IMO - Mock Test

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IMO - Mock Test - 7

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Weekly Quiz Competition

Question 1
1.2 / -0

P, Q, R, S and T are five friends sitting around a pentagonal park facing O as shown below.

If P and T interchange their positions and Q and R interchange their positions, then which of the following is true?

A
R is to the left of P.

B
Q is second to the right of R.

C
T is second to the left of P.

D
S is to the right of T.

Solution

After interchanging the positions, we have

So, T is second to the left of P.
Question 2
1.2 / -0

Using the below table, identify the correct expression.

P Q R S

+ - ×

A
17 Q 8 S 9 P 18 R 2 = 46

B
18 S 30 R 6 Q 5 P 0 = 85

C
27 Q 10 R 5 S 4 P 3 = -32

D
All of these

Solution

(1) 17 - 8 × 9 + 18 2 = -46
(2) 18 × 30 ÷ 6 - 5 + 0 = 85
(3) 27 - 10 5 × 4 + 3 = 22
So, option (2) is correct.
Question 3
1.2 / -0

In a unit test Sonakshi's marks in Mathematics are more than her marks in History, but not more than her marks in Geography. Her marks in Science are more than her marks in History, but not as much as in Mathematics and her marks in English are not as much as in Geography. In which subject did she score the lowest?

A
History

B
English

C
Science

D
Data Inadequate

Solution

According to the given information, marks in Geography > Mathematics > Science > History and marks in Geography > English.
There is no other relation given about English.
So, the data is inadequate.
Question 4
1.2 / -0

Select the correct mirror image of given below combination, if the mirror is placed vertically to the left?

A

B

C

D

Solution
Question 5
1.2 / -0

Which set is most similar to the given set?

(8, 18, 37)

A
(4, 9, 20)

B
(16, 33, 67)

C
(13, 30, 67)

D
(5, 12, 25)

Solution

8 × 2 + 2 = 16 + 2 = 18
18 × 2 + 1 = 36 + 1 = 37
5 × 2 + 2 = 10 + 2 = 12
12 × 2 + 1 = 24 + 1 = 25
Question 6
1.2 / -0

In the given Fig. (X), which one of the options will replace the question mark?

A

B

C

D

Solution

The number of circles in each element row-wise is increased by 1.
Question 7
1.2 / -0

Find the missing number in the number pattern given below.

A
810

B
892

C
576

D
816

Solution

The pattern is,
3 × 5 × 8 × 2 = 240
2 × 7 × 6 × 4 = 336
So, 5 × 9 × 6 × 3 = 810
Question 8
1.2 / -0

How many unit cubes were removed from the solid on the left to obtain the solid on the right?

A
24

B
28

C
26

D
30

Solution

Number of cubes in the figure given on the left side = 64.
Number of cubes in the figure given on the right side = 36
So, number of cubes removed = 64 - 36 = 28.
Question 9
1.2 / -0

Identify the figure from the options in which shape (X) is exactly embedded as one of its part.

A

B

C

D

Solution
Question 10
1.2 / -0

The given three figures (X), (Y) and (Z) shows a sequence of folding of a piece of paper. Figure (Z) shows the manner in which the folded paper has been cut. Identify the unfolded form of piece of paper.

A

B

C

D

Solution
Question 11
1.2 / -0

Choose a figure which is different from the rest of the figures.

A
S

B
R

C
Q

D
P

Solution

Only P has no line of symmetry.
Question 12
1.2 / -0

If R is denoted by N, D is denoted by T, I is denoted by U, O is denoted by I, E is denoted by R, T is denoted by O, U is denoted by D, N is denoted by C and C is denoted by E, then how will the word 'INTRODUCE' be written?

A
UCONIDTER

B
UCONITDER

C
UCONTIDER

D
UCOINTDER

Solution
Question 13
1.2 / -0

A truck departs from a distribution center. From there, it goes 2 blocks east, 3 blocks south and 3 blocks north. How far and in which direction must the truck go to get back to the distribution center?

A
4 blocks west

B
4 blocks east

C
2 blocks west

D
2 blocks east

Solution
Question 14
1.2 / -0

Which letter would replace the question mark?

