IMO - Mock Test

Result

IMO - Mock Test - 10

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Weekly Quiz Competition

Question 1
1.2 / -0

Directions: Find the next number in the following pattern. 22, 222, 2001, 16012, ?

A
30023

B
112079

C
112089

D
202021

Solution

The pattern is 22 × 10 + 2 = 222
222 × 9 + 3 = 2001
2001 × 8 + 4 = 16012
16012 × 7 + 5 = 112089
Question 2
1.2 / -0

Directions: Find out the number of triangles in the given picture.

A
10

B
12

C
14

D
16

Solution

△AGF, △AGB, △FGE, △AFE, △AFB, △CHD, △EHD, △BHC, △ECD, △BCD, △AEC and △FBD.
Thus, there are 12 triangles in all. Hence, answer option (2) is correct.
Question 3
1.2 / -0

Directions: Find out the incorrect term in the series.

45, 48, 43, 46, 49, 44

A
43

B
49

C
48

D
44

Solution

The series goes as +3, -5.
Therefore,
45 + 3 = 48,
48 - 5 = 43,
43 + 3 = 46,
46 - 5 = 41,
41 + 3 = 44
So, the incorrect number is 49.
Hence, answer option (2) is correct.
Question 4
1.2 / -0

If SNAP can written as RLXL, then BOLD can be written as

A
ANIZ

B
AMIA

C
AMIZ

D
DLOB

Solution

S - 1 = R
N - 2 = L
A - 3 = X
P - 4 = L
Similarly,
B - 1 = A
O - 2 = M
L - 3 = I
D - 4 = Z
Question 5
1.2 / -0

C is the father of S, S is the sister of B, B is the brother of A, D is the daughter of A and E is the brother of D. How is B related to E?

A
Uncle

B
Niece

C
Nephew

D
Mother

Solution

B is the uncle of E.
Question 6
1.2 / -0

Directions: Study the following figure and answer the question given below.

How many uneducated people are married?

A
8

B
9

C
10

D
11

Solution

Number of uneducated people who are married = 3 + 6 = 9.
Question 7
1.2 / -0

If the letters of English alphabet are all written in a straight line, then which of the following letters is the 11^th letter from the left of the 20^th letter from the left?

A
I

B
J

C
K

D
H

Solution

I is the 11^th letter to the left of the 20^th letter from the left.
Question 8
1.2 / -0

V, P, T, L, J, M, Z and X are sitting in a restaurant around the round table facing the centre, not necessary in the same order. Z is sitting opposite T and V is sitting opposite J. X is sitting third to the left of T. X is sitting fourth to the right of L. M is sitting exactly between Z and J.

What is the position of P with respect to J?

A
P is sitting third to the left of J.

B
P is sitting second to the right of J.

C
P is sitting 4^th to the left of J.

D
P is sitting 4^th to the right of J.

Solution

P is sitting 3^rd to the left of J.
Question 9
1.2 / -0

Four friends are standing in the queue facing South. C is standing third to the left of A and B is between A and D. B is standing at which of the following positions?

A
Second to the right of C

B
Immediate right of A

C
Second to the left of A

D
Immediate left of D

Solution

B is standing between A and D. B is second to the right of C.
Question 10
1.2 / -0

Five girls participated in a dance competition. Raveena ranked lower than Savita. Veena was ranked higher that Dyna. Kimmy ranked exactly between Raveena and Veena.

Who was ranked the highest?

A
Savita

B
Veena

C
Dyna

D
Kimmy

Solution

According to the question,
Raveena < Savita
Veena > Dyna

The ranking of the competition is Savita > Raveena > Kimmy > Veena > Dyna or Savita > Veena > Kimmy > Raveena > Dyna.
Thus, it is evident that Savita is ranked the highest.
Hence, answer option (1) is correct.
Question 11
1.2 / -0

Rock goes for a walk and starts from point A, walks for 7 km towards South. He reaches point B and moves to the right side and walks for 14 km and reaches point C. From point C, he moves to the right side and walks for 7 km and reaches point D. Then, he moves to the right side and walks for another 4 km and reaches point E. What is the required distance to reach point A again?

A
10 km

B
12 km

C
15 km

D
16 km

Solution

Required distance = AE = (14 - 4) km = 10 km
Question 12
1.2 / -0

The given image(X) is embedded in which of the following options?

A
(a)

B
(b)

C
(c)

D
(d)

Solution

From the figure, it is clear that figure (x) is embedded in figure (c). Hence, option (3) is correct.
Question 13
1.2 / -0

Which of the following mirror images is correct?

