, 21, 28, 35
11, 22, 33, 44, 55

Each sequence is an example of what kind of numbers?

A
Even numbers

B
Multiples

C
Primes

D
Odd numbers

Solution

2, 4, 6, 8, 10 are multiples of 2.
7, 14, 21, 28, 35 are multiples of 7.
11, 22, 33, 44, 55 are multiples of 11.
Therefore, the given numbers are the multiples of a certain number.
Question 38
1.2 / -0

Sneha earns Rs. 110 each week by taking care of pets. Which of the following is the best estimate of how much money she will earn in 28 weeks while taking care of the pets?

A
Rs. 2180

B
Rs. 2890

C
Rs. 2990

D
Rs. 3080

Solution

Amount earned in 1 week = Rs. 110
∴ Amount earned in 28 weeks = Rs. (110 × 28)
= Rs. 3080
Question 39
1.2 / -0

If one-third of a tank holds 80 litres of water, then the quantity of water that half of the tank holds is ______.

A
litres

B
100 litres

C
120 litres

D
240 litres

Solution

One-third of the tank holds 80 litres.
∴ Whole tank will hold 80 × 3 = 240 litres
∴ Half of the tank holds 240 ÷ 2 = 120 litres
Question 40
1.2 / -0

If cost of a toffee is 50 paise and cost of a chocolate is Rs. 10, then the ratio of the cost of toffee to the cost of a chocolate is _______.

A
5 : 1

B
1 : 20

C
1 : 5

D
20 : 1

Solution

Cost of a toffee = 50 paise
Cost of a chocolate = Rs. 10 = 1000 paise (Rs. 1 = 100 paise)
Ratio of the cost of toffee to the cost of a chocolate = 50 : 1000 = 1 : 20
Question 41
1.2 / -0

Dinesh joined 2 squares of area 81 cm² and 36 cm² together. What is the perimeter of the new figure now?

A
45 cm

B
48 cm

C
54 cm

D
60 cm

Solution

The new figure formed is shown below.

Area of ABCD = 81 cm² AB = 9 cm
Similarly, Area of BEFG = 36 cm²
So, BG = 6 cm
∴ Perimeter of the figure = 9 + 9 + 9 + 6 + 6 + 6 + 3 = 48 cm
Question 42
1.2 / -0

Sanya bought two dozen similar pens. She gave two Rs. 100 notes to the cashier and received Rs. 13.60 as change. How much did each pen cost?

A
Rs. 7.77

B
Rs. 6.76

C
Rs. 5.87

D
Rs. 8.46

Solution

Cost of 2 dozen pens = Rs. (100 × 2 - 13.60)
= Rs. (200 - 13.60)
= Rs. 186.40
Cost of 24 pens = Rs. 186.40
Cost of 1 pen = = Rs. 7.77
Question 43
1.2 / -0

Megha and Beena shared 272 beads. If Megha has thrice as many beads as Beena, then how many beads does Megha have?

A
68

B
204

C
104

D
202

Solution

Let the number of beads Beena has be x.
Then, the number of beads Megha has = 3x
Total number of beads = 272
According to question,
x + 3x = 272
4x = 272 x = 68
So, number of beads that Megha has = 68 × 3 = 204
Question 44
1.2 / -0

A man spends of his monthly income on house rent, on food and on other items. He saves Rs. 800 in the end. What was his monthly income?

A
Rs. 24,000

B
Rs. 22,000

C
Rs. 25,000

D
Rs. 20,000

Solution

Let the income of man be x.
∴ Total expenditure =
=
∴ Fraction of savings =
Amount of money saved = Rs. 800
= 24,000
∴ Total monthly income = Rs. 24,000
Question 45
1.2 / -0

Mohit sliced an orange into circular pieces to put into a bowl of punch. The piece shown below have a radius of 4 centimetres. Which expression can be used to find the approximate circumference of this piece of orange?

A
× (4)²

B
4 ×

C
2 × × 7

D
2 × × 4

Solution

Radius = 4 cm
Circumference = 2r = 2 × × 4

Question 46

1.2 / -0

Match Column-I with Column-Il. If a, b, c, are whole numbers, then

Column-I	Column-Il
(i) a + b = b + a	(a) Distributivity of multiplication
(ii) (a + b) + c = a + (b + c)	(b) Commutativity under addition
(iii) a × (b + c) = a × b + a × c	(c) Associativity of addition
	(d) Commutativity under multiplication

(i) - (c), (ii) - (d), (iii) - (a)

(i) - (b), (ii) - (c), (iii) - (d)

(i) - (a), (ii) - (b), (iii) - (c)

(i) - (b), (ii) - (c), (iii) - (a)

Solution

(i) a + b = b + a is commutative property under addition.
(ii) (a + b) + c = a + (b + c) is associative property under addition.
(iii) a × (b + c) = a × b + a × c is distributive property of multiplication over addition.

Question 47
1.2 / -0

Figure P is made up of six identical squares. Two squares were removed from figure P to form figure Q. The perimeter of figure P is 240 cm. What is the perimeter of figure Q?

A
220 cm

B
180 cm

C
200 cm

D
160 cm

Solution

Let the side of each square be x.
So, perimeter of figure P = 12x
240 = 12x
x = 20 cm
∴ Perimeter of figure Q = 10x = 10 × 20 = 200 cm
Question 48
1.2 / -0

Study the statements given below and choose the correct answer.

Statement-1 : Numbers having more than two factors are known as composite numbers.
Statement-2 : A number for which sum of all its factors is equal to twice the number is called a perfect number.

A
Statement-1 is true and statement-2 is false.

B
Statement-1 is false and statement-2 is true.

C
Both statements are true.

D
Both statements are false.

Solution

A composite number is a positive integer that can be formed by multiplying two smaller positive integers. Equivalently, it is a positive integer that has at least one divisor other than 1 and itself. Therefore, Statement-1 is true.
A perfect number is a positive integer that is equal to the sum of its positive divisors, excluding the number itself. For instance, 6 has divisors 1, 2 and 3, and 1 + 2 + 3 = 6, so 6 is a perfect number. Therefore, Statement-2 is true as well.
Hence, both the statements are true.
Question 49
1.2 / -0

Armaan received Rs. 2800 as a gift. He wanted to use the money to go to the movies and to buy a book. He wanted to save the money he was left with. Which is the correct order of steps to find the amount of money Armaan would have left to save?

Step K: Find the sum of the costs of the movie and the book.
Step L: Find the difference between Rs. 2800 and the sum of the costs of the movie and the book.
Step M: Identify the cost of the movie and the cost of the book.

A
L, K, M

B
M, K, L

C
L, M, K

D
K, L, M

Solution

The following are the steps to find the amount of money Armaan would have left to save:
(I) Step M: Identify the cost of the movie and the cost of the book
(II) Step K: Find the sum of the costs of the movie and the book.
(III) Step L: Find the difference between Rs. 2800 and the sum of the costs of the movie and the book.
So, the correct order is, M, K, L.
Question 50
1.2 / -0

The capacity of a drum is 50 L and that of a bucket is L. If 5 buckets of water are poured into the drum, then what fraction of the drum remains empty?

A
1/4

B
1/2

C
3/4

D
1/8

Solution

Capacity of 1 bucket = L
∴ Quantity of water poured into the drum
= 5 × Capacity of 1 bucket
= 5 ×
Now, capacity of drum = 50 L
Quantity of water poured = L
∴ Fraction of drum that remains empty
₌