A
M

B
P

C
E

D
W

Solution

The pattern is
E = 5, H = 8, 5 + 8 = 13 = M
N = 14, A = 1, 14 + 1 = 15 = O
Similarly, I = 9, D = 4, 9 + 4 = 13 = M
Question 15
1.2 / -0

Six friends P, Q, R, S, T and U are sitting around a hexagonal table, each at one corner and are facing the centre of the hexagon. P is second to the left of U. Q is neighbour of R and S. T is second to the left of S. Who is sitting opposite to P?

A
R

B
Q

C
T

D
S

Solution

According to the given information, we have
P is second to the left of U.
T is second to the left of S.
So, there are two possibilities for the sitting arrangement of R and S.

But, T is second to the left of S.

Then, possibility (2) will be cancelled.
And, the above is the correct solution.
So, S is sitting opposite to P.
Question 16
1.2 / -0

The difference between place values of digit 5 in 456.385 is ______

A
49995

B
499.95

C
49.995

D
49.999

Solution

Difference between the place values of 5
= 50.000 - .005
= 49.995
Question 17
1.2 / -0

Find the least number which on adding 9 to it becomes exactly divisible by 15, 25, 30 and 45.

A
410

B
450

C
380

D
441

Solution

Least number which is exactly divisible by 15, 25, 30 and 45 is L.C.M of the given numbers.

L.C.M = 2 × 3 × 3 × 5 × 5 = 450
Required number is 9 less than 450 = 450 – 9 = 441
Question 18
1.2 / -0

Which of the following square(s) must be shaded so that given figure is symmetric along both lines LM and AB?

A
R and S

B
P only

C
Q and P

D
Q only

Solution

Square Q and Square P must be shaded to make the given figure symmetric about line AB and line LM respectively.
Question 19
1.2 / -0

Find the value of CXVI + XIII + VI + CCLXV - XVI.

A
CD

B
CCCLXXXIV

C
CCCLXXXV

D
M

Solution

CXVI = 100 + 10 + 6 = 116
XIII = 13, VI = 6
CCLXV = 200 + 50 + 10 + 5 = 265
XVI = 16
CXVI + XIII + VI + CCLXV - XVI = 116 + 13 + 6 + 265 - 16 = 384
And, 384 = CCCLXXXIV
Question 20
1.2 / -0

Fill in the blanks:

Every natural number has a ______ except ______ and has a ____.

A
successor, 0, predecessor

B
successor, 1, predecessor

C
predecessor, 0, successor

D
predecessor, 1, successor

Solution

Natural number = { 1,2,3,4 ...................}
Every natural number has a predecessor except 1 and has a successor.
Question 21
1.2 / -0

Which of the following diagrams correctly describes the factors of 15 and 12?

A

B

C

D

Solution
Question 22
1.2 / -0

Select the INCORRECT match.

A
One pair of parallel side - Trapezium

B
Parallelogram with 4 right angles - Rectangle

C
Parallelogram with 4 sides of equal length - Rhombus

D
A rhombus with 4 right angles - kite

Solution

A rhombus has a 4 equal sides and
A rhombus with 4 right angles is a square. because square has equal sides and every angle is 90°.
Question 23
1.2 / -0

Which of the following statements is correct?

A
14 tenths 4 thousandths = 0.144

B
2 tenths 13 hundredths = 0.213

C
4 hundredths 2 tenths = 0.024

D
7 tenths 17 hundredths = 0.87

Solution

(1) 14 tenths 4 thousandths = = 1.4 + 0.004 = 1.404

(2) 2 tenths 13 hundredths = = 0.33

(3) 4 hundredths 2 tenths = = 0.24

(4) 7 tenths 17 hundredths = = 0.87
Question 24
1.2 / -0

Mihika makes 8 gift packs containing chocolates for Diwali. She puts 12 vanilla chocolates, 14 milk chocolates and 8 nut chocolates in each pack. With the help of which property, can you calculate the total number of chocolates in 8 packs?