A

B

C

D

Solution

The correct mirror image is option (1). It is a horizontal mirror.
Question 14
1.2 / -0

Directions: Find the missing number on the same pattern as followed in the given figure.

A
652

B
562

C
256

D
650

Solution

The number in the centre of the rhombus has been formed by picking the last digits of the numbers given in the circles. For example: 5, 8 and 0 are picked from the circles of the first figure, combined together and written as 580 in the rhombus.
Question 15
1.2 / -0

If A denotes '', B denotes '', C denotes '' and D denotes '', then which of the following statements is true?

A
15B5C7D2 = 8

B
8A6C9B1 = 10

C
19C9C4B6 = 14

D
18A6B5B10 = 7

Solution

According to the given statement, A = '', B = '', C = '', and D = ''.
The expression in the first option becomes 15 ÷ 5 + 7 - 2 = 8.
Or, 3 + 7 - 2 = 8
Or, 10 - 2 = 8
Or, 8 = 8
Thus, answer option (1) is correct.
Question 16
1.2 / -0

If 3a²= b²≠ 0, then the value of is

A

B

C

D
b

Solution

= = =
Question 17
1.2 / -0

If a + b + c = 0, then what is the value of ?

A
1

B
x³

C

D
x^1/2

Solution
Question 18
1.2 / -0

What will be the approximate diameter of a circle if the area of the circle is 1964.28 cm²?

A
25 cm

B
40 cm

C
50 cm

D
100 cm

Solution

Area of a circle = r², where =and 'r' is the radius of circle.
1964.28 cm² = × r²1964.28 × cm² = r² cm = r,

r = 25 cm
D = Diameter of the circle = 2r
D = 50 cm
Question 19
1.2 / -0

Directions: Find the value of x.

A
5°

B
50°

C
65°

D
100°

Solution

Angle subtended by an arc at the centre of the circle is twice the angle subtended by it at any point on the remaining part of the circle.
Thus, the required angle is 100°/2 = 50°
Thus, answer option (2) is correct.
Question 20
1.2 / -0

A rectangular pyramid has height of 13 mm, length 18 mm and width 18 mm. What is the volume of this rectangular pyramid?

A
1,404 mm³

B
1,424 mm³

C
1,425 mm³

D
1,432 mm³

Solution

Volume of the rectangular pyramid: Volume = bh = × Area of base × Height
Area of base = 18 × 18 = 324
The height of rectangular pyramid = 13 mm

Now, volume = × area of base × height
= × 324 × 13 = 1,404
The volume of rectangular pyramid is 1,404 mm³.
Question 21
1.2 / -0

In the figure, the value of x would be

A
60 degree

B
120 degree

C
130 degree

D
140 degree

Solution

As the opposite angles of a cyclic quadrilateral are supplementary, x + 60° = 180°.
Or, x = 120°
Question 22
1.2 / -0

If a + b = - 4, what will be the value of a³ + b³ + 64?

A
- 12

B
12

C
- 12ab

D
12ab

Solution

Given, a + b = -4.
Cubing both sides, we get
(a + b)³ = (- 4)³
We know, (a + b)³= a³ + b³ + 3ab(a + b)
a³ + b³+ 3ab(a + b) = - 64
Or, a³ + b³ + 64 = - 3ab(a + b)
= -3ab(- 4)
a³ + b³ + 64 = 12ab
Question 23
1.2 / -0

In the given figure, K = 100° and L is the line which bisects K. Calculate angle KBG.

A
100°

B
80°

C
60°

D
40°

Solution

We know that KGB = 90° and K = 100°.
This means that BKG = 50° [As line L bisects K].
Therefore, KBG = 180° - 90° - 50°.
KBG = 180° - 140°
KBG = 40°.
Question 24
1.2 / -0

Ellie rolls a dice two times. What is the probability that the sum of numbers on the top face of each dice is more than 10?

A
0.055

B
0.073

C
0.083

D
0.111

Solution

Number of outcomes when a dice is rolled twice = 36.
Favourable observation if the sum is more than 10: 6 and 6, 5 and 6 and 6 and 5.
Number of favourable outcomes = 3

Probability =
Probability = = 0.083

Hence, answer option (3) is correct.
Question 25
1.2 / -0

The pie chart shows the percentage of people who play a certain game. What is the number of people playing table tennis if total number of people is 75000?

It is to be noted that all persons play 1 game only.

