IMO - Mock Test

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IMO - Mock Test - 5

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Weekly Quiz Competition

Question 1
1 / -0

Find out the pattern followed in the series given below:

15, 16, 19, 28, 55, 136

A
Triple the difference each time.

B
Add 3 in the difference.

C
Take away 3.

D
Divide by 3.

Solution

The pattern is as follows:
Triple the difference each time.
16 - 15 = 1
19 - 16 = 3; (1 x 3 = 3)
Question 2
1 / -0

If + means x, - means ÷, ÷ means + and x means -, then find the value of 25 + 5 x 25 - 25.

A
124

B
50

C
25

D
5

Solution

25 + 5 x 25 - 25 = ?

25 × 5 - 25 ÷ 25

= 125 - 1 = 124
Question 3
1 / -0

Sophie ranked 9 in a class of 55 students. What was the rank of Sophie from the bottom?

A
45

B
46

C
47

D
48

Solution

If a student is at rank 9 in a class of 55 students, to get the rank from the bottom, we have to subtract 9 from 55, which gives 46.
After that, add 1 for that student.
Question 4
1 / -0

Anup went shopping on 5^th April, which was a Friday, and decided to go again after 5 days. What day would it be on which Anup went shopping again?

A
Sunday

B
Saturday

C
Friday

D
Thursday

Solution

Day on which Anup went shopping = Friday

Next visit would be after 5 days, that is, after Saturday, Sunday, Monday, Tuesday and Wednesday, which is a Thursday.
Question 5
1 / -0

If "COMPUTER" is coded as "DNNOVSFQ", then how will you code "BOTTLE" in the same way?

A
CNUSMD

B
CNNUMD

C
BBNNG

D
SSDFVA

Solution

C + 1 = D
O - 1 = N
M + 1 = N
P - 1 = O
U + 1 = V
T - 1 = S
E + 1 = F
R - 1 = Q
In the same way, "BOTTLE" is coded as "CNUSMD".
Question 6
1 / -0

The length of a rectangle is 5 m less than four times its width. If the perimeter of the rectangle is 180 m, what is its area?

A
1248 m²

B
1298 m²

C
1340 m²

D
1349 m²

Solution

Let the width of the rectangle be x.
So,
Length = 4x – 5
Perimeter = 2(4x – 5 + x) = 180
5x – 5 = 90
5x = 95
⇒ x = 95/5 = 19
Length = 4 × 19 – 5 = 71 m
Width = 19 m
Area = 71 × 19 = 1349 m²
Question 7
1 / -0

What would be the perimeter of the square if the side of the square is equal to the breadth of the rectangle, whose length is 22 cm, which is twice its breadth?

A
32 cm

B
40 cm

C
44 cm

D
88 cm

Solution

Length of the rectangle = 2(breadth)

22 = 2 x breadth

Breadth = 22/2

Breadth = 11 cm

Side of the square = Breadth of the rectangle

Side of the square = 11 cm

Perimeter of the square = 4(side)

= 4 x 11 = 44 cm
Question 8
1 / -0

What is the value of x in 7(3x + 2) – 4(6x – 1) = 7(x + 2) – 7(5x – 6) + 12?

A
3

B
-2

C
-1

D
2

Solution

7(3x + 2) - 4(6x - 1) = 7(x + 2) - 7(5x - 6) + 12
21x + 14 - 24x + 4 = 7x + 14 - 35x + 42 + 12
-3x + 18 = -28x + 68
25x = 50
x = 2
Question 9
1 / -0

Find the additive inverse of -5/17.

A
5/17

B
17/5

C
-17/5

D
None of these

Solution

The additive inverse of -5/17 is 5/17. For a fraction, the definition of additive inverse remains the same. If a number is positive, then the additive inverse will be the negative version of the same number. The opposite is also true. If a number is negative, then the additive inverse will be the positive version of that same number.
Question 10
1 / -0

A rectangle with sides 7 cm and 4 cm has area 5 times larger than another rectangle. Find the width of smaller rectangle if its length is 2.1 cm.

A
2.67 cm

B
4.21 cm

C
4.82 cm

D
2.13 cm

Solution

Area of larger rectangle = 7 × 4 = 28 cm²

Area of smaller rectangle = 28/5 sq. cm = 5.6 sq. cm

Length of smaller rectangle = 2.1 cm

Width of smaller rectangle = 5.6/2.1 = 2.67 cm
Question 11
1 / -0

The area of a rectangular field is 350 ft². Its dimensions are in the ratio 2 : 7. What is the length of the fencing of the field?

A
90 ft

B
80 ft

C
70 ft

D
60 ft

Solution

Let the length and width of the rectangular field be 7x and 2x, respectively.
So,
Area = L × W
350 = 7x × 2x
⇒ 14x² = 350
⇒ x² = 25
x = 5 ft
⇒ Length = 7x = 7 × 5 = 35 ft
Width = 2x = 2 × 5 = 10 ft
Perimeter = 2(L + W) = 2(35 + 10) = 90 ft
Question 12
1 / -0

If 384a is divisible by 9, then 'a' is

A
9

B
2

C
3

D
4

Solution

3 + 5 + 4 + a = 18 [For 384a to be divisible by 9, the sum of all digits must be divisible by 9]
Or, 18 – 15 = a
Or, a = 3
Question 13
1 / -0

When rounded off to the nearest thousands, I become 31,000. Find me out of the following.