A
Commutative property

B
Associative property

C
Distributive property

D
None of these

Solution

Total number of chocolates = 8 (12 + 14 + 8) or 12 × 8 + 14 × 8 + 8 × 8 = 8 × (12 + 14 + 8)
Question 25
1.2 / -0

The breadth of a rectangle is w cm and the length is 5 times as long as its breadth. What is the perimeter of the rectangle?

A
5w² cm

B
12w cm

C
(10 + 2w) cm

D
(25 + w²) cm

Solution

We have, breadth = w cm
Length = 5w cm
So, perimeter = 2(5w + w) = 2 × 6w = 12w cm
Question 26
1.2 / -0

The pie chart shows the number of students who choose different co-curricular activities in a school. An equal number of students choose Basketball and Volleyball and 96 students choose Table Tennis.

The ratio of the number of students who choose Basketball to those who choose Soccer is 2 : 7. How many students choose Soccer?

A
160

B
158

C
172

D
168

Solution

Let the total number of students be x.
Central angle for table Tennis students = 90°
Number of students who choose Table Tennis = 96

So, total number of students = 384
Now, it is given that
Number of Basketball students = Number of Volleyball students
Central angle for Basketball students = Central angle for Volleyball students
Also, central angle for Basketball and Volleyball together = 90°
2 × Central angle for Basketball = 90°
Central angle for Basketball students

= = 45°

Number of students who choose Basketball

= = 48

Now, let number of students who choose Basketball be 2y and number of students who choose soccer be 7y.
Then, Basketball students = 2y
48 = 2y y = 24
So, number of students who choose soccer = 7y = 7 × 24 = 168
Question 27
1.2 / -0

Find the difference between the place value of 7 in 5369.70184 and face value of 3 in 536970184.

A
2.3

B
2.7

C
230000

D
69997

Solution

Place value of 7 in 5369.70184 = 0.70000
Face value of 3 in 536970184 = 3
Difference = 3 - 0.7 = 2.3
Question 28
1.2 / -0

Which digit makes the given sentence true?

5831470? is divisible by 5.

A
4

B
5

C
9

D
1

Solution

A number is divisible by 5 if its unit's digit is either 0 or 5.
So, the given number is divisible by 5 when its unit's digit is 5.
Question 29
1.2 / -0

QS and TV are parallel lines and WP is a transversal. Which angles are supplementary angles?

A
VUW and QRP

B
VUW and SRU

C
VUW and VUR

D
VUW and TUR

Solution

Supplementary angles are those angles whose sum is 180°.
From options, VUW + VUR = 180°
So, option (3) is correct.

Question 30

1.2 / -0

A veterinarian weighed all the dogs that visited her office last month. Use the data to complete the frequency chart shown below.
Dog weights (Ibs)
23, 27, 27, 39, 43, 45, 46, 47, 49, 50, 53, 55, 58, 58, 59, 64, 71, 83, 84, 86, 88, 89
Find the missing number.

Dog weights
Weight (lbs)	20 - 29	30 - 39	40 - 49	50 - 59	60 - 69	70 - 79	80 - 89
Number of dogs	3	1		6	1	1	5

5

6

9

8 Solution

Number of dogs weighing between 40 to 49 (both inclusive) = 5

Question 31
1.2 / -0

Prachi took a total of 2 hours to write 30 party invitations. Which of the following equations can be used to find m, the number of minutes Prachi took to write 1 invitation?

A
(60 30) 2 = m

B
(60 × 30) + 2 = m

C
(60 2) × 30 = m

D
(60 × 2) ÷ 30 = m

Solution

Time taken to write 30 invitations = 2 hours = 2 × 60 minutes
Time taken to write 1 invitation (m) =
m = (2 × 60) 30
Question 32
1.2 / -0

How many right angles are there in 3 complete turns?

A
16

B
12

C
8

D
4

Solution

Right angles in one complete turn = = 4
Right angles in 3 complete turns = 4 × 3 = 12
Question 33
1.2 / -0

An oil tank contains litres of oil. It is then filled with litres of oil. Later, litres of oil is pumped out from the tank. What is the volume of oil left in the tank in litres?