A
33750

B
37500

C
41250

D
None of these

Solution

The percentage is out of 100.
Therefore, for finding the percentage of table tennis players, we will add the given percentages and will subtract them from 100.
Required percentage = 100% - (15% + 10% + 20%) = 55%
So, the number of people who play table tennis = 55% of 75000 = 41250
Thus, answer option (3) is correct.
Question 26
1.2 / -0

A test consists of 40 questions in all (logical reasoning and non-reasoning) and the total marks for this test are 200. The logical reasoning questions are worth 4 marks each and the non-reasoning questions are worth 6 marks each. How many logical reasoning questions are there in the test?

A
10

B
20

C
30

D
40

Solution

Let the logical reasoning questions be x and non-reasoning questions be y.
Now, A.T.Q
x + y = 40 ......(i)
4x + 6y = 200 .....(ii)
Multiplying eq. (i) by 4 and subtracting it from equation (ii), we get
2y = 40
y = 20
x + y = 40
x + 20 = 40
x = 40 - 20 = 20
So, the number of logical reasoning questions = 20
Question 27
1.2 / -0

The sum of digits of a two-digit number is 10. If 18 is added to the number the digits are interchanged. Find the original number.

A
64

B
46

C
37

D
35

Solution

Let the digit at unit's place be y and the digit at tens place be x.
A.T.Q.
x + y = 10....(1)
10x + y + 18 = 10y + x
This implies that 9y - 9x = -18
Therefore, y - x = 2......(2)
Adding equation (1) and (2), we get
2y = 12
y = 6
Put the value of y in equation (1).
Hence, x = 4
Thus, the original number = 10x + y = 10(4) + 6 = 46.
Question 28
1.2 / -0

What is the value of the following expression?

A
0.77

B
0.828282....

C

D
None of these

Solution

2.6666.... - 1.8333..... = 0.8333.....
0.83333... + 18.43555... =
Question 29
1.2 / -0

Find the value of y in the given equation, if x = 2.

41x² + xy – 14.5x + 25 – 18xy = 0

A
3

B
4

C
5

D
8

Solution

41x² + xy – 14.5x + 25 – 18xy = 0If x = 2, equation becomes
164 + 2 × 2y – 29 + 25 - 36y = 0
160 = 36y – 4yy =

y = 5
Question 30
1.2 / -0

In the given figure, PQ = PR and angle PRS is 115°. Find the value of ∠QPR.

A
50°

B
65°

C
70°

D
75°

Solution

∠PRS + ∠PRQ = 180° (Linear pair)
∠PRQ = 180° – 115° = 65°
∠PRQ = ∠PQR (PQ = PR)
∠PRQ + ∠PQR + ∠QPR = 180°
65° + 65° + ∠QPR = 180°
∠QPR = 180° - 130° = 50°
Question 31
1.2 / -0

Which of the following statements is true?

A
One and only one circle can pass through two given points.

B
A minimum of 3 points are required to uniquely define a line.

C
Four non-collinear points may or may not be concyclic.

D
Any 3 points can uniquely define a circle.

Solution

Option 1: Minimum of 3 non-collinear points are required to uniquely define a circle. Hence, infinite number of circles can pass through 2 given points.
Option 2: Minimum of 2 points are sufficient to define a line. In fact, 3 points may or may not lie on the same line.
Option 3: 3 non-collinear points will definitely lie on a unique circle. The 4th may or may not lie on the same circle. Hence, 4 points may or may not be concyclic.
Option 4: Any 3 points do not uniquely define a circle. Any 3 non-collinear points define a circle uniquely.
Question 32
1.2 / -0

Find the area of an isosceles triangle if the perimeter of triangle is 30 cm and one of the equal sides is 12 cm in length.

A
9 cm²

B
9 cm²

C
cm²

D
19 cm²

Solution

Let third side of the triangle be x cm.
Perimeter of triangle = 30 cm
12 cm + 12 cm + x cm = 30 cm
x = 6

s = cm = 15 cm

By Heron's formula, area of triangle =

= cm²

= cm²
= 9 cm²
Question 33
1.2 / -0

If the product of abscissa and ordinate of a point is negative, then the point lies in which of the following quadrants?

A
1^stquadrant or 3^rdquadrant

B
1^stquadrant or 4^rdquadrant

C
2^ndquadrant or 3^rdquadrant

D
2^ndquadrant or 4^thquadrant

Solution

A.T.Q.
xy = Negative, which means that either x is negative and y is positive or x is positive and y is negative.
So, the point lies in either 2^nd quadrant or in 4^th quadrant.
Question 34
1.2 / -0

Directions: Find the mean of the following.

x + 2, x + 4, x + 6, x + 8, x + 10, x + 12, x + 14

A
x + 4

B
x + 6

C
x + 8

D
x + 10

Solution

By visual inspection, it is sufficient to point out that the mean is going to be the median, which in this case is x + 8.
Hence, answer option (3) is correct.
Question 35
1.2 / -0

If 4x + 5y = 9 and x and y are positive integers, then y could be

A
5

B
4

C
3

D
None of these

Solution

Here, x and y should be positive.
Now, 4x + 5y = 9
Going through options, if y = 5, then using value of y in the equation, we get
4x + 25 = 9
Or, 4x = -16
Or, x = -4, which is not possible.
Neither y = 4 nor y = 3 is possible. This is because both would give negative values of x.
The only possible value could be x = y = 1.
Question 36
1.2 / -0

The diameter of a circular floor design at Gagan's house is 4 m. Calculate the area of floor design.

