IMO - Mock Test

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IMO - Mock Test - 5

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Weekly Quiz Competition

Question 1
1 / -0

A group of boys are standing in a row. One boy is nineteenth in order from both the ends. How many boys are there in the group?

A
27

B
37

C
38

D
39

Solution

Total number of boys in the row = (Rank of the boy from the front) + (Rank of the boy from the back) - 1
= 19 + 19 - 1 = 37
Question 2
1 / -0

What will come next in the series.

BAB, BCD, BEF, ?

A
BGH

B
BHG

C
BTF

D
BGD

Solution

First element of all the terms is the same.
The second letter is A + 2 = C, C + 2 = E, E + 2 = G.
The third letter is B + 2 = D, D + 2 = F, F + 2 = H

So, the next term is BGH.
Question 3
1 / -0

Find the missing number indicated by (?).

3 15 4

7 38 5

3 ? 5

A
15

B
18

C
19

D
20

Solution

(3 × 4) + 3 = 15
(7 × 5) + 3 = 38
(3 × 5) + 3 = 18
Question 4
1 / -0

In a certain code, SEARCH is coded as VHDUFK. FIT will be coded as

A
GJU

B
ILW

C
HKV

D
JMX

Solution

SEARCH is coded as VHDUFK, where each alphabet is moved 3 steps ahead.
S becomes V,
E becomes H,
A becomes D,
R becomes U,
C becomes F and
H becomes K.
Thus, FIT will be coded as F - I, I - L and T as W.
Question 5
1 / -0

Find out the alternative which will replace the question mark.

Mean : Selfish : : Beautiful : ?

A
Elegant

B
Ignorant

C
Crude

D
Drab

Solution

Since mean and selfish are synonyms of each other, synonym of beautiful is elegant.
Question 6
1 / -0

If DFG is coded as WUT, then what will be the code of KMN?

A
MNP

B
PNM

C
LMN

D
QON

Solution

Look at the analogy carefully. D is the 4^th letter, F is the 6^th letter and G is the 7^th letter from the starting. Similarly, W, U and T are the 4^th, 6^thand 7^th letters, respectively from the end.
Therefore, K, M and N are the 11^th, 13^th and 14^th letters from the starting, respectively.
Similarly, answer should be the 11^th, 13^th and 14^th letters from the end i.e. PNM.
Question 7
1 / -0

The given equations are solved on the basis of a certain system.

6 - 4 = 12,
8 - 4 = 32,
9 - 4 = 45.
Solve 7 - 3 = ? on the basis of the above system.

A
28

B
21

C
14

D
10

Solution

6 - 4 = 2 and the same is multiplied by 6 (1^st number) 6 x 2 = 12

8 - 4 = 4 and the same is multiplied by 8 => 4 x 8 = 32

In the same way, 7 - 3 = 4 and the same is multiplied by 4 x 7 (first number) = 28
Question 8
1 / -0

If Black is Green, Green is Yellow, Yellow is Blue, Blue is Pink, Pink is Violet and Violet is Maroon, then what would be the colour of the sky?

A
Black

B
Violet

C
Red

D
Pink

Solution

We know that the colour of the sky is Blue. But, as per the instruction given in the question, the colour of the sky is Pink.
Question 9
1 / -0

Find the simplified answer.

(6ab + 5a)²- (6ab - 5a)²= ?

A
17a²b

B
17ab²

C
60ab²

D
120a²b

Solution

Using identity

a²- b²= (a - b)(a + b), we have, [(6ab + 5a) - (6ab - 5a)]

= [(6ab + 5a) + (6ab - 5a)]

= (6ab + 5a - 6ab + 5a)(6ab + 5a + 6ab - 5a)

= (10a)(12ab)

= 120a²b
Question 10
1 / -0

Which of the following is the product of the numbers so obtained when 351 is divided into two parts in the ratio 2 : 7?

A
21,294

B
20,294

C
25,295

D
31,295

Solution

2x + 7x = 351
9x = 351
x = 351/9
x = 39
2x = 39 × 2 = 78
7x = 39 × 7 = 273
Product = 21,294
Question 11
1 / -0

Which of the following is the smallest natural number by which 13720 should be divided so that the quotient is a perfect cube?

A
2

B
4

C
5

D
7

Solution

Here, after factorising 13720,

13720 = 2 x 2 x 2 x 7 x 7 x 7 x 5.

The prime factor 5 does not appear in a group of three. So, 13720 is not a perfect cube.

In the factorisation, 5 appears only once.

If we divide the number by 5, then the prime factorisation of the quotient will not contain 5.

So, 13720 ÷ 5 = 2 x 2 x 2 x 7 x 7 x 7 x 7

Hence, the smallest number by which 13720 should be divided to make it a perfect cube is 5.

The perfect cube in this case is 2744.
Question 12
1 / -0

Which of the following is the smallest natural number by which the number 49000 should be multiplied to obtain a perfect cube?

A
2

B
3

C
5

D
7

Solution

Here, we have

49000 = 2 x 2 x 2 x 5 x 5 x 5 x 7 x 7.

In this factorisation, we find that there is no triplet of 7.

So, 49000 is not a perfect cube. To make it perfect cube we multiply it by 7.

Thus, 49000 x 7 = 2 x 2 x 2 x 5 x 5 x 5 x 7 x 7 x 7 = 343000, which is a perfect cube.
Question 13
1 / -0

Solve the given equation.

