IMO - Mock Test

Result

IMO - Mock Test - 2

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Weekly Quiz Competition

Question 1
1 / -0

Find the odd one out from the following:

8, 27, 125, 333, 1331, 2197

A
125

B
333

C
1331

D
2197

Solution

2³= 8

3³ = 27

5³= 125

7³= 343

11³= 1331

13³= 2197

Series contains the cube of prime numbers.

Thus, 333 is the odd one in this series as it is not a cube number.
Question 2
1 / -0

Complete the following series:

59, 71, 95, 131, 179, 239, ?

A
240

B
299

C
251

D
311

Solution

59

59 + 12 = 71

71 + (12 × 2) = 95

95 + (12 × 3) = 131

131 + (12 × 4) = 179

179 + (12 × 5) = 239
So, the next term will be: 239 + (12 × 6 ) = 239 + 72 = 311
Question 3
1 / -0

In a certain code language, "GLASS" is coded as HMBTT. How will you code MIC in that language?

A
NJD

B
NID

C
HJD

D
SDF

Solution

GLASS is coded as HMBTT.

The pattern followed is:

G is H (G + 1)
L is M (L + 1)
A is B (A + 1)
S is T (S + 1)
S is T (S + 1)
Question 4
1 / -0

Goel drove a longer distance than Anil drove, but a shorter distance than Arnav drove. Who drove the longest distance?

A
Arnav

B
Goel

C
Anil

D
Everybody covers the same distance.

Solution

Distance covered by Geol > Distance covered by Anil
Distance covered by Arnav > Distance covered by Goel
Hence, Distance covered by Arnav > Distance covered by Goel > Distance covered by Anil
Question 5
1 / -0

Complete the following series:

6, 9, 18, 21, 42, 45, ___

A
80

B
87

C
90

D
93

Solution

6 + 3 = 9
9 × 2 = 18
18 + 3 = 21
21 × 2 = 42
45 + 3 = 45, and so on.

So, the missing number is (45 × 2) = 90.
Question 6
1 / -0

Complete the series:

233, 250A, 284B, 335C, 403D, ?

A
332E

B
340E

C
488E

D
738E

Solution

Here we have two series:

The 1^st series is a number series:

233 + 0 = 233

233 + 17 = 250

250 + 34 = 284

284 + 51 = 335

335 + 68 = 403

403 + 85 = 488

Hence, the last term is 488.

The 2^nd series is an alphabet series:

A + 1 = B
B + 1 = C
C + 1 = D
D + 1 = E...and so on.
Question 7
1 / -0

Find the smallest number by which 243 must be multiplied to obtain a perfect cube.

A
3

B
4

C
5

D
6

Solution

243 = 3 × 3 × 3 × 3 × 3
Here, two 3's are left. Therefore, it does not complete the triplet. So, to make 243 a cube, one more 3 is required.
In that case, 243 × 3 = 3 × 3 × 3 × 3 × 3 × 3 = 729, which is a perfect cube.
Hence, the smallest natural number by which 243 must be multiplied to make it a perfect cube is 3.
Question 8
1 / -0

Find the value of 'a' if 3^2a × 3^-2 = 3⁴.

A
1

B
2

C
3

D
4

Solution

3^2a × 3^-2 = 3⁴.

Since bases are the same, the powers can be added.
Therefore,
3^{2a - 2} = 3⁴.

On both sides, the bases are the same, so we can equate the powers.
2a - 2 = 4,
2a = 4 + 2 = 6
a = 3
Question 9
1 / -0

Find out the roots of the given quadratic equation:

x² + x – 56 = 0

A
8, -7

B
8, 7

C
-8, 7

D
1, 0

Solution

x² + 8x – 7x + 56 = 0

x(x + 8 ) - 7(x + 8) = 0

(x + 8) (x – 7) = 0

x = -8, 7
Question 10
1 / -0

Which of the following are the factors of 8xy - 4y + 6 - 12x ?

A
(2x + 1)(4y - 6)

B
(2x - 1)(4y + 6)

C
(2x - 1)(4y - 6)

D
(2x + 1)(4y + 6)

Solution

8xy - 4y + 6 - 12x = 4y(2x - 1) + 6(1 - 2x)

= 4y(2x - 1) - 6(2x - 1)
= (2x - 1)(4y - 6)
Question 11
1 / -0

Nakul sold 2 cars. First car he sold at 22% profit and the second one he sold at 18% loss. If the total cost price of each car is Rs. 80,000, find the total profit.

A
Rs. 3200

B
Rs. 800

C
Rs. 3000

D
Rs. 3300

Solution

Profit on selling the first car = 80000 + 17600 (22% of 80000) = Rs. 97,600

Profit on selling the second car = 80000 – 14400 (18% of 80000) = Rs. 65,600

Total cost of both the cars = 80000 + 80000 = Rs. 1,60,000

Total selling price = 97600 + 65600 = Rs. 1,63,200

Total profit = 163200 – 160 000 = Rs. 3200
Question 12
1 / -0

Find the largest angle in a quadrilateral if the angles are in the ratio 2 : 4 : 3 : 1.

A
144°

B
152°

C
114°

D
103°

Solution

Let the angles be 2x, 4x, 3x and x.
According to the angle sum property of quadrilateral,
2x + 3x + 4x + x = 360°
10x = 360°
x = 36°
Therefore, largest angle = 4(36^o) = 144^o
Question 13
1 / -0

What minimum number should be divided by 392 to make the number a perfect cube?