A
30,432

B
31,312

C
31,567

D
30,339

Solution

31,312 round down to 31,000.
Question 14
1 / -0

The difference between the measures of two complementary angles is 20°. Find the measure of both the angles.

A
30°, 60°

B
20°, 70°

C
35°, 55°

D
40°, 50°

Solution

Let one angle be x.
Complementary angle is ⇒ 90 – x
(90 – x) – x = 20
90 – 2x = 20
70 = 2x
x = 35
90 – x = 90 – 35 = 55
Angles are 35°, 55°.
Question 15
1 / -0

Write the Roman Numeral for 567?

A
LDXVII

B
DLXVII

C
CLXVII

D
LCXVII

Solution

D – 500, LX – 60, VII – 7

567 = 500 + 60 + 7 = DLXVII
Question 16
1 / -0

Two angles in a triangle are in the ratio 4 : 5. If the sum of these angles is equal to the third angle, then the third angle is _____.

A
180^o

B
40^o

C
50^o

D
90^o

Solution

Let the three angles be 4x, 5x and 9x.
Now, according to the question:
4x + 5x + 9x = 180°
18x = 180°
x = 10°
Third angle = 90°
Question 17
1 / -0

Find the difference between the smallest 8-digit number and the largest 5-digit number.

A
99999

B
1000000

C
1000999

D
9900001

Solution

Smallest 8-digit number = 10000000
Largest 5-digit number = 99999
Difference = 10000000 – 99999
= 9900001
Question 18
1 / -0

In an election, there were two candidates A and B. A got 72% votes and was elected by a margin of 11,000 votes. The total number of votes polled was

A
12,000

B
18,000

C
25,000

D
29,000

Solution

Let the total number of votes polled be x.

So, A got 0.72x.
And, B got x – 0.72x = 0.28x

Difference = 0.72x – 0.28x = 0.44x

According to the question:
0.44x = 11,000
x = 25,000
Question 19
1 / -0

Sam scored 236 marks out of 280 in his assessments. Find his percentage score.

A
85.18%

B
84.28%

C
86.21%

D
88.23%

Solution

Marks scored by Sam = 236
Total marks = 280
% marks of Sam = 236/280 × 100
= 84.28%
Question 20
1 / -0

In a firm, 30% of the employees are female. Find the number of female employees if number of male employees are 280.

A
84

B
100

C
120

D
400

Solution

Let the total number of employees be x.

So, 30% of x are females. ----- (1)

And 70% of x are males. ------ (2)

If the number of males is 280, then 280 = 70% of x

or 280/0.7 = x

x = 400

So, the number of females = 30% of 400 = 0.3 × 400 = 120
Question 21
1 / -0

Area of house A is 2456 m², area of house B is 89,632 m², and area of house C is 5632 m². What is the difference between the total area of houses A and C together, and the area of house B?

A
81,514 m²

B
81,524 m²

C
81,534 m²

D
81,544 m²

Solution

Total of area of houses A and C = 2456 m² + 5632 m²= 8088 m²

The required difference = 89,632 m²- 8088 m²= 81,544 m²
Question 22
1 / -0

A rectangular hotel room is 13 m x 20 m. The owner of the hotel wants to re-carpet the room with carpet that costs Rs. 1450 per sq.m. How much will it cost to re-carpet the room?

A
Rs. 3,75,000

B
Rs. 3,76,000

C
Rs. 3,77,000

D
Rs. 3,78,000

Solution

Area of a rectangle = Length × Width

Area of the rectangular hotel room = 13 x 20 = 260 m²

Now, total cost to re-carpet the room = Rs. 260 x 1450 = Rs. 3,77,000
Question 23
1 / -0

In a kitchen garden, a snail covers 230 cm in 1 minute, while Ankit covers or walks 4 m in just 30 seconds. What is the total distance covered by both of them together in one minute?

A
10.1 m

B
10.2 m

C
10.3 m

D
10.4 m

Solution

Distance covered by the snail in one minute = 230 cm
Distance covered or walked by Ankit in 30 seconds = 4 m
Distance covered by Ankit in one minute or 60 seconds = 8 m
We know that 1 m = 100 cm, so 230 cm will be 230 ÷ 100 = 2.3 m
Now, the total distance covered in metres = 8 m + 2.3 m = 10.3 m
Question 24
1 / -0

Pharrell invited 50 friends on her birthday party. She thought of serving snacks and a soft drink and bought 4 bottles of soft drink of volume 2 litres each, and 1 bottle of soft drink of volume 1 litre. What volume of soft drink will be served to each person if it is distributed among 50 of her friends equally?