[x(4x + 5y) – y(3x - 2y)] - y²- 3x²

A
(x + y)²

B
(x - y)²

C
x² - 3y² - 2xy

D
2x + 2y - y²- 3x²

Solution

[x(4x + 5y) – y(3x - 2y)] - y²- 3x²

= 4x²+ 5xy - 3xy + 2y²- y²- 3x²

= x²+ y²+ 2xy = (x + y)²
Question 14
1 / -0

What will be the value of x² + y³ - z if x = 5, y = 7 and z = 2?

A
366

B
368

C
477

D
468

Solution

x = 5

So, x²= 25

y = 7

Therefore,

y³ = 7 × 7 × 7 = 343

z = 2

So, the answer will be 25 + 343 - 2 = 366
Question 15
1 / -0

Three numbers are in the ratio 1 : 2 : 3. Sum of their squares is 2016. Find the sum of squares of the smallest and the largest number?

A
1440

B
865

C
548

D
127

Solution

Let the first number be a.
Let the second number be 2a.
Let the third number be 3a.
A.T.Q.
a²+ (2a)²+ (3a)² = 2016
a²+ 4a²+ 9a²= 2016
a²= 2016 ÷ 14
a²= 144
a = 12 (smallest)
2a = 2 x 12 = 24
3a = 3 x 12 = 36 (largest)
Square of the smallest number = 12 x 12 = 144
Square of the largest number = 36 x 36 = 1296
Sum of squares of the smallest and largest number = 144 + 1296 = 1440
Question 16
1 / -0

An electrician needs 2 rolls of electrical wire to wire each room in a house. How much of a room can he wire with 1/3of a roll of wire?

A
1/6

B
2/3

C
1/8

D
1/9

Solution

Applying unitary method, 2 rolls of wire are required for 1 room.

1 roll of wire will be required for 1/2 room.

Applying unitary method, 2 rolls of wire are required for 1 room.

1 roll of wire will be required for 1/2 room.

1/3 of a wire will cover 1/2 × 1/3 = 1/6 of a room.

The electrician has enough wire for 1/6 of a room.
Question 17
1 / -0

The list price of an article was 20% more than the cost price. The shopkeeper suffered 20% loss when he sold the article at Rs. 4800. What was its list price?

A
Rs. 6000

B
Rs. 4800

C
Rs. 7200

D
Rs. 7000

Solution

Let x be the cost price.
Sale price = Rs. 4800
Loss = 20% of x
So, sale price = 80% of x = Rs. 4800
So, cost price = x = Rs. 6000
list price = Cost price + profit
Profit = 20% of cost price = 20% of Rs. 6000 = Rs. 1200
So, list price = Rs. 6000 + Rs. 1200 = Rs. 7200
Question 18
1 / -0

Brad has 6 cans of regular soda and 9 cans of diet soda. He wants to create some identical refreshment tables that will operate during the American football game. He also does not want to have any sodas left over. What is the greatest number of refreshment tables that Brad can stock?

A
2

B
3

C
5

D
6

Solution

We have the prime factorisation for each number.
6 = 2 x3
9 = 3 x 3
Next, the common factors of both the numbers = 3.
So, the highest common factor is 3. That means that the greatest possible number of tables is 3 because 6 cans of regular soda could be placed onto 3 refreshment tables with 2 cans of regular soda on each table and 9 cans of diet soda could be placed onto 3 refreshment tables with 3 cans of diet soda on each table.
The greatest number of refreshment tables Brad can stock is 3.
Question 19
1 / -0

A particular service has a cost of Rs. 40 excluding service tax of 12.5%. What is the total cost including service tax?

A
Rs. 60

B
Rs. 55

C
Rs. 50

D
Rs. 45

Solution

Total cost with service tax = Cost without service tax + Service tax
Service tax = 12.5% of cost = 12.5% of 40 = 5
So, total cost including service tax = 40 + 5 = 45
The total cost including service tax is Rs. 45.
Question 20
1 / -0

Peter can throw a ball to a distance of 115 metres. If Sam can throw the ball 20% farther than Peter, then find the distance of Sam's throw.

A
128 m

B
130 m

C
138 m

D
145 m

Solution

Distance of Peter's throw = 115 m
Distance of Sam's throw = 115 x 120/100 = 138 m

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Re-Attempt Weekly Quiz Competition

IMO - Mock Test - 5

Result

IMO - Mock Test - 5

Score

-

Rank

-

SHARING IS CARING

Question 1

27

37

38

39

Solution

Question 2

BGH

BHG

BTF

BGD

Solution

Question 3

15

18

19

20

Solution

Question 4

GJU

ILW

HKV

JMX

Solution

Question 5

Elegant

Ignorant

Crude

Drab

Solution

Question 6

MNP

PNM

LMN

QON

Solution

Question 7

28

21

14

10

Solution

Question 8

Black

Violet

Red

Pink

Solution

Question 9

17a2b

17ab2

60ab2

120a2b

Solution

Question 10

21,294

20,294

25,295

31,295

Solution

Question 11

2

4

5

7

Solution

Question 12

2

3

5

7

Solution

17a²b

17ab²

60ab²

120a²b

(x + y)²

(x - y)²

x² - 3y² - 2xy

2x + 2y - y²- 3x²