A

B

C

D

Solution

Volume of oil in tank litres
= litres
Volume of oil added = litres = litres
Volume of oil pumped out = litres
= litres.
Volume of remaining oil in tank

=

=

= litres = litres
Question 34
1.2 / -0

If (k - 8) is the highest common factor of 56 and 77, then the value of k is _____.

A
7

B
11

C
15

D
16

Solution

H.C.F. of 56 and 77 = 7
So, k - 8 = 7 k = 15.
Question 35
1.2 / -0

The number of edges in the given figure is _______.

A
8

B
9

C
10

D
11

Solution

Number of edges = 9
Question 36
1.2 / -0

An unknown number of apples were distributed among Garima and Amit in the ratio 5 : 7. If Amit got 84 apples, then the difference between the number of apples received by Garima and Amit is _____.

A
46

B
32

C
20

D
24

Solution

Let the number of apples given to Garima = 5x
Number of apples given to Amit = 7x
84 = 7x x = 84 7 = 12
So, number of apples given to Garima = 12 × 5 = 60
Difference between number of apples given to Garima and Amit = 84 - 60 = 24
Question 37
1.2 / -0

Maya has an equal number of 20-paisa and 50-paisa coins. The total value of the coins is Rs. 16.10. If she spend five 50-paisa coins, then how many 50-paisa coins is she left with?

A
18

B
23

C
28

D
46

Solution

Let the number of each coin be x.
According to question,
20x + 50x = 1610
70x = 1610 x = 23
Number of 50 paise coins = 23
Number of coins spent = 5
So, number of coins left = 23 - 5 = 18
Question 38
1.2 / -0

In a class of 50 students, 15 are girls. 5 girls and 2/7 of the boys were chosen to play a match. The total number of students chosen to play a match is _______.

A
12

B
15

C
19

D
25

Solution

Total number of students = 50
Number of girls = 15
Number of boys = 50 - 15 = 35
Number of girls chosen for match = 5
Number of boys chosen for match = 35 × = 10
Total students chosen for match = 5 + 10 = 15
Question 39
1.2 / -0

The number of girls in a class is 5 times the number of boys. Which of the following cannot be the total number of children in the class?

A
24

B
30

C
35

D
42

Solution

Let number of boys be x.
Number of girls = 5x
So, total students x + 5x = 6x
That means total number of students of the class should be a multiple of 6.
35 is not a multiple of 6, so it cannot be the total number of students in the class.
Question 40
1.2 / -0

Meeku fenced up a square area. He used 100 poles on each side of the square. How many poles did he use altogether?

A
400

B
398

C
394

D
396

Solution

No. of poles in one side of square = 100 , but one pole at the corner is common to the adjoining sides.
So number of poles required = 400 - 4 = 396
Question 41
1.2 / -0

45% of Garima's savings is the same as 25% of Latika's savings. What is the ratio of Garima's savings to that of Latika's savings?

A
5 : 9

B
9 : 5

C
9 : 20

D
1 : 4

Solution

Let the savings of Latika and Garima be x and y respectively.
According to question,
45% of y = 25% of x

So, required ratio is 5 : 9.
Question 42
1.2 / -0

A and B take time in ratio of 2 to 3 to complete a work. If they do the work together, they finish it in 10 days. What part of work was done by A?

A
(3/5)^th

B
(1/5)^th

C
(2/5)^th

D
(4/5)^th

Solution

Let the time taken by A and B be 2x and 3x respectively.
According to the question, we have
2x + 3x = 10
5x = 10 x = 2
Time taken by A = 2 × 2 = 4 days
Part of the work done by A =
Question 43
1.2 / -0

Rajan sold a cycle at a loss of Rs. 300. If he had sold it at Rs. 3000, he would have made a profit of Rs. 600. At what price did he sell the cycle?