A
4π m²

B
6π m²

C
8π m²

D
10π m²

Solution

The area of a circle is A = πr²First, we have to find the radius.
d = 2r
d/2 = r
4/2 m = r
2 m = r
The radius is 2 m.
Now, we have to find the area.
A = πr²= π x r²= 4π m²
Question 37
1.2 / -0

If the volume of a given rectangular prism is 1,080 cubic metres, then what is the value of d?

A
10 m

B
15 m

C
20 m

D
25 m

Solution

The rectangular prism is 12 m wide and 9 m high.
Volume of a rectangular prism: Volume = Length × Width × Height
1,080 m³ = d × 12 m × 9 m
1,080 m³ = d × 108 m²
(1,080 ÷ 108) m = d
10 m = d
Question 38
1.2 / -0

In the following figure, triangle ACE is right angled at C. AC is the angle bisector. Find the measure of angle CAB.

A
18°

B
28°

C
72°

D
162°

Solution

Given that ∠ECA = 90°
∠AEC = 72° (Vertically opposite angles)
In triangle ECA, ∠AEC + ∠ECA + ∠EAC = 180°
∠EAC = 180° - (90° + 72°)
∠EAC = 18°
As AC is the angle bisector, ∠EAC = ∠CAB = 18°
Question 39
1.2 / -0

Karan's teacher used a model of railway tracks and placed a stick in the middle to teach him how to find angles. Karan's teacher told them that QS and NP are parallel lines and angle POR is equal to 56°. What is the value of angle SRT?

A
56°

B
58°

C
60°

D
62°

Solution

Corresponding angles are congruent.
Angle POR and angle SRT are corresponding angles. So, they have the same measure.
Therefore, SRT = POR
SRT = 56°
Question 40
1.2 / -0

Cassie already knew 3 starter recipes before starting culinary school and she will learn 1 new starter recipe during each week of the school. After 32 weeks of culinary school, how many total starter recipes will Cassie know?

A
35

B
36

C
37

D
38

Solution

After 32 weeks of culinary school, Cassie will know a total of 35 starter recipes.
Question 41
1.2 / -0

First angle of a quadrilateral is 120°. If the measure of its other 3 angles is equal to each other, then find the value of any one of the other angles.

A
80°

B
100°

C
150°

D
200°

Solution

Sum of all the angles of a quadrilateral = 360°
According to the question,
120° + x + x + x = 360°, where x is the measure of any 1 of the other angles because all other angles are equal.
120° + 3x = 360°
3x = (360°- 120°) = 240°
Therefore, x = = 80°
Question 42
1.2 / -0

A piece of wood makes two triangles, ΔABC and ΔDEF on the edges of equal lengths such that AB = DE, BC = EF and AC = DF. If BAC = 60° and DFE = 45°, then what is the value of DEF?

A
45°

B
50°

C
55°

D
75°

Solution

ABC DEF by SSS property.

So, A = D = 60°C = F = 45°and B = E = 75° [Using angle sum property of triangle in ABC]
Question 43
1.2 / -0

PQSR is a quadrilateral. A, B and C are points on lines PR, PS and QS, respectively such that angle PAB is right angled triangle and angle CBS = 60°. What is the measure of angle APB?

A
80°

B
50°

C
30°

D
20°

Solution

Since angle PAB = 90° and angle CBS = 60° = Angle PBA [Vertically opposite angles].
Therefore, according to angle sum property 90° + 60° + Angle APB = 180°
Angle APB = 30°
Question 44
1.2 / -0

There are 100 cards in a box numbered from 1 - 100. If one card is drawn at random, then what is the probability that the card number is a multiple of both 2 and 6?

A

B

C

D
None of these

Solution

Total number of cards n{E} = 100
Card numbers which are multiple of both 2 and 6 = n(S) = 16 (6, 12, 18, 24, 30, 36, 42, 48, 54, 60, 66, 72, 78, 84, 90 and 96)

Required probability P(E) =
Question 45
1.2 / -0

Tripit has a kite which has been labelled and two of its angles have been measured. Now, he wants to compute angle D. What would be the measure of angle D?