A
7

B
14

C
49

D
None of these

Solution

The prime factorisation of 392 is 2 x 2 x 2 x 7 x 7.
In the given prime factorisation, the number 7 occurs only two times and hence, we need to remove these 7s.
So, we need to divide 7 × 7 by the prime factorisation to make it a perfect cube. Hence, the required number is 49.
Question 14
1 / -0

Ussen is 3 years older than Salman and 3 years younger than Sohail, while Salman and Arbaaj are twins. How many years older is Sohail than Arbaaj?

A
6

B
5

C
4

D
3

Solution

Let the age of Useen be A years, the age of Salman be B years, the age of Sohail be C years and the age of Arbaaj be D years.
Since Salman and Arbaaj are twins, so B = D.

Now, A = B + 3 and A = C - 3

Thus, B + 3 = C - 3
Or D + 3 = C - 3 (as B = D)
C - D = 6
C = D + 6
Question 15
1 / -0

What is the solution for the following equation if we substitute the value of variable as 2?

5x² – x – 5

A
1

B
3

C
13

D
15

Solution

Putting the value of x = 2 in the equation, we get

5 × 2² - 2 - 5 = 20 - 7 = 13
Question 16
1 / -0

Ramakant makes a cuboid of sides 14 cm, 7 cm, 7 cm. How many such cuboids will he need to form a cube.

A
2

B
26

C
4

D
49

Solution

Ramakant makes a cuboid of sides 14 cm, 7 cm, 7 cm.

So, Volume of the cube = 2 × 7 × 7 × 7

To make it a perfect cube we need 2 × 2 = 4 cuboids.
Question 17
1 / -0

Simplify the following expression:

(7xy²- 8x²y + 3xy) - (-6x²y + 9xy²+ 5xy)

A
2xy(y - x - 1)

B
-2xy(y - x - 1)

C
-2xy(y + x + 1)

D
2xy(y - x + 1)

Solution

Subtracting:

(7xy²- 8x²y + 3xy) - (-6x²y + 9xy²+ 5xy)

= -2xy²- 2x²y - 2xy

= -2xy(y + x + 1)
Question 18
1 / -0

A cricketer scored a total of 82 runs in 104 balls. He hit 6 sixes, 9 fours, 3 twos and 4 singles. Find the percentage of the total runs that came through sixes.

A
34.61%

B
43.90%

C
45.00%

D
47.32%

Solution

Total runs = 6 × 6 + 9 × 4 + 3 × 2 + 4 × 1 = 36 + 36 + 6 + 4 = 82
Number of runs scored by sixes = 6 × 6 = 36

Required percentage = 36/82× 100

= 43.90%
Question 19
1 / -0

The average of marks obtained by 10 students is x. If each observation is increased by 5, then what is the new average?

A
x

B
5x

C
x + 5

D
None of these

Solution

Average of marks obtained 10 students = x
Sum of 10 students = 10x
If each observation is increased by 5, then
New sum = 10x + (10 × 5) = 10(x + 5)
Then, new average = 10(x + 5)/10
= x + 5
Question 20
1 / -0

A metro train passes through a station every 5 minutes. How many trains will pass through the station in 2/3 of an hour if a train has just passed now?

A
9

B
8

C
5

D
2

Solution

There are 60 minutes in an hour.
In 2/3 of an hour, there are 60 × 2/3 = 40 minutes.
A metro train passes the station every 5 minutes.
Number of trains which pass through the station in 40 minutes = 40/5 = 8
Total number of trains passed = 9 (including the 1 train that has just passed)
Question 21
1 / -0

What will be the lateral surface area (in sq. units) of the cube if its volume is 216 cu. units?

A
216

B
146

C
144

D
288

Solution

Let the side of the cube be 'S'.
Volume of the cube = 216 cu. units
S³ = 216 cu. units
S³ = 6 × 6 × 6 = 6³
So, S = 6 units
Hence, lateral surface area = 4S² = (4 × 6²) sq. units = 4 × 36 sq. units = 144 sq. units
Question 22
1 / -0

Which of the following numbers is not a perfect cube?

A
2744

B
4096

C
5184

D
4913

Solution

5184 = 2 × 2 × 2 × 2 × 2 × 2 × 3 × 3 × 3 × 3

As it has one 3 extra which is not making a group of 3, so it is not a perfect cube.
Question 23
1 / -0

Study the statements given below and choose the correct option.

Statement-1: A line segment joining two points on a circle's circumference and passing through the circle's centre is known as the longest chord of the circle.
Statement-2: (56.32)² lies between 3150 and 3450.

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

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

C
Both statements are true.

D
Both statements are false.

Solution

Statement-1: A line segment joining two points on a circle's circumference and passing through the circle's centre is known as diameter, which is the longest chord of the circle.
So, statement-1 is true.
Statement-2: (56.32)² = 3171.9424
So, yes it lies between 3150 and 3450.

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Re-Attempt Weekly Quiz Competition

IMO - Mock Test - 2

Result

IMO - Mock Test - 2

Score

-

Rank

-

SHARING IS CARING

Question 1

125

333

1331

2197

Solution

Question 2

240

299

251

311

Solution

Question 3

NJD

NID

HJD

SDF

Solution

Question 4

Arnav

Goel

Anil

Everybody covers the same distance.

Solution

Question 5

80

87

90

93

Solution

Question 6

332E

340E

488E

738E

Solution

Question 7

3

4

5

6

Solution

Question 8

1

2

3

4

Solution

Question 9

8, -7

8, 7

-8, 7

1, 0

Solution

Question 10

(2x + 1)(4y - 6)

(2x - 1)(4y + 6)

(2x - 1)(4y - 6)

(2x + 1)(4y + 6)

Solution

Question 11

Rs. 3200

Rs. 800

Rs. 3000

Rs. 3300

Solution

Question 12

144°

152°

114°

103°

Solution