A
Rs. 2400

B
Rs. 2000

C
Rs. 2100

D
Rs. 2500

Solution

We have S.P. = Rs. 3000
Profit = Rs. 600
C.P. = S.P. - Profit = Rs. (3000 - 600) = Rs. 2400
Now, C.P. = Rs. 2400
Loss = Rs. 300
S.P. = C.P. - Loss = Rs. (2400 - 300) = Rs. 2100
Question 44
1.2 / -0

Ms. Neha needs to replace the batteries in 20 calculators. Each calculator uses 4 batteries. The batteries are sold in packages of 16. How many packages of batteries does Ms. Neha need to buy?

A
64

B
4

C
80

D
5

Solution

Number of batteries used in 1 calculator = 4
So, number of batteries used in 20 calculators
= 4 × 20 = 80
Number of batteries in 1 package = 16
Number of packages needed = 80 16 = 5
Question 45
1.2 / -0

Sasha is using a wooden strip m long to make a picture frame. If she cuts off a piece that is m long, then which fraction best represents the portion that is left of the original strip?

A
m

B
1 m

C
m

D
m

Solution

Total length = m
Length of piece cut off = m

Length of piece left = ^m
Required fraction = m
Question 46
1.2 / -0

In the number line shown below, PQ = QR = RS. Find the approximate value of Q, R and Q + R.

A
Q = 2.9, R = 2.7, Q + R = 5.8

B
Q = 2.6, R = 2.8, Q + R = 5.4

C
Q = 2.7, R = 2.8, Q + R = 5.5

D
Q = 2.7, R = 2.9, Q + R = 5.6

Solution

PS = 3.1 - 2.5 = .6
PQ = QR = RS = .6/3 = .2
So, Q = 2.7, R = 2.9 and Q + R = 2.7 + 2.9 = 5.6
Question 47
1.2 / -0

Which of the following options hold?

Statement 1: If the HCF of two numbers is one of the numbers, then their LCM is the other number.
Statement 2: The LCM of two numbers is greater than the larger of the numbers.

A
Statement 1 is true and Statement 2 is false.

B
Statement 1 is false and Statement 2 is true.

C
Both the Statements are true.

D
Both the Statements are false.

Solution

Suppose two numbers is 12, 24
LCM ( 12, 24 ) = 24
HCF ( 12, 24 ) = 12
The LCM of two numbers is either equal to larger number or greater than the larger of the numbers.
Question 48
1.2 / -0

Fill in the blanks:

(i) The opposite sides of a parallelogram are __P__ and __Q__.
(ii) A quadrilateral having only one pair of opposite sides parallel is called a __R__.
(iii) A parallelogram having all the sides equal is called a __S__.

A
P - equal, Q - parallel, R - rectangle, S - rhombus

B
P - equal, Q - non-parallel, R - trapezium, S - kite

C
P - equal, Q - parallel, R - trapezium, S - rhombus

D
P - equal, Q - parallel, R - trapezium, S - kite

Solution

(i) The opposite sides of a parallelogram are equal and parallel.

(ii) A quadrilateral having only one pair of opposite sides parallel is called a trapezium.

(iii) A parallelogram having all the sides equal is called a rhombus.
Question 49
1.2 / -0

In a maths quiz, there are 20 questions. If all questions are answered correctly, a student's score will be 20; if all questions are answered incorrectly, a student's score will be -20. Part way through this quiz, Varun has a score of 2.

Find his new score, if

(a) he answers 2 of the next 5 questions correctly and 3 of them incorrectly.
(b) he answers 4 of the next 5 questions incorrectly and 1 of them correctly.

A
(a) 2, (b) 1

B
(a) -2, (b) -1

C
(a) 1, (b) -1

D
(a) 1, (b) 0

Solution

Score for 1 correct answer = +1
Score for 1 incorrect answer = -1
(a) Score for 2 correct answers = +2
Score for 3 incorrect answers = -3
New score = 2 + 2 - 3 = 1
(b) Score for 1 correct answer = +1
Score for 4 incorrect answers = -4
New score = 2 - 4 + 1 = -1
Question 50
1.2 / -0

There were 180 members in the club last year. The membership decreased by 15% this year. How many members are there this year?

A
27

B
135

C
153

D
207

Solution

Number of members in the club last year = 180
Number of members this year = 180 - 15% of 180
= 180 - 27 = 153