A
170 millilitres

B
180 millilitres

C
190 millilitres

D
200 millilitres

Solution

Total volume of soft drink available = (4 × 2 + 1 × 1) L = 9 L

Distributing 9 L of soft drink among 50 of her friends =9/50 = 0.18 L = 180 mL

So, each of her friends will be served 180 mL of soft drink in the party.
Question 25
1 / -0

The height of a tower is 50 m. Two-fifth of the tower is coloured in red and of the remaining portion, again two-third is coloured in green and the remaining in white. Find out the length of the portion coloured in white?

A
30 m

B
25 m

C
20 m

D
10 m

Solution

Height of the tower = 50 m

2/5 of the total height = 20 m, which is coloured in red

Remaining portion = 50 - 20 m = 30 m

2/3 of the total height = 2/3 of 30 m = 20 m, which is coloured in green

Remaining portion = 30 - 20 m = 10 m, which is coloured in white
Question 26
1 / -0

Price of a cake is Rs. 230 and price of an ice-cream is Rs. 55. How much will a student have to spend to buy 3 ice creams and 2 cakes?

A
Rs. 625

B
Rs. 650

C
Rs. 670

D
Rs. 800

Solution

Price of a cake = Rs. 230

Price of 2 cakes = Rs. 230 × 2 = Rs. 460

Price of an ice-cream = Rs. 55

Price of 3 ice-creams = Rs. 55 × 3 = Rs. 165

Total money needed to buy both the things = Rs. 460 + Rs. 165 = Rs. 625
Question 27
1 / -0

On a trip, 560 students went to Shimla. Out of the total students, the ratio of the boys to girls was 3 : 4. What is the difference between the numbers of girls and boys?

A
80

B
90

C
105

D
120

Solution

Total number of students = 560

Number of boys = 3/7 of 560 = 240

Number of girls = 4/7 of 560 = 320

Difference between the numbers of boys and girls = 320 - 240 = 80
Question 28
1 / -0

Which of the following properties is not true regarding a rhombus?

A
Two pairs of sides are of different lengths.

B
Diagonally opposite angles measure the same.

C
Diagonals are perpendicular to each other and bisect each other.

D
Diagonals bisect interior angles.

Solution

All the sides in a rhombus are the same or congruent. So, the property mentioned in option 1 is not correct about a rhombus.
Question 29
1 / -0

A Private Limited Company, in its first year, makes a profit of Rs. 1,00,420 and in the second year, it doubles the profit made in the first year, and in the third year, it doubles the profit made in the second year. How much profit has the company made in its three years?

A
Rs. 2,00,840

B
Rs. 7,02,940

C
Rs. 4,01,680

D
Rs. 5,01,680

Solution

Profit made in the first year = Rs. 1,00,420
Profit made in the second year = Rs. 1,00,420 × 2 = Rs. 2,00,840
Profit made in the third year = Rs. 1,00,420 × 4 = Rs. 4,01,680
Total profit made in three years = Rs. 1,00,420 + 2,00,840 + 4,01,680 = Rs. 7,02,940
Question 30
1 / -0

Sham bought 5 white balls. Then he bought red balls two more than white balls, and pink balls twice the number of red balls. The costs of a white ball, a red ball and a pink ball are Rs. 50, Rs. 55, and Rs. 65 respectively. How much did he pay to the shopkeeper?

A
Rs. 620

B
Rs. 840

C
Rs. 1295

D
Rs. 1545

Solution

There are 5 white balls, so the cost of 5 white balls is 5 × 50 = Rs. 250
Number of red balls is two more than that of white balls, that means 5 + 2 = 7 red balls, so the cost of 7 red balls is Rs. 55 × 7 = Rs. 385
Number of pink balls is twice that of red balls, that means 7 × 2 = 14 pink balls, so the cost of 14 pink balls is Rs. 65 × 14 = Rs. 910

Therefore, total cost of all the balls is Rs. 250 + 385 + 910 = Rs. 1545

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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

Triple the difference each time.

Add 3 in the difference.

Take away 3.

Divide by 3.

Solution

Question 2

124

50

25

5

Solution

Question 3

45

46

47

48

Solution

Question 4

Sunday

Saturday

Friday

Thursday

Solution

Question 5

CNUSMD

CNNUMD

BBNNG

SSDFVA

Solution

Question 6

1248 m2

1298 m2

1340 m2

1349 m2

Solution

Question 7

32 cm

40 cm

44 cm

88 cm

Solution

Question 8

3

-2

-1

2

Solution

Question 9

5/17

17/5

-17/5

None of these

Solution

Question 10

2.67 cm

4.21 cm

4.82 cm

2.13 cm

Solution

Question 11

90 ft

80 ft

70 ft

60 ft

Solution

Question 12

9

2

3

4

Solution

1248 m²

1298 m²

1340 m²

1349 m²

180^o

40^o

50^o

90^o

81,514 m²

81,524 m²

81,534 m²

81,544 m²