A
89°

B
90°

C
91°

D
92°

Solution

A kite has exactly one pair of opposite congruent angles. The sum of interior angles of a quadrilateral is 360°.

B and D are opposite angles and so, B = D.

Now, A + B + C + D = 360°
A + D + C + D = 360° (Substitute B = D)
A + 2D + C = 360°

107° + 2D + 75° = 360°

182° + 2D = 360°

2D = 360° - 182°
D = 89°
Question 46
1.2 / -0

Richard and his family are at the pet store getting supplies for a their cat. The pet store has 2 kinds of type-1 dishes and 4 kinds of type-2 dishes. If they get one of each item, then how many different combinations of supplies can Richard's family get?

A
8

B
10

C
12

D
14

Solution

By applying fundamental principle of counting, total number of different combinations of supplies = 2 × 4 = 8.
Question 47
1.2 / -0

A rectangular park has a rectangular gymnasium built inside. The dimensions of the park are 20.5 m and 24.4 m and the dimensions of the gymnasium are 13.2 m and 11.1 m. Calculate the area of the remaining part of the park.

A
353.68 m²

B
354.70 m²

C
355.72 m²

D
356.74 m²

Solution

Length of gymnasium = 13.2 m
Width of gymnasium = 11.1 m
Area of gymnasium = Length × Width
= 13.2 m × 11.1 m
= 146.52 m²
The length and width of the outer rectangle are 24.4 m and 20.5 m, respectively.
Area of outer rectangle = 24.4 m × 20.5 m = 500.2 m²
Shaded or remaining area = (500.2 - 146.52) m² = 353.68 m²
Hence, answer option (1) is correct.

Question 48

1.2 / -0

Directions: Select the correct match.

Let g(x) =

Column I	Column II
1. g(x) is a polynomial	As numerator and denominator
2. g(x) is a equation	As it can be g(x) = 0
3. g(x) is a rational number	As it is of the form p over q where q not equals 0
4. g(x) is not a polynomial	As the exponents of x are not whole numbers

1

2

3

4 Solution

g(x) =
=
= 1 - 5x^-1 + 4x^-2 - 3x^-3
Clearly, exponents of x are in fractions and negative numbers.
So, g(x) is not a polynomial.

Question 49
1.2 / -0

In the given figure, P, Q, R and S are four points on a circle. PR and QS intersect at a point T such that ∠PTQ = 130°and ∠RQT = 15°. Find ∠PSQ.

A
115°

B
120°

C
117°

D
125°

Solution

In triangle TQR,
∠QRT + ∠RQT = ∠QTP (Exterior angle property of a triangle)
∠QRT + 15° = 130°
∠QRT = 115°
However, ∠PSQ = ∠QRT (Angles in the same segment of the circle)
Therefore, ∠PSQ = 115°
Question 50
1.2 / -0

In a farmhouse, a swimming pool is constructed. The length of the pool is 12 m and the width is 9 m. As swimming pools are deeper from one side and shallow from the other, the deeper side is 4 m deep and the shallow side is 1 m deep. What will be the total volume of that swimming pool?

A
260 m³

B
270 m³

C
280 m³

D
287 m³

Solution

Volume will be length x breadth x height. In this case, two heights are given. So, we will take average.

Volume = [12 × 9 × ()] m³= 12 × 9 × 2.5 m³= 270 m³

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IMO - Mock Test - 10

Result

IMO - Mock Test - 10

Score

-

Rank

-

SHARING IS CARING

Question 1

30023

112079

112089

202021

Solution

Question 2

10

12

14

16

Solution

Question 3

43

49

48

44

Solution

Question 4

ANIZ

AMIA

AMIZ

DLOB

Solution

Question 5

Uncle

Niece

Nephew

Mother

Solution

Question 6

8

9

10

11

Solution

Question 7

I

J

K

H

Solution

Question 8

P is sitting third to the left of J.

P is sitting second to the right of J.

P is sitting 4th to the left of J.

P is sitting 4th to the right of J.

Solution

Question 9

Second to the right of C

Immediate right of A

Second to the left of A

Immediate left of D

Solution

Question 10

Savita

Veena

Dyna

Kimmy

Solution

Question 11

10 km

12 km

15 km

16 km

Solution

Question 12

(a)

(b)

(c)

(d)

Solution

P is sitting 4^th to the left of J.

P is sitting 4^th to the right of J.

x³

x^1/2

1,404 mm³

1,424 mm³

1,425 mm³

1,432 mm³